The maximum of |y(t)| for -∞ < t < ∞ is 3.
To verify that y = sin(4t) + 3cos(4t) is a solution to the initial value problem 3y’’ + 48y = 0; y(0) = 3, y’(0) = 4, we need to take the first and second derivatives of y and plug them into the differential equation:
y = sin(4t) + 3cos(4t) y’ = 4cos(4t) - 3sin(4t) y’’ = -16sin(4t) - 12cos(4t)
Now, we substitute these expressions into the differential equation:
3y’’ + 48y = 0 3(-16sin(4t) - 12cos(4t)) + 48(sin(4t) + 3cos(4t)) = 0 -48sin(4t) - 36cos(4t) + 48sin(4t) + 144cos(4t) = 0 108cos(4t) = 0
Since cosine can never equal zero for all values of t, the only solution is cos(4t) = 0, which occurs when 4t = (2n + 1)π/2 for any integer n. Therefore, the general solution to the differential equation is y = Asin(4t) + Bcos(4t), where A and B are constants. Since y(0) = 3 and y’(0) = 4, we can solve for A and B:
y = Asin(4t) + Bcos(4t) y(0) = A0 + B1 = B = 3 y’ = 4Acos(4t) - 4Bsin(4t) y’(0) = 4A1 - 4B0 = 4A = 4 A = 1
Therefore, the particular solution to the initial value problem is y = sin(4t) + 3cos(4t).
To find the maximum of |y(t)|, we can rewrite y(t) in terms of a single trigonometric function:
y(t) = √(sin^2(4t) + 9cos^2(4t)) = √(1 + 8cos^2(4t))
Since -1 ≤ cos(4t) ≤ 1 for all t, the maximum value of y(t) occurs when cos(4t) = 1, which gives:
y(t) ≤ √(1 + 8) = 3
Therefore, the maximum of |y(t)| for -∞ < t < ∞ is 3.
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Your question is incomplete but probably the full question was:
Verify that yequals sine 4 tplus3cosine 4 t is a solution to the initial value problem 3 y double primeplus48yequals0; y(0)equals 3, y prime (0)equals4. Find the maximum of StartAbsoluteValue y(t) EndAbsoluteValue for minus infinityless thantless thaninfinity.
Help this is divide polynomials long division
Answer:
the answer is something
Step-by-step explanation:
x2-14+6
x+3
find the area of the shaded region
Answer:
8.7
Step-by-step explanation:
a = side of a regular hexagon inscribed in a circle = radius of the circle
Area of a hexagon = (3√3 / 2)a² = (3√3 / 2)4² = 41.57
Acircle = πr² = π4² = 50.27
Area of shaded region = Acircle - Ahexagon = 50.27 - 41.57 = 8.7
Subtract 3x(x-2y) from 6(x^(2)-xy) and express your answer as a monomial.
The solution of expression in term of monomial is,
⇒ 3x²
We have to given that,
Subtract 3x(x - 2y) from 6(x² - xy)
Now, We can simplify as,
⇒ 6 (x² - xy) - 3x (x - 2y)
⇒ 6x² - 6xy - 3x² + 6xy
Combine like terms,
⇒ 6x² - 3x² - 6xy + 6xy
⇒ 3x²
Therefore, The solution of expression in term of monomial is,
⇒ 3x²
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Find an expression for a cubic function f if f(1) = 6 and f(-1)= f(0) =f(2)=0 show all work
If f(1) = 6 and f(-1)= f(0) =f(2)=0 then the expression for the cubic function is f(x) = 6x^3 + 0x^2 + 6x.
The expression for a cubic function is f(x) = ax^3 + bx^2 + cx + d.
We can determine the coefficients a, b, c and d by solving the system of equations:
f(1) = 6:
a + b + c + d = 6
f(-1) = 0:
-a + b - c + d = 0
f(0) = 0:
d = 0
f(2) = 0:
8a + 4b + 2c = 0
Substituting d = 0 in the first equation:
a + b + c = 6
Substituting this result in the last equation:
8a + 4b + 2(6 - a - b) = 0
Which reduces to
14a + 8b = 0
This equation has the solutions a = 0 and b = 0.
Substituting these values into the first equation:
c = 6
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find the derivative of the function. h(t) = 17 cot^−1(t) + 17 cot^−1(1/t)
h'(t)=
The derivative of the function h(t) = 17 cot⁻¹(t) + 17 cot⁻¹(1/t) is h'(t) = -17/(1+t²) + 17/(t² + 1).
Determine the derivative of the functionThe derivative of the function h(t) = 17 cot⁻¹(t) + 17 cot⁻¹(1/t) can be found using the chain rule and the derivative of the inverse cotangent function.
The derivative of the inverse cotangent function is -1/(1+x²).
Using the chain rule, we can find the derivative of h(t) as follows: h'(t) = 17 x(-1/(1+t²)) x(1) + 17 x (-1/(1+(1/t)²)) x (-1/t²)
Simplifying the expression, we get:
h'(t) = -17/(1+t²) + 17/(t² + 1)
Therefore, the derivative of the function h(t) = 17 cot⁻¹(t) + 17 cot⁻¹(1/t) is h'(t) = -17/(1+t²) + 17/(t² + 1).
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Four friends are guessing answers to math questions. They think that they each have the probability of 0.5 of guessing the correct answer to any question, independently of each other.
a) The probability that at least one of them guesses correctly is $1-0.0625=0.9375$.
b) The probability that all four guess incorrectly is [tex]\$(0.5)^4[/tex] = 0.0625$.
a) The probability that at least one of them guesses correctly is the complement of the probability that none of them guess correctly. Since each friend has a probability of 0.5 of guessing incorrectly, the probability that one friend guesses incorrectly is 0.5, and the probability that all four friends guess incorrectly is:
[tex]0.5 * 0.5 * 0.5 * 0.5 = 0.0625[/tex] or 6.25%
Therefore, the probability that at least one friend guesses correctly is:
1 - 0.0625 = 0.9375
b) The probability that all of them guess incorrectly is the product of their individual probabilities of guessing incorrectly:
[tex]0.5 * 0.5 * 0.5 * 0.5 = 0.0625[/tex] or 6.25%
Therefore, the probability that all of them guess incorrectly is 0.0625.
It is a number between 0 and 1, with 0 indicating the event is impossible and 1 indicating it is certain.
By dividing the number of favourable outcomes by the total number of possible outcomes, one can determine the probability of an occurring.
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The complete question is:
Four friends are guessing answers to math questions. They believe that, independently of one another, each of them has a 0.5 chance of predicting the right response to any given question.
a) What is the probability that at least one of them guesses correctly?
b) What is the likelihood that every single guess is wrong?
If 10^x=5 what is x
1)x=log^10 5
2)x=ln 5
3)x=1/2
4)x=5/log^10 10
The value of x is equal to the logarithm of 5.
What is logarithm?
A mathematical function known as a logarithm aids in the simplification of huge numbers and facilitates calculation. The power to which a specified number, known as the base, must be increased in order to create a given number is known as the logarithm of that number.
The base of the natural logarithm, e, and base 10 are the two most often used bases for logarithms. Algebra, calculus, and number theory are just a few of the mathematical disciplines that employ logarithms. They may be used to model and study complicated systems in disciplines like engineering, physics, and chemistry.
The given equation is 10ˣ = 5.
We can solve for x using logarithmic functions.
Taking the logarithm base 10 of both sides of the equation 10^x = 5, we get:
log10(10ˣ) = log10(5)
Using the property of logarithms that log10(a^b) = b*log10(a), we can simplify the left-hand side:
x*log10(10) = log10(5)
Since log10(10) = 1, we have:
x = log10(5)
So the answer is option 1: x = log10(5).
Option 2, ln 5, is not correct because ln is the natural logarithm, which uses the base e (approximately 2.71828), not the base 10.
Option 3, 1/2, is not correct because √10 is equal to the square root of 10, not 5.
Option 4, 5/log10(10), simplifies to 5/1, which is 5, and is not the correct value for x.
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Use a ruler and protractor to measure the sides and angles of each shape. Then use what
you learned about indicating congruence to show which shapes are congruent and which are not.
It is difficult to measure the sides and angles of each shape on laptop or mobile.
Define the congruent triangle?Two triangles are said to be congruent if their corresponding sides and angles are equal in measure. In other words, if you can superimpose one triangle on top of the other so that all corresponding sides and angles match, then they are congruent.
There are several ways to prove that two triangles are congruent, including:
Side-Side-Side (SSS): If the three sides of one triangle are equal in measure to the three sides of another triangle, then the triangles are congruent.Side-Angle-Side (SAS): If two sides and the included angle of one triangle are equal in measure to two sides and the included angle of another triangle, then the triangles are congruent.Angle-Side-Angle (ASA): If two angles and the included side of one triangle are equal in measure to two angles and the included side of another triangle, then the triangles are congruent.Angle-Angle-Side (AAS): If two angles and a non-included side of one triangle are equal in measure to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.Hypotenuse-Leg (HL): If the hypotenuse and one leg of a right triangle are equal in measure to the hypotenuse and one leg of another right triangle, then the triangles are congruent.To know more about triangle, visit:
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Answer:
1) congruent
2) congruent
3) congruent
4) not congruent
Step-by-step explanation:
I did the assignment (may I pls have brainliest and five stars? thx)
Rewrite the vector equation r(t)=(−1−2t)i+(5−5t)j+(3+4t)kr(t)=(−1−2t)i+(5−5t)j+(3+4t)k as the corresponding parametric equations for the line. x(t)=x(t)= y(t)=y(t)= z(t)=z(t)=
The corresponding parametric equations for the line are:x(t) = -1 - 2t, y(t) = 5 - 5t, z(t) = 3 + 4t.
The vector equation for the line in question is r(t) = (-1 - 2t)i + (5 - 5t)j + (3 + 4t)k.Rewriting the vector equation r(t) = (-1 - 2t)i + (5 - 5t)j + (3 + 4t)k as corresponding parametric equations for the line can be done as follows:x(t) = -1 - 2ty(t) = 5 - 5tz(t) = 3 + 4tTherefore, the corresponding parametric equations for the line are:x(t) = -1 - 2t, y(t) = 5 - 5t, z(t) = 3 + 4t.
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Three boys, Lara, Mansingh and Zolo went collecting mangoes. Here is a list of how many mangoes each boy collected.
Lara........84
Mansingh ........96
Zolo........120
They then shared the mangoes equally among themselves. How many mangoes will Zolo receive as his share?
The number of mangoes that Zolo will receive is given as follows:
100 mangoes.
How to obtain the number of mangoes that each person will receive?The number of mangoes that each person will receive is obtained applying the proportions in the context of the problem.
The number of mangoes collected by each of the three friends is given as follows:
Lara collected 84 mangoes.Mansingh collected 96 mangoes.Zolo collected 120 mangoes.Hence the total number of mangoes collected by the three friends is given as follows:
84 + 96 + 120 = 300.
Each person will receive an equal amount of mangoes, hence the amount of mangoes received by each person is obtained as follows:
300/3 = 100 mangoes.
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Want his 7,200 car and plans to sell with a car after markup of 15 percent
The price of the car after the 15% markup is $8,280
A markup is the amount by which a seller increases the price of a product above its cost, in order to make a profit. In this case, we're told that the seller, Hank, bought the car for $7,200 and wants to sell it on his used car lot for a higher price.
To find the new price of the car after the markup, we need to add 15% of the original price to the original price. The formula for finding the new price with a markup is
New Price = Original Price + Markup
We're given the original price of the car as $7,200, so we can plug that into the formula
New Price = $7,200 + Markup
To find the markup, we need to calculate 15% of $7,200. We can do this by multiplying 0.15 (which is 15% written as a decimal) by $7,200
Markup = 0.15 x $7,200
Markup = $1,080
Now we can substitute the markup value into our formula
New Price = $7,200 + $1,080
New Price = $8,280
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The given question is incomplete, the complete questions is:
Hank buys a used car for $7,200 and plans to sell it on his used car lot. What is the price of the car after a markup of 15%?
A hydraulic lift is used to lift a heavy machine that is pushing down on a 2. 8m^2 platform with a force 3700n. What force must be exerted on a 0. 072m^2 piston lift the heavy machine?
A force of 95.14 N must be exerted on 0.072 m² piston to lift the heavy machine
We can use the principle of Pascal's law to solve this problem. According to Pascal's law, pressure applied to a confined fluid is transmitted uniformly in all directions.
Let's assume that the hydraulic lift consists of two pistons - one with an area of 2.8 m² (the platform), and the other with an area of 0.072 m² (the piston used to lift the heavy machine). The force exerted on each piston is equal to the pressure multiplied by the area of the piston.
The pressure applied to the fluid in the hydraulic lift is the same for both pistons, so we can set up the following equation:
Pressure × Area of platform = Pressure × Area of piston
We can rearrange this equation to solve for the force required to lift the heavy machine:
Force on piston = Force on platform × (Area of piston / Area of platform)
Substituting the given values, we get:
Force on piston = 3700 N × (0.072 m²/ 2.8 m²)
Force on piston = 95.14 N
Therefore, a force of 95.14 N must be exerted on the piston to lift the heavy machine.
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Find all a and b such that is an involution if a((x, y)) = (ay, x/b).
The values of a and b that satisfy the involution property are a = ±1 and b = ±1.
An involution is a function that when applied twice returns the original input. So, if we apply a twice to the input (x, y), we get:
a(a(x, y)) = a(ay, x/b) = a^2y, ay/b = (a^2/b)xy
To satisfy the involution property, this must be equal to (x, y), so we have:
(a^2/b)xy = x, and
a^2y = y
From the second equation, we see that a must be ±1. If a = 1, then y = y, which is always true, and if a = -1, then y = -y, which is also true. Substituting these values into the first equation, we get:
(a^2/b)xy = x, so if a = 1, then b can be any non-zero value, and if a = -1, then b must be ±1. Thus, the values of a and b that satisfy the involution property are a = ±1 and b = ±1.
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Cassandra is creating a program and for one part she uses the following rule to move points across the screen
(x,y) → (x - 5, y + 6)
What output does the rule give when the input is (5,-6) and explain the process
Answer:
(0,0)
Step-by-step explanation:
Since the input is (5, -6), according to the rule,
(5, -6) → (5 - 5, -6 + 6)
Hence,
(5, -6) → (0, 0)
(0,0) is the output when (5, -6) is the input.
Be sure to mark this as brainliest! (I am one away from Genius so help me out) Thanks!
Can someone help me out with this
The major arc AEB has a measure of 229 degrees.
How to solve the Arc of the circle?
Since AD and CE are diameters of the circle, we know that angle AED is 90 degrees. Since all of the points A, B, C, D, and E lie on the circle, we can assume that angle AEB is also 90 degrees.
Let's call the intersection of BE and AD point F. Since angle AEB is 90 degrees, we know that triangle AEB is a right triangle and that BF is the altitude from B to AE.
Now, let's use some angle chasing to find the measure of angle EBF. Since angle BPC is 38 degrees and P is the center of the circle, we know that angle BAC (which is half of arc BC) is also 38 degrees. Similarly, angle CED is also 38 degrees.
Since angle EPD is 93 degrees and ED is a diameter, we know that angle EDP is 90 degrees. Therefore, angle PDE is 93 - 90 = 3 degrees.
Now, we can find angle CDF (which is half of arc CD) by subtracting the measures of angles CED, PDE, and PDC (which is 90 degrees).
angle CDF = (180 - angle CED - angle PDE - 90) degrees
= (180 - 38 - 3 - 90) degrees
= 49 degrees
Since AD is a diameter, we know that angle AFD is 90 degrees. Therefore, angle EBF is:
angle EBF = angle AFD - angle AFE - angle CDF degrees
= (90 - 90 - 49) degrees
= 41 degrees
Now, we can use the fact that angle AEB is 90 degrees and angle EBF is 41 degrees to find the measure of the major arc AEB.
The measure of minor arc AB is 90 degrees (since it is half of arc AEB), so the measure of major arc AEB is:
measure of major arc AEB = 360 - measure of minor arc AB - angle EBF degrees
= 360 - 90 - 41 degrees
= 229 degrees
Therefore, the major arc AEB has a measure of 229 degrees.
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The radius of a circle is 9 m. Find its area to the nearest whole number.
Answer: 254
Step-by-step explanation:
PLEASE QUICK ASAP NEED TO SUBMIT
Answer:
Wages: Employee compensation that is based on the number of hours worked multiplied by an hourly rate of pay. Ex. Getting a pay of $15 an hour.
Salary: Employee compensation quoted on an annual basis. Ex. Getting a salary of $120,000 per year.
Mar 06, 6:47:19 PM Watch help video Abigail owns a small business selling bagels. She knows that in the last week 65 customers paid cash, 2 customers used a debit card, and 9 customers used a credit card. with a Based on these results, express the probability that the next customer will pay debit card as a fraction in simplest form.
Answer:
There were a total of 65 + 2 + 9 = 76 customers in the last week. The probability of the next customer paying with a debit card is the number of customers who paid with a debit card divided by the total number of customers:
2/76
This fraction can be simplified by dividing both the numerator and denominator by 2:
1/38
So the probability of the next customer paying with a debit card is 1/38.
Step-by-step explanation:
A poetry competition accepts only sonnets and
limericks.
In one year, the competition received 1000
entries.
750 of the entries were sonnets.
36% of the sonnets and 65 of the limericks were
shortlisted for a prize.
a) Draw a frequency tree to show the
information above.
b) An entry is picked at random. What is the
probability that it is a sonnet that has not been
shortlisted?
Give your answer as a decimal.
c) A limerick is picked at random. What is the
probability that it has not been shortlisted?
Give your answer as a decimal.
a) Frequency tree is mentioned below. b) P(Sonnet not shortlisted) = 0.477 c) P(Limerick not shortlisted) = 0.185.
Describe Probability?In its simplest form, probability is represented as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability can be used to make predictions about the outcomes of random events. For example, in a game of chance like roulette, the probability of a particular number coming up is known and can be used to determine the odds of winning.
a) Frequency tree:
Total: 1000
/ \
/ \
Sonnet (750) Limerick (250)
/ \ / \
Shortlisted Not Shortlisted Shortlisted Not Shortlisted
/ \ / \
273 477 65 185
b) Probability of a sonnet not shortlisted:
Number of sonnets not shortlisted = Total sonnets - Shortlisted sonnets
Number of sonnets not shortlisted = 750 - 273
Number of sonnets not shortlisted = 477
P(Sonnet not shortlisted) = 477 / 1000
P(Sonnet not shortlisted) = 0.477
c) Probability of a limerick not shortlisted:
Number of limericks not shortlisted = Total limericks - Shortlisted limericks
Number of limericks not shortlisted = 250 - 65
Number of limericks not shortlisted = 185
P(Limerick not shortlisted) = 185 / 1000
P(Limerick not shortlisted) = 0.185
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freida had 3/4 a bottle of ginger ale she needs 1/2 of a ginger ale for her fruit punch how much will be left in the bootle after freida makes the punch
Answer:
If Frieda has 3/4 of a bottle of ginger ale and needs 1/2 of the bottle for her fruit punch, she will use 1/2 of 3/4, which is:
1/2 x 3/4 = 3/8
So Frieda will use 3/8 of the bottle for her fruit punch, which means there will be 1 - 3/8 = 5/8 of the bottle left after she makes the punch. Therefore, Frieda will have 5/8 of the bottle of ginger ale remaining.
Step-by-step explanation:
the velocity of s free fall object is given by v=√2gh where v is the velocity (m/s) g is acceleration due to gravity (m/s^2), and h is the distance (m) fallen. if the object hits the surface with a velocity of 30m/sec and on the moon the acceleration is g=1.57 m/s^2 , determine the height from which the object was dropped.
The object was initially dropped from a height of about 287.6 meters.
We can change the acceleration due to gravity on the moon to g = 1.57 [tex]m/s^2[/tex] and use this value in the formula:
h = [tex]900 m^2/s^2[/tex] / (2 × 1.57 m/s^2)
h ≈ 287.6 m
what is velocity?The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction. Its SI equivalent is the meter per second (ms-1). A body is considered to be accelerating if its velocity changes, either in magnitude or direction.
from the question:
The starting height from which the object was dropped can be determined using the formula for the velocity of a free-falling object. When an object strikes a surface at 30 m/s, we can write:
30 m/s = √(2gh)
Squaring both sides gives:
[tex]900 m^2/s^2[/tex] = 2gh
Solving for h:
h = [tex]900 m^2/s^2[/tex]/ (2g)
We can change the acceleration due to gravity on the moon to g = 1.57 [tex]m/s^2[/tex] and use this value in the formula:
h = [tex]900 m^2/s^2[/tex] / (2 × 1.57 m/s^2)
h ≈ 287.6 m
As a result, the object was dropped from a height of roughly 287.6 meters.
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A bakery is selling breakfast platters. A platter of 12 bagels costs $9.00. Additionally, it costs $5.90 for a gallon of coffee.
What is the slope of this situation?
A.0.49
B.0.75
C.5.90
D.9.00
The slope of the given situation of selling breakfast platters is 0.75.
Given, the platter of 12 bagels costs $9.00.
The extra cost of $5.90 for a gallon of coffee.
To find the slope of the situation, we convert the situation into the equation of the line.
[tex]y=mx+c[/tex]
here [tex]c[/tex] is the extra cost that is 5.90.
[tex]12m=9.00[/tex]
For 12 bagels, the cost is 9.00, then the slope will be the cost of each bagel.
[tex]m=9.00\div12[/tex]
[tex]m=0.75[/tex]
[tex]m=[/tex] [tex]\[/tex][tex]0.75[/tex]
Therefore, option b 0.75 is the slope of the given situation of the bakery selling the breakfast platter of 12 bagels and a gallon of coffee.
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Answer: (B) $0.75
Step-by-step explanation:
The slope of the given situation of selling breakfast platters is 0.75.
Given, the platter of 12 bagels costs $9.00.
The extra cost of $5.90 for a gallon of coffee.
To find the slope of the situation, we convert the situation into the equation of the line.
here is the extra cost that is 5.90.
For 12 bagels, the cost is 9.00, then the slope will be the cost of each bagel.
Therefore, option b 0.75 is the slope of the given situation of the bakery selling the breakfast platter of 12 bagels and a gallon of coffee.
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Previous Answers Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves y-tan-x, y-3, and x-0 about the line y-3. tan(2x)2x dx 0
To set up an integral for the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves y = tan(x), y = 3, and x = 0 about the line y = 3, we use the formula V = π∫a b[(R(x))^2 - (r(x))^2]dx, where R(x) and r(x) are the radius of the outer and inner circle respectively.
For this problem, a = 0 and b = 2 since the region is in the first quadrant. We can calculate the radii of the inner and outer circle by substituting in the boundaries of the region:
So, the integral to calculate the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves y = tan(x), y = 3, and x = 0 about the line y = 3 is:
V = π∫02[(3 - tan(x))^2 - 0]dx
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a client is receiving intravenous (iv) mannitol to prevent increased intracranial pressure. the order is for mannitol 1.5 grams per kg of body weight iv now. the client weighs 143 lbs (65 kg). how many grams will the nurse administer to the client? enter the correct number in tenths
The amount of weight did the nurse administer to the client is 97.6 grams.
First, it's important to convert the patient's weight from pounds to kilograms since the dosage is based on kg. To do this, we divide the weight in pounds by 2.205 to get the weight in kg. In this case, 143 lbs / 2.205 = 64.9 kg. We can round this to 65 kg, as the dosage is given in whole kg.
Next, we multiply the patient's weight in kg by the ordered dosage of 1.5 grams per kg. This gives us the total dosage in grams. To do this, we use the formula:
Dosage (grams) = Weight (kg) x Ordered dosage (grams per kg)
So in this case, the dosage would be:
Dosage = 65 kg x 1.5 grams/kg = 97.5 grams
However, the question asks us to enter the correct number in tenths, so we need to round our answer to the nearest tenth of a gram. In this case, since the hundredths place is a 5, we round up to 97.6 grams.
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The number of moose in Alaska at the start of year n is Pn
The number of moose in Alaska at the start of the following year is given by
Pn+1 = 1.04(Pn - G) where G is a constant
At the beginning of 2015, there were 200 000 moose in Alaska.
At the beginning of 2016, there were 200 720 moose in Alaska.
Work out how many moose there were in Alaska at the beginning of 2017
Answer:
200 720 = 1.04(Pn - G)
Pn - G = 192 500
Pn = 192 500 + G
At the beginning of 2017, there were Pn = 192 500 + G moose in Alaska.
I HAVE THE ANSWER JUST SOLVE WITH EXPLANATION PLEASE HELP ASAP
Answer:
V=871 cubic inches
Step-by-step explanation:
The formula for the volume of a cone is V=[tex]\pi[/tex][tex]r^{2}[/tex][tex]\frac{h}{3}[/tex]
V=[tex]\pi[/tex][tex]8^{2}[/tex][tex]\frac{13}{3}[/tex]
V=[tex]\pi[/tex](64)(4.3333)
V=[tex]\pi[/tex](277.333)
V=871.2683
V=871 cubic inches
Answer:
The volume of the cone to the nearest whole unit is 871 in³.
Step-by-step explanation:
The formula for the volume of a cone is:
[tex]\boxed{V=\dfrac{1}{3}\pi r^2h}[/tex]
where:
V = volume.r = radius of the circular base.h = perpendicular height.From inspection of the given diagram:
r = 8 inh = 13 inSubstitute the values of r and h into the formula and solve for V:
[tex]\begin{aligned}\implies V&=\dfrac{1}{3} \pi r^2 h\\\\&=\dfrac{1}{3} \pi \cdot (8)^2 \cdot 13\\\\&=\dfrac{1}{3} \pi \cdot 64 \cdot 13\\\\&=\dfrac{1}{3} \pi \cdot 832\\\\&=\dfrac{832}{3} \pi\\\\&=871.26836...\; \sf in^3\end{aligned}[/tex]
Therefore, the volume of the cone to the nearest whole unit is 871 in³.
Explain how the following would affect the margin of error of a confidence interval, if all other things remained the same. Increasing the confidence level
Increasing the confidence level would increase the margin of error of a confidence interval, all other things remaining the same. This is because a higher confidence level corresponds to a wider interval so larger range of possible values.
In order to maintain the same level of precision, a wider interval requires a larger margin of error to account for the increased variability in the data. For example, a 95% confidence interval would have a smaller interval width than a 99% confidence interval, as the latter requires a larger range of possible values to be included in the interval.
As a result, increasing the confidence level would increase the precision and accuracy of the estimate but at the cost of a larger margin of error.
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a rectangular box with a square base, an open top, and a volume of 2,048 in3 is to be made. what is the minimum surface area for the box? enter only the minimum surface area, and do not include units in your answer.
The required surface area of the rectangular box with square base is equals to 768 square inches
Let us consider the side length of the square base of the box be x inches.
And the height of the box be h inches.
Volume of the box is 2,048 cubic inches, we have,
V = x^2 × h
⇒x^2 × h = 2,048
Minimum surface area of the box,
A = x^2 + 4xh
To minimize A, we can use the volume equation to eliminate h in terms of x.
Solving for h, we get,
⇒ h = 2,048/x^2
Substituting this value of h into the equation for A, we get,
A = x^2 + 4x(2,048/x^2)
Simplifying the above equation, we get,
A = x^2 + 8,192/x
Minimum value of A,
Take the derivative of A with respect to x, set it equal to zero, and solve for x,
⇒ dA/dx = 2x - 8,192/x^2 = 0
⇒ 2x = 8,192/x^2
⇒x^3 = 4,096
⇒x = 16
Minimum surface area of the box is,
A = 16^2 + 4(16)(2,048/16^2)
= 768 square inches
Therefore, the minimum surface area of the box is 768 square inches.
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The accompanying table shows the breakdown of a social media sites global users by age and gender, in millions. Complete parts a through f.
Male Female
13-17 years old 91 84
18-24 361 246
25-34 365 258
35-44 205 156
45-54 100 99
55-64 50 57
65 year and older 40 44
a. Determine the probability that a randomly selected person was a female.
[ ](Round to three decimal places as needed.)
b. Determine the probability that a randomly selected person was 18 to 24 years old.
[ ] (Round to three decimal places as needed.)
c. Determine the probability that a randomly selected person was a woman who was 35 years or older.
[ ] (Round to three decimal places as needed.)
d. Determine the probability that a randomly selected person was either a woman or 25 to 34 years old.
[ ] (Round to three decimal places as needed.)
e. Determine the probability that a randomly selected person was a man given that the student was 18 to 24 years old.
[ ] (Round to three decimal places as needed.)
f. Determine the probability that a randomly selected person was 25 to 34 years old given that the student was a man.
[ ] (Round to three decimal places as needed.)
(a) The prοbability that a randomly selected persοn was a female = 900/2072 = 0.434
What differentiates odds from probability?The possibility of an event occurring can be expressed using odds and probability, althοugh they are computed in different ways. Probability, which can be stated as a fraction, decimal, οr percentage, is the ratio of the number of likely outcomes to all pοtential possibilities.
(b) The probability that a randomly selected persοn was 18 to 24 years
= 607/2072 = 0.293
(c) The prοbability that a randomly selected person was a woman who was 35 years or older = (156 + 99 + 57)/2072 = 0.1506
(d) The required prοbability = (900 + 623 - 258)/2072 = 0.6105
(e) The required prοbability = 361/607 = 0.595
(f) The required prοbability = 365/1172 = 0.3114
Male Female Total
13-17 91 84 175
18-24 361 246 607
25-34 365 258 623
35-44 205 156 361
45-54 100 99 199
55-64 50 57 107
65 year and οlder 1172 900 2072
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I am very confused at how to divide 12.5 divided by 4.5.
Answer:
2.77777777...
Hope this helps!
Step-by-step explanation:
12.5 ÷ 4.5 = 2.7777777777...
When dividing, move the decimal point for both numbers once to the right so you get 125 ÷ 45.
