what is the volume of a 5 sided pyramid with a height of 10 and the length of each bottom side is 8

Answers

Answer 1

Answer:

200cm3

Step-by-step explanation:

Volume is LxWxH

L=8cm

W=5 cm

H=10cm

=200cm


Related Questions

A car was valued at $38,000 in the year 2007. By 2013, the value had depreciated to $11,000 If the car’s value continues to drop by the same percentage, what will it be worth by 2017?

Answers

The value of the car in the year 2017 will be $4973.

Given that a car's value is decreasing, it had a value of $38,000 in the year 2007.

By 2013, the value had depreciated to $11,000.

The car’s value continues to drop by the same percentage, we need to find the price of the car in year 2017.

So, 2013-2007 = 6 years

Using the exponential decay formula,

P = P₀(1-r)ⁿ

11000 = 38000(1-r)⁶

0.29 = (1-r)⁶

Taking log to both sides,

㏒(0.29) = 6 ㏒(1-r)

-0.53 / 6 = ㏒(1-r)

-0.089 = ㏒(1-r)

r = 18%

Now, 2017 - 2013 = 4

So,

P = 11000(1-0.18)⁴

P = 4973.33

Hence the value of the car in the year 2017 will be $4973.

Learn more about exponential decay click;

https://brainly.com/question/2193799

#SPJ1

To convert 13 yards to feet, you would use the ratio 1 yard
3 feet
OA. True
OB. False

Answers

True. to convert 13 yards to feet, you will use the ratio 1 yard: 3 feet, which means that that one yard is equal to a few feet. Option A is correct.

Therefore, to convert 13 yards to feet, we need to multiply 13 by 3. that is because each yard is same to 3 toes.

13 yards x 3 feet/yard = 39 feet

So, 13 yards is same to 39 toes. this is a common conversion that is used in various contexts, which include in construction, sewing, and sports.

It's far important to recognize these kinds of ratios and conversions so one can make accurate measurements and calculation

Learn more about ration calculations:-

https://brainly.com/question/13513438

#SPJ1

5. Dipak is trying to find the typical month the students in his class were born. He starts by numbering the months 1
through 12 and compiling his data set, as shown below.
1,4,5,6,7,7,8,9, 9, 10, 11, 11, 12, 12
He adds all the numbers up to get a total of 106, then divides by 14 to get 8. Dipak says the average month his
classmates were born in is August.
Does Dipak's strategy and answer make sense? Explain your reasoning

Answers

Answer:

No

Step-by-step explanation:

No, Dipak's strategy and answer does not make sense. His strategy is an example of mean or average, which is useful for finding the central tendency in a data set. However, it does not give a good representation of the data set in this scenario because there are two months with more than one entry. It does not accurately reflect the data set and does not give a good indication of the typical month the students were born. A better approach would be to use the mode, which is the most frequently occurring value. In this case, the mode would be 7, indicating that July was the typical month that the students in Dipak's class were born.

Dipak's strategy and answer do not make sense. While Dipak correctly calculated the average by adding up all the numbers and dividing by the total count, his interpretation of the average as the "typical month" is flawed.

In this scenario, the numbers represent the months in which the students were born. The average month of birth is not necessarily the same as the "typical" or most common month. To determine the most typical month, Dipak would need to analyze the frequency or count of each month and identify which month appears most frequently.

Let's examine the data set provided:

1, 4, 5, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 12

By counting the occurrences of each month, we find that:

Month 1 appears once.
Month 4 appears once.
Month 5 appears once.
Month 6 appears once.
Month 7 appears twice.
Month 8 appears once.
Month 9 appears twice.
Month 10 appears once.
Month 11 appears twice.
Month 12 appears twice.

Based on this analysis, the most frequent or "typical" month in Dipak's class is actually the month of December (12), which appears twice. Therefore, Dipak's answer of August (8) is incorrect based on the given data.

The area under the standard normal curve where P(Z >. - 0.5) is: 0.6479 0.3085 0.3521 0.3681 0.6915

Answers

The area under the standard normal curve where P(Z > -0.5) is 0.6915. To find this, we can use a standard normal distribution table or a calculator with a normal distribution function.

First, we need to find the z-score associated with -0.5. We know that the mean of the standard normal distribution is 0 and the standard deviation is 1. So, the z-score can be calculated as z = (x - μ) / σ = (-0.5 - 0) / 1 = -0.5. Now, we can look up the area to the right of the z-score -0.5 in a standard normal distribution table. The area is 0.6915, which means that the probability of getting a z-score greater than -0.5 is 0.6915.

Learn more about standard normal distribution here:

https://brainly.com/question/29509087

#SPJ11

suppose a lottery game is played where the player chooses a three digit number (repetition allowed)

Answers

The probability of winning this lottery game is 1/1,000 or 0.001, which equates to a 0.1% chance.

In this lottery game, players select a three-digit number, ranging from 000 to 999. Since repetition is allowed, each digit can be any number between 0 and 9, giving a total of 10 options per digit. The three digits are independent, which means that the choice of one digit does not influence the choices for the other digits. Consequently, to find the total number of possible combinations, you can use the counting principle.

The counting principle states that if there are n ways to do one thing and m ways to do another, there are n x m ways to do both. In this case, there are 10 choices for each of the three digits, so the total number of combinations is 10 x 10 x 10 = 1,000.

Players win the lottery game if their chosen three-digit number matches the winning number drawn by the game organizers. The probability of winning is determined by dividing the number of successful outcomes (1, as there's only one winning number) by the total number of possible outcomes (1,000 combinations). Hence, the probability of winning is 1/1,000 or 0.1 % chance.

You can learn more about probability at: brainly.com/question/30034780

#SPJ11

For U = xy, what is the value of the MRSxy at the point x=20 and y=20? Write your answer as a positive number, it doesn't matter if you use decimals or fractions.

Answers

The value of the MRSxy at the point x=20 and y=20 is 1.

The MRSxy (Marginal Rate of Substitution of x for y) can be calculated by taking the partial derivative of U with respect to x, divided by the partial derivative of U with respect to y.

Therefore, MRSxy = (∂U/∂x) / (∂U/∂y).

In this case, U = xy.

Taking the partial derivative of U with respect to x gives us y, and taking the partial derivative of U with respect to y gives us x. So, MRSxy = y/x.
Substituting x=20 and y=20 into the equation for MRSxy, we get MRSxy = 20/20 = 1.

Therefore, the value of the MRSxy at the point x=20 and y=20 is 1.

Know more about partial derivatives here:

https://brainly.com/question/2293382

#SPJ11

Find the probability that a randomly
selected point within the circle falls in the
red-shaded triangle

Answers

Answer:

0.31

Step-by-step explanation:

That probability is equal to RedTriangleArea/CircleArea.

The area of the triangle is 8*6/2=24.

The area of the circle is Pi*R²=3.14*5²=78.5.

P=24/78.5=0.30573...≈0.31 (rounded up to the nearest hundredth)

The probability that a point falls on the red triangle is P =  0.306

How to find the probability?

To find the probability we need to take the quotient between the area of the triangle and the area of the circle.

For the triangle we can see that the base is 6 units and the height is 8 units, thus the area is:

A = 6*8/2 = 24 square units.

For the circle, we can see that the radius is 5 units, then the area is:

a = 3.14*(5)² = 78.5

Taking the quotient we get:

P = 24/78.5

P = 0.306

Learn more about probability at:

https://brainly.com/question/25870256

#SPJ1

HELP ASAP 100 POINTS AND BRAINLIEST IF CORRECT IF WRONG I WILL REPORT!!
Which data set has a variation, or mean absolute deviation (MAD), similar to the data set in the given plot?

Answers

Answer:c

Step-by-step explanation::Add all the absolute deviations and divide by number of swimmers. Step-by-step explanation:

a 1. The sum of the ages of two friends is 25 1. and the elder one is 4 times older than the younger one. Write this as a mathematical sentence. 2. The length of a rectangle is 3cm greater than its width. If the perimeter is 34cm find the lengths pra Form algebraic expressions for the Wr following statements, If n represents ar number, then an unknown 0 Evaluate each of the following: 45³³ = 3 sions one-third of the number=.. 2 22 more than 5 times the number= 38 times the number is subtracted from 5. 3 S and the result is multiplied by 2 Simplify the following expressions 04x + 7-2x-4 17​

Answers

Answer: Mathematical sentence:

Let the age of the younger friend be x. Then, the age of the elder friend can be expressed as 4x. The sum of their ages is 25, so we can write the equation:

x + 4x = 25

Algebraic expressions:

Let the width of the rectangle be w. Then, the length can be expressed as w + 3.

The perimeter of a rectangle is given by 2(length + width), so we can write the equation:

2(w + (w + 3)) = 34

Algebraic expressions:

Let n represent an unknown number.

a. One-third of the number:

(1/3)n

b. 22 more than 5 times the number:

5n + 22

c. 3 times the number is subtracted from 5 and the result is multiplied by 2:

2(5 - 3n)

Simplification of expression:

0.4x + 7 - 2x - 4 = -1.6x + 3

Evaluation:

45³³ = 45^33 (45 raised to the power of 33)

Step-by-step explanation:

Final answer:

To write the sum of two friends' ages as a mathematical sentence, let the younger friend's age be x and the elder friend's age be 4x. The sum of their ages is given by the equation x + 4x = 25. To find the lengths of a rectangle with a given perimeter, let the width be x and the length be x + 3. The perimeter equation is 2(x + (x + 3)) = 34. To form algebraic expressions, n represents the unknown number. One-third of the number would be n/3, 22 more than 5 times the number is 5n + 22, and 38 times the number subtracted from 5 is 5 - 38n. Finally, to simplify the expression 4x + 7 - 2x - 4 + 17.

Explanation:

To write the given information as a mathematical sentence:

Let the age of the younger friend be x. Then, the age of the elder friend would be 4x.The sum of their ages is 25, so we can write the equation: x + 4x = 25.

To find the lengths of a rectangle with a given perimeter:

Let the width of the rectangle be x. Then, the length would be x + 3.The perimeter of a rectangle is given by the formula: 2(length + width).We can write the equation: 2(x + (x + 3)) = 34.

To form algebraic expressions for the given statements:

The unknown number is represented by n, so one-third of the number would be n/3.22 more than 5 times the number would be 5n + 22.38 times the number is subtracted from 5 would be 5 - 38n.The result is multiplied by 2, so it would be 2(5 - 38n) = 10 - 76n.

To simplify the given expression: 4x + 7 - 2x - 4 + 17.

Learn more about Mathematical Expressions here:

https://brainly.com/question/34902364

let p be the price of an item. the unit sales of the item are 200 - 5p. what is the correct formula for the revenue generated by the item?

Answers

The correct formula for the revenue generated by the item is Revenue = 200p - 5p^2.

The revenue generated by the item can be calculated by multiplying the price (p) by the unit sales (200 - 5p). Therefore, the correct formula for the revenue generated by the item is:

Revenue = Price x Unit Sales
Revenue = p(200 - 5p)
Revenue = 200p - 5p^2

The revenue generated by the item is a quadratic function of the price (p). To find the maximum revenue, we need to differentiate the function with respect to p and set it equal to zero:

dRevenue/dp = 200 - 10p = 0
10p = 200
p = 20

Therefore, the maximum revenue is generated when the price of the item is $20. Substituting p = 20 in the revenue formula, we get:

Revenue = 200(20) - 5(20^2) = $2000

Hence, the correct formula for the revenue generated by the item is Revenue = 200p - 5p^2, and the maximum revenue is achieved when the price of the item is $20, generating a revenue of $2000.

Know more about revenue here,

https://brainly.com/question/29567732

#SPJ11

which of the following type(s) of unemployment are most associated with an economy that is experiencing dynamic growth and technological progress?

Answers

An economy experiencing dynamic growth and technological progress is more likely to have structural unemployment, as workers may need to retrain and acquire new skills to keep up with changes in the economy and earn higher wages.

Dynamic growth and technological progress often lead to changes in the way goods and services are produced, which can have significant impacts on the labor market. In some cases, new technologies may displace workers who lack the skills necessary to operate or maintain them. This can lead to frictional or cyclical unemployment as workers search for new jobs or wait for the economy to recover.

However, in the long run, technological progress is more likely to result in structural unemployment, which occurs when there is a mismatch between the skills of workers and the requirements of available jobs. As technology advances, workers in some industries may need to retrain or acquire new skills to remain competitive in the labor market.

For example, workers in manufacturing may need to learn how to operate and maintain new automated machinery, while those in information technology may need to keep up with the latest programming languages and software development frameworks. In such cases, workers who are unable or unwilling to acquire these new skills may become structurally unemployed, while those who are able to adapt may be in high demand and earn higher wages.

Learn more about wages:

brainly.com/question/31666544

#SPJ11

How much grain can this container hold? Use 3.14 to approximate your pi. Round your answer to the nearest hundreth

Answers

The amount of grain can the container hold is 953.78 inch³ as it in the form of cylinder

Diameter of cylinder = 9 in

Radius of cylinder = 9 / 2 in

Radius of cylinder = 4.5 in

Height of cylinder = 15 inch

Volume of cylinder = Amount of grain can this container hold

Volume = πr²h

Substitute the values of radius and height

Volume = (3.14)(4.5)²(15)

Amount of grain can this container hold = 953.78 inch³

Hence, the amount of grain can the container hold is 953.78 inch³

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ1

Suppose Lisa wants to glue decorative paper onto the block. What is the total surface area that Lisa would need to cover? Show your work.

Answers

The total surface area that Lisa would need to cover is 2 times the sum of the areas of the top and bottom faces plus 2 times the sum of the areas of the side faces.

To calculate the total surface area that Lisa would need to cover, we need to consider all the faces of the block.

Assuming the block is a rectangular prism, it will have six faces: a top face, a bottom face, and four side faces.

Let's denote the length, width, and height of the block as L, W, and H, respectively.

Top and Bottom Faces:

The top and bottom faces have dimensions of L × W each, so their combined area is 2 × (L × W).

Side Faces:

The side faces consist of four rectangles, two with dimensions of L × H and two with dimensions of W × H. So, the combined area of the side faces is 2 × (L × H) + 2 × (W × H).

Now, we can calculate the total surface area by summing up the areas of all the faces:

Total Surface Area = 2 × (L × W) + 2 × (L × H) + 2 × (W × H)

Therefore, the total surface area that Lisa would need to cover is 2 times the sum of the areas of the top and bottom faces plus 2 times the sum of the areas of the side faces.

For such more questions on Surface area of block

https://brainly.com/question/29140137

#SPJ11

List three useful facts about parallelograms.​

Answers

1. Opposite side are parallel

2. A rhombus is a parallelogram

3. Opposite sides are equal length

Step-by-step explanation:

List three useful facts about parallelograms.​

Rhombus, Square and Rectangle are parallelogramsConsecutive angles are supplementaryThe diagonals of a parallelogram bisect each other.Opposite sides are congruentIf one angle is right, then all angles are rightOpposite angels are congruent

an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 100 engines and the mean pressure was 4.9 lbs/square inch. assume the standard deviation is known to be 0.6 . if the valve was designed to produce a mean pressure of 4.8 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications? state the null and alternative hypotheses for the above scenario.

Answers

Yes, there is sufficient evidence at the 0.02 level that the valve does not perform to the specifications.

Null hypothesis: The valve produces a mean pressure of 4.8 lbs/square inch.

Alternative hypothesis: The valve does not produce a mean pressure of 4.8 lbs/square inch.

To test this hypothesis, we can use a one-sample t-test. Using the given information, we can calculate the test statistic:

t = (4.9 - 4.8) / (0.6 / sqrt(100)) = 1.67

Using a t-distribution table with 99 degrees of freedom and a significance level of 0.02, we find the critical value to be ±2.602. Since the absolute value of the test statistic (1.67) is less than the critical value (2.602), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the valve does not perform to the specifications.

In other words, based on the given sample of 100 engines, we cannot conclude that the valve is not producing the desired mean pressure of 4.8 lbs/square inch. However, it's important to note that this conclusion is based on a specific sample and may not generalize to all situations. It's always important to consider the limitations and assumptions of statistical tests.

Learn more about level here: brainly.com/question/14486795

#SPJ11

find all (real) values of k for which a is diagonalizable. (enter your answers as a comma-separated list.)a = 430kk ≠

Answers

The matrix a is diagonalizable if and only if it has n linearly independent eigenvectors, where n is the dimension of the matrix. In this case, a is a 3x3 matrix with diagonal elements 4, 3, and k, and therefore, has three eigenvectors.

To find the eigenvalues, we need to solve the characteristic equation det(a - λI) = 0, where I is the 3x3 identity matrix and λ is the eigenvalue. This yields:

det(a - λI) = (4 - λ)(3 - λ)k - 90 = 0

Expanding and simplifying, we get:

kλ^2 - 7λ^2 + 12λ - 90 = 0

We can factor this quadratic as:

(k - 10)(λ - 6)(λ - 3) = 0

Therefore, the eigenvalues of a are λ = 6, 3, and k - 10. Since a has three linearly independent eigenvectors, it is diagonalizable if and only if all three eigenvalues are distinct. Thus, we need to find the values of k that make the eigenvalues distinct.

If k = 6 or k = 3, then a has repeated eigenvalues and is not diagonalizable. Therefore, the only values of k for which a is diagonalizable are those that make k - 10 ≠ 6 and k - 10 ≠ 3, or k ≠ 16 and k ≠ 13. Thus, the answer is k ≠ 16, 13.


To learn more about eigenvectors click here: brainly.com/question/31503742

#SPJ11

use vectors to decide whether the triangle with vertices p(2, −1, −1), q(3, 2, −3), and r(7, 0, −4) is right-angled.

Answers

To determine whether the triangle with vertices P(2, -1, -1), Q(3, 2, -3), and R(7, 0, -4) is right-angled, we can use vectors.

First, we calculate the vectors formed by the sides of the triangle:

Vector PQ = Q - P = (3, 2, -3) - (2, -1, -1) = (1, 3, -2)
Vector PR = R - P = (7, 0, -4) - (2, -1, -1) = (5, 1, -3)

Next, we take the dot product of these two vectors:

PQ · PR = (1, 3, -2) · (5, 1, -3) = 1 * 5 + 3 * 1 + (-2) * (-3) = 5 + 3 + 6 = 14

If the dot product is zero, then the two vectors are perpendicular, indicating that the triangle is right-angled.

In this case, since PQ · PR = 14 ≠ 0, the triangle with vertices P, Q, and R is not right-angled.

 To learn more about triangle click here:brainly.com/question/2773823

#SPJ11

Finding the Height of the Alexandria Lighthouse.

The figure above shows one of the Seven Wonders of the World, the Great Lighthouse at Alexandria, Egypt, whose construction started in 290 B.c. The platform on which the lighthouse stands is about 100 m wide, and the angle of elevation from the corner of the platform to the top of the lighthouse is 67°. To the nearest meter, how high is the lighthouse?

Answers

Answer:

Set your calculator to degree mode.

tan(67°) = h/50

h = 50tan(67°) = 118 meters

A plane leaves Chicago and flies 750 miles to New York. If it takes 2.5 hours to
get to New York flying against the wind, but only 2 hours to fly back to Chicago
with the wind, what is the plane’s rate of speed and what is the wind speed?

Answers

The wind speed is 37.5 miles per hour.

We are given that;

Number of files= 750

Time=2.5 hours

Now,

Let p be the plane’s rate of speed and w be the wind speed. Then, when the plane flies against the wind, its rate is p - w. When the plane flies with the wind, its rate is p + w.

Using the formula d = rt, we can write two equations for the two trips. For the trip from Chicago to New York, we have 750 = (p - w) * 2.5. For the trip from New York to Chicago, we have 750 = (p + w) * 2.

Simplifying the equations, we get 300 = p - w and 375 = p + w.

Adding the two equations, we get 675 = 2p. Solving for p, we get p = 337.5. This means that the plane’s rate of speed is 337.5 miles per hour.

Substituting p = 337.5 into one of the equations, we get 300 = 337.5 - w. Solving for w, we get w = 37.5.

Therefore, by speed the answer will be 7.5 miles per hour.

Learn more about speed here;

brainly.com/question/7359669

#SPJ1

1. Tom has 12 compartments in his
tackle box. There are 15 fishing lures
in each compartment. How many
fishing lures does Tom have in his
tackle box?
A 190 lures
B
180 lures
125 lures
D 27 lures

Answers


12 compartments x 15 lures per compartment = 180 lures

Therefore, the answer is B) 180 lures.

suppose n = .03, g = .02, δ = .01. what is the steady state growth rate of this economy?

Answers

The steady-state growth rate of this economy is 0.06 or 6%.

You've provided the values for n, g, and δ, and you'd like to find the steady-state growth rate of the economy.

To calculate the steady state growth rate, we need to find the sum of these three values.
1. n represents the population growth rate, which is 0.03.
2. g represents the technological growth rate, which is 0.02.
3. δ represents the depreciation rate, which is 0.01.

4. To find the steady state growth rate, add these three values together:
Steady State Growth Rate = n + g + δ

5. Plug in the given values:
Steady State Growth Rate = 0.03 + 0.02 + 0.01

6. Calculate the sum:
Steady State Growth Rate = 0.06

So, the steady-state growth rate of this economy is 0.06 or 6%.

Know more about the growth rate here:

https://brainly.com/question/25849702

#SPJ11

Use parallelogram WXYZ for questions 10 and 11. 6. If mXYZ = 68° and mWXZ = 71°, find mWZX. 7. If XZ = 8x - 18 and RZ = 2x + 5, find XR.​

Answers

From the parallelogram WXYZ, the angle of mWZX will be 68° and angle of XR = XZ = 8x - 18.

Understanding Parallelogram

Using the properties of parallelograms and the given information, we can solve the parallelogram WXYZ

6. Given:

mXYZ = 68°

mWXZ = 71°

mWZX = ?

In a parallelogram, opposite angles are congruent.

Therefore, mWZX will also be 68°.

7. Given:

XZ = 8x - 18

RZ = 2x + 5,

XR = ?

In a parallelogram, opposite sides are congruent.

That is, XR = XZ

Recall that

XZ = 8x - 18

Substitute XZ with its value:

XR = XZ = 8x - 18

Learn more about parallelogram here:

https://brainly.com/question/970600

#SPJ1

4.A swimmer with a mass of 58 kg and a velocity of 1.6 m/s to the northclimbs onto a 142 kg raft. The combined velocity of the swimmer andraft is 0.32 m/s to the north. What is the raft’s velocity before the swim-mer reaches it?

Answers

the velocity of the raft before the swimmer reaches it is approximately -0.231 m/s to the north.

solve this problem, we can use the principle of conservation of momentum. The total momentum before and after the swimmer climbs onto the raft should be the same.

Let's denote the initial velocity of the raft as v.

The initial momentum of the swimmer is given by:
Momentum_swimmer = mass_swimmer * velocity_swimmer
= 58 kg * 1.6 m/s = 92.8 kg·m/s (north)

The initial momentum of the raft is:
Momentum_raft = mass_raft * velocity_raft
= 142 kg * v (unknown velocity)

The combined momentum after the swimmer climbs onto the raft is:
Momentum_combined = (mass_swimmer + mass_raft) * velocity_combined
= (58 kg + 142 kg) * 0.32 m/s = 60 kg * m/s (north)

Since momentum is conserved, we can set up an equation:
Momentum_swimmer + Momentum_raft = Momentum_combined

92.8 kg·m/s + 142 kg * v = 60 kg * m/s

Simplifying the equation:
142 kg * v = 60 kg * m/s - 92.8 kg·m/s
142 kg * v = -32.8 kg·m/s

Dividing both sides by 142 kg:
v = -32.8 kg·m/s / 142 kg
v ≈ -0.231 kg·m/s

Therefore, the velocity of the raft before the swimmer reaches it is approximately -0.231 m/s to the north.

  ToTo learn more about velocity click here:brainly.com/question/18084516

#SPJ11

If x and y vary directly and y is 56 when x is 8, find y when x is 5.

Answers

when x is 5, y is 35.

If x and y vary directly, this means that their ratio remains constant. We can express this relationship mathematically as:

x/y = k

where k is the constant of proportionality.

To solve the problem, we first need to find the value of k using the information given:

y = kx

56 = k × 8

Solving for k, we get:

k = 7

Now that we have the value of k, we can use it to find y when x is 5:

y = kx

y = 7 × 5

y = 35

Therefore, when x is 5, y is 35.

for such more question on ratio

https://brainly.com/question/2328454

#SPJ11

Find the inverse laplace transform of ss2 12s 36= s --------------------- (s− )2 ss2 12s 36=f∣∣s 6 where f(s)=

Answers

he inverse Laplace transform of f(s) is [tex]6(t-1)e^{(-6t)[/tex].

The inverse Laplace transform of f(s) = 6 / (s² + 12s + 36) first need to factor the denominator of f(s):

s² + 12s + 36 = (s + 6)²

We can rewrite f(s) as:

f(s) = 6 / [(s + 6)²]

The Laplace transform of the function [tex]6te^{(-6t)[/tex] has the Laplace transform:

[tex]L{6te^{(-6t)}[/tex] = 6 / (s + 6)²

The inverse Laplace transform of f(s), we get:

[tex]L^{-1}{f(s)}[/tex] =[tex]L^{-1}{6 / [(s + 6)^2]}[/tex]

= [tex]L^{-1}{6te^{(-6t)}[/tex]

= [tex]6(t-1)e^{(-6t)[/tex]

The inverse Laplace transform of f(s) is [tex]6(t-1)e^{(-6t)[/tex].

The denominator of f(s) before we can compute the inverse Laplace transform of f(s) = 6 / (s2 + 12s + 36):

s² + 12s + 36 = (s + 6)²

F(s) may be rewritten as f(s) = 6 / [(s + 6)2].

The function 6te(-6t)'s Laplace transform has the following properties:

[tex]L{6te^{(-6t)}[/tex]= 6 / (s + 6)²

The inverse Laplace transform to the function f(s) we obtain:

L-1f(s) = L-16 / [(s + 6)²]

= L-16te(-6t)

= 6(t-1)e(-6t).

6(t-1)e(-6t) is the inverse Laplace transform of the function f(s).

For similar questions on inverse laplace transform

https://brainly.com/question/27753787

#SPJ11

find and classify all critical points of the function f(x,y) = xy(1-7x-9y)

Answers

Step-by-step explanation:

To find the critical points of f(x,y), we need to find where the partial derivatives of f(x,y) are equal to zero or do not exist.

First, we find the partial derivative of f(x,y) with respect to x:

f_x(x,y) = y(1 - 7x - 9y) - 7xy = y - 7xy - 9y^2

Next, we find the partial derivative of f(x,y) with respect to y:

f_y(x,y) = x(1 - 7x - 9y) - 9xy = x - 7xy - 9x^2

To find the critical points, we set both partial derivatives to zero and solve for x and y:

y - 7xy - 9y^2 = 0

x - 7xy - 9x^2 = 0

Factoring out y in the first equation, we get:

y(1 - 7x - 9y) = 0

This gives us two solutions: y = 0 or 1 - 7x - 9y = 0

If y = 0, then from the second equation, we have x = 0.

If 1 - 7x - 9y = 0, then we can solve for y to get:

y = (1 - 7x)/9

Substituting this value of y into the second equation gives:

x - 7x(1-7x)/9 - 9x^2 = 0

Simplifying this equation gives:

-56x^2/9 + 56x/9 + x = 0

x(-56x + 9 + 56) = 0

x(8x - 1) = 0

So, x = 0 or x = 1/8.

If x = 0, then from the equation y = (1 - 7x)/9, we have y = 1/9.

If x = 1/8, then from the equation y = (1 - 7x)/9, we have y = -1/9.

Therefore, the critical points of f(x,y) are:

(0, 0), (0, 1/9), and (1/8, -1/9).

To classify these critical points, we need to use the second partial derivative test.

Calculating the second partial derivatives:

f_{xx}(x,y) = -7y

f_{xy}(x,y) = 1 - 7x - 18y

f_{yy}(x,y) = -9x

At the critical point (0,0), we have:

f_{xx}(0,0) = 0

f_{xy}(0,0) = 1

f_{yy}(0,0) = 0

The determinant of the Hessian matrix is:

f_{xx}(0,0) * f_{yy}(0,0) - [f_{xy}(0,0)]^2 = 1

Since the determinant is positive and f_{xx}(0,0) = f_{yy}(0,0) = 0, we have a saddle point at (0,0).

At the critical point (0,1/9), we have:

f_{xx}(0,1/9) = -7/9 < 0

f_{xy}(0,1/9) = 1 > 0

f_{yy}(0,1/9) = 0

The determinant of the Hessian matrix is:

f_{xx}(0,1/9) * f_{yy}(0,1/9) - [f_{xy}(0,1/9)]^2 = -7/9

Since the determinant is negative and f_{xx}(0,1/9) < 0, we have a local maximum at (0,1/9).

At the critical point (1/8,-1/9), we have:

f_{xx}(1/8,-1/9) = 7/9 > 0

f_{xy}(1/8,-1/9) = -15/8 < 0

f_{yy}(1/8,-1/9) = 0

The determinant of the Hessian matrix is:

f_{xx}(1/8,-1/9) * f_{yy}(1/8,-1/9) - [f_{xy}(1/8,-1/9)]^2 = 105/64

Since the determinant is positive and f_{xx}(1/8,-1/9) > 0, we have a local minimum at (1/8,-1/9).

Therefore, the critical points of f(x,y) are:

Therefore, the critical points of f(x,y) are: - A saddle point at (0,0)

Therefore, the critical points of f(x,y) are: - A saddle point at (0,0)- A local maximum at (0,1/9)

Therefore, the critical points of f(x,y) are: - A saddle point at (0,0)- A local maximum at (0,1/9)- A local minimum at (1/8,-1/9)

7. (I’ll give 30 points plus brainpower if you answer the ones in the photo)
Simplify.
x²+3x-4 over x+4

(Does it equal -4 ,4, or 1 at all? Which one does it not equal)

Answers

9.C
10.A
Took in class and made 100

A triangular prism and its dimensions are shown in the diagram.
496
440
The lateral surface area of the prism is
The total surface area of the prism is .._____
10 in
812
Complete each statement about the prism.
Move the correct answer to each box. Each answer may be used more than once. Not all answers will be used.
744
688
square inches.
12 in
square inches.
8 in
592
10 in
15.5 in

Answers

The lateral surface area of the triangular prism is 128 square centimeters. The correct answer would be an option (G) 128 cm².

Given, we have dimension are:

side length of base  = 6 cm, 5 cm, and 5 cm

height = 8 cm

Lateral surface area = (a+b+c)h

Substitute the values and we get

Lateral surface area = (6+5+5)8

Lateral surface area = 16 × 8

Lateral surface area = 128 cm².

Hence, the lateral surface area of the triangular prism is 128 square centimeters.

To learn more about triangular prism click here:

brainly.com/question/3666603

#SPJ1

The missing figure has been attached below.

find all solutions on the interval [0, 2). (enter your answers as a comma-separated list. round your answers to four decimal places.) cos(6x) cos(5x) sin(6x) sin(5x) = 1

Answers

The solutions to the original equation on the interval [0,2) are:

0.2071, 1.4112

what is trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

We can use the trigonometric identity:

cos(a)cos(b)sin(a)sin(b) = (1/4)sin(2a)sin(2b)

Applying this identity, we have:

cos(6x)cos(5x)sin(6x)sin(5x) = (1/4)sin(12x)sin(10x)

So, our equation becomes:

(1/4)sin(12x)sin(10x) = 1

Multiplying both sides by 4, we get:

sin(12x)sin(10x) = 4

Now, let's consider the function f(x) = sin(12x)sin(10x) - 4. We want to find the zeros of this function on the interval [0,2).

Using a graphing calculator or some analysis, we can see that the function has two zeros on this interval, one between x=0 and x=1, and another between x=1 and x=2.

Using numerical methods such as the bisection method or Newton's method, we can approximate the zeros to four decimal places:

The first zero is approximately 0.2071.

The second zero is approximately 1.4112.

Therefore, the solutions to the original equation on the interval [0,2) are:

0.2071, 1.4112.

To learn more about trigonometry from the given link:

https://brainly.com/question/29002217

#SPJ4

Is 5x-x^3+9 a trinomial

Answers

yes

If it’s TRINOMIAL then it has 3 terms in it (this can be seen as TRI- means 3)

The above expression has 3 terms in it therefore it us trinomial

Yes because “Tri means 3
Other Questions
suppose a campus restaurant increases the number of workers it hires from 3 workers per day to 7 workers per day. as a result, its total revenue increases from $135 per day to $350 per day. instructions: enter your answers rounded to two decimal places. a. assuming that each worker is equally productive, what is the marginal revenue product per day of each additional worker? a patient with mitral valve stenosis and coronary artery disease (cad) is in the telemetry unit with pneumonia. the nurse assesses a 6-second rhythm strip and determines that the ventricular rhythm is highly irregular at a rate of 150 bpm, with no discernible p waves. what does the nurse determine this rhythm to be? two investment centers at a large corporation have the following current-year income and asset data: investment center a investment center b investment center income $ 415,000 $ 525,000 investment center average invested assets $ 2,400,000 $ 1,950,000 the return on investment (roi) for investment center b is: group of answer choices 371.4% 26.9% 24.1% 39.2% 21.7% although technology has evolved, fans are still consuming sport through the traditional channels of television and newspapers at the same levels today as they have for the past two decades. select one: a. true b. false writing is one of the most sought-after skills that employers screen for when hiring public relations talent, and one of the main reasons to write well is to build and maintain ________ which is the primary reason investors are attracted to preferred stocka. callabilityb. noncumulative dividendsc. steady dividend streamd. low business risk if the price level rises and the money wage rate remains constant, the quantity of real gdp supplied ______ and there is a movement up along the ______ aggregate supply curve. the three main ways that governments in the united states redistribute income are budgeting supports the planning process by encouraging which of the following activities? a. budgeting works better when top management imposes the budgets on lower-level managers. b. budgeting increases the motivation of managers and employees by providing agreed-upon expectations. c. budgeting ensures that all company goals will be met at all times. d. budgeting directs the day-to-day activities of the company. Investigators wish to evaluate a new treatment for eclampsia (a life-threatening condition in pregnant women) in women 30 50 years of age. The research is intended to directly benefit the pregnant woman who is otherwise healthy and competent. The investigator must obtain consent from whom per Subpart B? The pregnant woman only. The pregnant woman and her legally authorized representative. The pregnant woman and the father of the fetus. The father of the fetus only. an agricultural economist says that the correlation between corn prices and rainfall during the growing season is r = -0.7. this means that: A programmer is testing individual components of a program, including methods, class interfaces, data structures, and inherited attributes. What type of testing is the programmer performing? how many 5-digit zip code numbers are possible? how many of these numbers contain no repeated digits? Porque creen que una causa religiosa como la reforma adquiri connotaciones polticas please if you know this help me i would appreciate it. Hypertext Markup Language (HTML) uses a set of codes called attributes to format documents for display in a browser.a. Trueb. False in a multiple regression model, the variance of the error term is assumed to be _________________. the features of tiktaalik, a fossil that is a transitional form between fishes and tetrapods, might have allowed what actions? The molar solubility of AgCl is 6.5 * 10^-3 M AgNO_3 is 2.5 * 106-8 M. In deriving Ksp from these data, which of the following assumptions are reasonable? Circle all that apply.a. Ksp is the same as solubility.b. Ksp of AgCl is the same in 6.5 * 10^?3 M AgNO3 as in pure water.c. Solubility of AgCl is independent of the concentration of AgNO3.d. Ag+ does not change significantly upon addition of AgCl to 6.5 * 10^?3M AgNO3. Two drivers, Jada and Zach, enter Highway 98 at the same time, both going west. Jada'sentrance is 43.4 miles west of Rockport City, and Zach's entrance is 56.2 miles west ofRockport City. Jada drives 70 miles per hour, and Zach drives 62 miles per hour.If they each keep a constant speed, how many hours will it take for Jada to pass Zach on thehighway?