e altitude of a triangle is increasing at a rate of 1 cm!min while the area of the triangle is increasing at a rate of 2 cm !min. at what rate is the base of the triangle changing when the altitude is 10 cm and the area i

absolute maximum =  3.033

absolute minimum = -1.846

A point where the function achieves its highest value is known as an absolute maximum point. Similar to this, an absolute minimum point is the location at which the function's maximum value is obtained.

f(x) = x[tex]e^{-x^{2}/50 }[/tex] , [−2, 10]

f'(x) = x[tex]e^{-x^{2}/50 }[/tex] (-2x/50) + [tex]e^{-x^{2}/50 }[/tex] (1)  = 0

-2[tex]x^{2}[/tex]/50 + 1 = 0

2[tex]x^{2}[/tex]/50 = 1

2[tex]x^{2}[/tex] = 50

[tex]x^{2}[/tex] = 25

x = +5 , -5

f(-2) = -2 [tex]e^{-2^{2} /50}[/tex] = -1.846

f(10) = 1.3353

f(5) = 3.033

absolute maximum = 3.033

absolute minimum = -1.846

To know more about absolute maximum and minimum click:

brainly.com/question/29449130

#SPJ4

The first and fourth quadrant of a coordinate grid should be used to display the given data .

In the question ,

it is given that ,

from the time the storm has started the temperature change is from 0° to - 20° .

we know that time cannot be in negative , and temperature can be both negative and positive .So only quadrant 1 and 4 can be used for representation .

Y = temperature

X = time

Quadrant 1 = (+x , +y) this can be used because x can only be positive and y is also positive.

Quadrant II = (-x , +y) this cannot be used because x cannot be negative

Quadrant III = (-x , -y) this cannot be used because x cannot be negative

Quadrant IV = (+x , -y) this can be used because x can only be positive and y can be negative.

Therefore , only 1 and 4 quadrants can be used .

The given question is incomplete , the complete question is

An equation is written to represent the relationship between the temperature in Alaska during a snow storm, y, as it relates to the time in hours, x, since the storm started. if the storm lasted five hours and the temperature saw a drop from 0° to - 20°, which quadrant(s) of a coordinate grid should be used to display this data ?

Learn more about Quadrants here

https://brainly.com/question/1960547

#SPJ4

Answer:

6. X, Y and Z are different numbers. X is a factor of Y. Z is a multiple of Y. Which of the following is DEFINITELY true?

7. The following graph shows Vinit's journey as he cycled from his home to a park, 4 kilometers away in 800 seconds. Which of these can be said based on this graph?

8. How many TENS must be added to 7 000 to make it 70 000.

Step-by-step explanation:

Using the laws of inequality, the inequality x-36>4x can be solved as x>-12.

In mathematics, the term "inequality" refers to a relationship between two expressions or values that is not equal to each other. The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. Both mathematical phrases, equations and inequalities, are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are deemed to be equal. The symbols >,,, or indicate that the two expressions in an inequality are not necessarily equal.

Here,

x-36>4x

3x<-36

-3x>36

x>-12

The solution for the inequality x-36>4x is x>-12 using properties of inequality.

To know more about inequality,

https://brainly.com/question/12679763

#SPJ4

There are 6 probability  5 card poker hands with at least 3 Aces that can be dealt from a standard deck of 52 cards.

A standard deck of 52 cards contains 4 Aces, so the maximum number of Aces that can be dealt in a 5 card hand is 3. To determine the number of possible 5 card poker hands with at least 3 Aces, we must first consider the different combinations of 3 Aces in a 5 card hand. There are 6 possible combinations: AAAxx, AAxxA, AxxAA, xAAAX, xAxxA, and xxAAA. This means that there are 6 possible 5 card poker hands with at least 3 Aces that can be dealt from a standard deck of 52 cards. To calculate this, we first counted the number of Aces in the deck and then calculated the number of possible combinations of 3 Aces in a 5 card hand. Finally, we multiplied this number by the number of remaining cards in the deck (48) to get the total number of possible hands.

4 Aces x 6 combinations = 24

24 x 48 remaining cards = 1,152

Learn more about probability  here

https://brainly.com/question/11234923

#SPJ4

The Perimeter of the Pathway around the pool is 38.4m

What is Perimeter?

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.

Solution:

Length of the Pathway = 12m + 80cm + 80cm = 12m + 1.6m = 13.6m

Breadth of the Pathway = 4m + 80cm + 80 cm = 4m + 1.6m = 5.6m

Perimeter of Rectangle = 2(l+b)

Perimeter = 2(13.6 + 5.6)

Perimeter = 2(19.2)

Perimeter = 38.4m

To learn more about Permieter from the given link

https://brainly.com/question/19819849

#SPJ1

The inverse matrix R⁻¹ does not exist

The inverse of a matrix written as A⁻¹ is such that when the inverse matrix multiplies A, the result is the identity matrix.

Given the matrix [tex]R = \left[\begin{array}{ccc}0&0\\1&3\end{array}\right][/tex], to determine if this matrix has an inverse it must satisfy the following condition.

For a matrix A to have an inverse, its determinant must not be equal to zero. That is det(A) ≠ 0

So, to determine if the above matrix has an inverse, its determinant must not equal zero.

So, the determinant of the matrix det(R) = 0 × 3 - 0 × 1

= 0 - 0

= 0

Since the determinant equals zero, thus we see that its inverse R⁻¹ does not exist

Learn more about inverse of a matrix here:

https://brainly.com/question/28762482

#SPJ1

Answer:

C) 9/40

Step-by-step explanation:

1 - [tex]\frac{2}{5}[/tex] - [tex]\frac{3}{8}[/tex]     Make equivalent fractions with 40 as the denominator

[tex]\frac{2}{5}[/tex] x [tex]\frac{8}{8}[/tex] = [tex]\frac{16}{40}[/tex]   Another name for [tex]\frac{8}{8}[/tex] is one.  This is how we can make equivalent fractions.

[tex]\frac{3}{8}[/tex] x [tex]\frac{5}{5}[/tex] = [tex]\frac{15}{40}[/tex]

1 can also be written [tex]\frac{40}{40}[/tex]

[tex]\frac{40}{40}[/tex] - [tex]\frac{16}{40}[/tex] - [tex]\frac{15}{40}[/tex] = [tex]\frac{9}{40}[/tex]

All of the above options a) implement an expansion strategy b)attract capital c)reduce tax burdens d)easy entry into an industry e)take advantage of limited liability ,are correct.

A corporation is generally set up to take advantage of limited liability. This means that the owners of the corporation (the shareholders) are not personally responsible for the debts and obligations of the corporation. The other options you have listed are also potential reasons for setting up a corporation, but they are not the primary purpose of a corporation.

An expansion strategy refers to a company's plan for growth and expansion, and setting up a corporation can be one way to implement this strategy. Attracting capital refers to the process of raising funds for a business, and a corporation may be able to attract more capital because it is a separate legal entity that can issue stocks and bonds. Reducing tax burdens refers to the process of minimizing the amount of taxes a business has to pay, and a corporation may be able to do this because it is taxed as a separate entity. Finally, setting up a corporation can also make it easier for a business to enter an industry because it provides a legal framework for the business and can make it easier to raise capital.

To learn more about tax, visit:

brainly.com/question/29115944

#SPJ4

The rate at which the diameter decreases is  -0.16cm/min

Diameter:

In geometry, diameter refers the straight line that goes from one side to the other side of a circle, passing through the center.

Given,

Here we need to find if a snowball melts so that its surface area decreases at a rate of 1cm^2/min, find the rate at which the diameter decreases when the diameter is 10 cm. Finish solving the problem. Write an equation that relates the quantities.

Here  we obtained the equation that relates the surface area S and the diameter D of a sphere given by

=> S = πD²

Now, we have differentiate the equation as,

=> dS/dt = d/dt (πD²)

=> dS/dt = π d/dt (D²)

​=> dS/dt = 2πD dD/dt

Now, Solving for dD/dt, which is the unknown for this problem, we have

=> dD/dt ​= 1/2πD​ x dS​/dt

Now, substituting the given values, the rate of change of the diameter when D=10 cm and dS/dt as (-1) is

=> dD/dt = 1/2 x π x 10 (-1)

=> dD/dt = -1/20π

=> dD/dt = -0.16cm/min

To know more about Diameter here.

https://brainly.com/question/5501950

#SPJ4

From the given options, Option A and Option D will represent the proportionality relation between x and y.

Equivalence between two variables that are related to one another and preserve a particular amount is referred to as a proportional relationship.

It is a mathematical concept that describes how two variables are related when they do so in equivalency and is also known as the "Relation of Proportionality."

Let the variables x and y are proportional to each other

=> x ∝ y

=> x = ky

=> x/y = k  [ where k is proportionality constant ]  

Here we will use the formula x/y = k to check the given variables' proportionality

Now check given options given below

Option A

x  0    1/5    2/5    3/5

y  0   1/10  2/10     3/10  

For  x = 1/5 and y = 1/10

=>  [tex]\frac{x}{y} = \frac{1}{5} \times \frac{10}{1}[/tex]  = 2

For  x = 2/5 and  y= 2/10

=>  [tex]\frac{x}{y} = \frac{2}{5} \times \frac{10}{2}[/tex]  = 2

Therefore, Table A represents the proportionality relation

Option B:

x -   0     1/2   1/3   1/4

y -   0     1/3   1/4   1/5

For  x = 1/2 and y = 1/3

=>  [tex]\frac{x}{y} = \frac{1}{2} \times \frac{3}{1}[/tex]  = 3/2

For  x = 1/3 and y = 1/4

=>  [tex]\frac{x}{y} = \frac{1}{3} \times \frac{4}{1}[/tex]  =  4/3  

Therefore, Table B doesn't represent the proportionality relation

Option C:

x -  0    1    3     5  

y -  0    1    9    25

For  x = 1 and y = 1

=>  [tex]\frac{x}{y} = \frac{1}{1} = 1[/tex]    

For  x = 3 and 9

=>  [tex]\frac{x}{y} = \frac{9}{3} = 3[/tex]  

Therefore, Table C doesn't represent the proportionality relation

Option D:

x -   0    1      3      4

y -   0    5    15    20

For  x = 1 and y = 5

=>  [tex]\frac{x}{y} = \frac{1}{5} = 1/5[/tex]    

For  x = 3 and y = 15

=>  [tex]\frac{x}{y} = \frac{3}{15} = \frac{1}{5}[/tex]  

Therefore, Table D will represent the proportionality relation

Therefore,

From the given options, Option A and Option D will represent the proportionality relation between x and y.

Learn more about Proportional at

https://brainly.com/question/22483071

#SPJ1

The percentage change of the first quantity with reference to the second quantity: 480 units, 560 units is: -14.29%.

First step is to find the difference between the two numbers

Difference = New Number - Original Number

Difference =  480 -560

Decrease  = -80

Now let find the percentage change

Percentage change = Decrease  / Original Number × 100

Percentage change = -80 /560 × 100

Percentage change = -14.29%

Therefore we can conclude that the percentage change is -14.29%.

Learn more about percentage change here:https://brainly.com/question/11360390

#SPJ1

The manufacturer of allay pain reliever offered a free sample of the product to visitors who registered at its website. in this case, the communications objective of the website was to increase awareness of Allay Pain Reliever and generate customer leads.

Communication objectives are the aims and principles that guide how a person or company interacts with customers, staff, or other stakeholders. Workplaces can establish and uphold uniform standards for every contact by adopting communication strategies.

In order to achieve marketing goals with an increase in the rate of purchases or information requests, the communication objectives must first develop a good consumer attitude.

To know more about  communication objectives visit:

https://brainly.com/question/28263316

#SPJ4

A The population mean is greater than 10 B The population mean is equal to 10 C The population mean is less than 10 D The population mean is not equal to 10 with probability.

1. The average weight of female athletes is a discrete random variable because it can take on a discrete set of values.

2. A sample point is a single point in a sample space, which is a set of all possible outcomes of an experiment.

3. The standard deviation is a measure of spread of a random variable, which measures how much the values in the set deviate from the mean.

4. The median of the set of numbers is 4, since there are an equal number of numbers below and above the median.

5. The variance of the set of numbers is 36, since it is calculated by taking the sum of the squares of the differences between each number and the mean, and dividing by the number of values.

6. The null hypothesis for a hypothesis test is that the population mean is equal to 10.

Learn more about population mean here

https://brainly.com/question/19538277

#SPJ4

On solving the provided question, we can say that - => K not equal to 0 at x= 0 and so, center of curvature exists.

In geometry, a curve's center of curvature is located at a point that is offset from the curve by an amount equal to the radius of curvature that lies on the normal vector. zero-curvature point at infinity. The center of the curve serves as the osculating circle. The sphere holding the spherical mirror's center serves as its center of curvature. A "C" is used to symbolize this. the center of a circle with a radius equal to the radius of curvature of a particular point on the curve, whose center is on the concave side of the curve and which is normal to that point.

The curvature K at the point (x,y) is given by if C is a graph of the twice differentiable function y = f(x)y=f(x).

[tex]K = \frac{|y^{''}|}{[1 + (y')^2 ]^{3/2}}[/tex]

Curvature of the given curve at x=0x=0 is

=> K not equal to 0 at x= 0

so,

center of curvature exists.

To know more about center of curvature visit:
https://brainly.com/question/1462533

#SPJ4

Following the Sampling Theorem of statistics, the answer is True.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data.

Each member of the group or community has an equal chance of being chosen when using probability sampling. According to probability-based statistical theory, this indicates that the sample is more likely to match the larger population, allowing for the drawing of more precise conclusions about the latter.

Yes, the quota sampling process occurs when the available or accessible people or material are selected. Due to large population size, Sampling process is preferred.

Since, Statistics convey characteristics of data to us. So yes, The sample is weighted so that predetermined characteristics are represented.

To learn more about sampling probability theorem visit:

https://brainly.com/question/28016369

#SPJ4

The smallest rational number among -5/16, -13/24, -3/4, and -7/12 is -3/4.

We have,

To determine the smallest rational number among -5/16, -13/24, -3/4, and -7/12, we need to compare their values.

Let's convert all the given rational numbers to have a common denominator of 48:

-5/16 = -15/48

-13/24 = -26/48

-3/4 = -36/48

-7/12 = -28/48

Now, the values of these rational numbers, when expressed with a common denominator, are:

-15/48, -26/48, -36/48, -28/48

Among these values, the smallest one is -36/48, which is equivalent to -3/4.

Therefore,

The smallest rational number among -5/16, -13/24, -3/4, and -7/12 is -3/4.

Learn more about rational numbers here:

https://brainly.com/question/24398433

#SPJ4

the original price was "x", which oddly enough is the 100%.

now, we know the TV is 75% off, that means the sale price is 100% - 75% = 25%, and we know that's 24 bucks.

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 24& 25 \end{array} \implies \cfrac{x}{24}~~=~~\cfrac{100}{25} \implies \cfrac{ x }{ 24 } ~~=~~ 4\implies x=96[/tex]

The solution for x in the pentagon is 90

From the question, we have the following parameters that can be used in our computation:

Shape = pentagon

This means that

n = 5

The sum of the internal angles is calculated as

Angles = 180(n - 2)

Substitute the known values in the above equation, so, we have the following representation

Angles = 180(5 - 2)

So, we have

Angles = 540

This means that

x + 90 + 90 + 135 + 135 = 540

So, we have

x + 450 = 540

Evaluate

x = 90

Hence, the value of x is 90

Read more about angles at

https://brainly.com/question/7620723

#SPJ1

The system of equations is:

28cm = 2*(W + L)

28.8cm = 2*(0.9*L + 1.2*W)

b) Solving that we will get L = cm and W = 6cm

c) The figure becomes a square of sides of 7.2cm

First, let's define the variables:

Remember that the perimeter of a rectangle is:

P = 2*(W + L)

We know that the perimeter is 28cm, then:

28cm = 2*(W + L)

And if we decrease the length by 10% and increase the width by 20% the perimeter is 28.8cm, then

28.8cm = 2*(0.9*L + 1.2*W)

Then the system of equations is:

28cm = 2*(W + L)

28.8cm = 2*(0.9*L + 1.2*W)

We can isolate L on the first equation to get:

28cm/2 - W = L

14cm - W = L

Replacing that in the other equation we get:

28.8cm = 2*(0.9*(14cm - W) + 1.2*W)

28.8cm = 1.8*(14cm - W) + 2.4*W

28.8cm = 25.2cm + 0.6*W

28.8cm - 25.2cm =  0.6*W

3.6cm/0.6 = W = 6 cm

So the width is 6cm, then the length is:

L  = 14cm - 6cm = 8cm

c) The modified dimensions are:

0.9*L = 0.9*8cm = 7.2 cm

The new width is:

1.2*W = 1.2*6cm = 7.2 cm

So the length is equal to the width, then the figure becomes a square.

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

By analizying the zeros on the graph, we conclude that the equation that could represent the graph is:

y = (x  + 5)²*(x - 3)²

On the graph, we have a polynomial.

Remember that the degree of the polynomial is related to the zeros of the polynomial. Here we can see that we have two double zeros, one at x = -5 and other at x = 3

We know that are double zeros because the curvature of the polynomial changes there.

Then the equation will be something like:

y = (x  + 5)²*(x - 3)²

So that is the correct option, top right.

Learn more about polynomials at:

https://brainly.com/question/4142886

#SPJ1

The correct answers are -

1. Probability of drawing a yellow is 12/99

2. Odds in favour of drawing are 12/87

3. Probability and odds are related through favourable and unfavourable outcomes.

Firstly calculating the total number of candies.

Total number of candies = 115 + 75 + 95 + 60 + 45 + 50 + 55

Performing addition on Right Hand Side of the equation

Total number of candies = 495

Now, the probability of drawing a yellow = number of yellow candies ÷ total number of candies

Probability of drawing a yellow = 60 ÷ 495

Performing division on Right Hand Side of the equation

Probability of drawing a yellow = 0.12

Now, for calculation of second part and answer of third part, relating the probability and odds.

Odds = favourable outcomes ÷ non favourable outcomes

Simplifying the probability in fractional form = 12/99

Favourable outcomes = 12

Non favourable outcomes = 99 - 12

Non favourable outcomes = 87

Odds = 12/87

Thus, probability is 0.12 and odds are 12/87.

Learn more about probability -

https://brainly.com/question/13604758

#SPJ4

The complete question is attached in the figure.

Answer: n = 4

9 = x

y = 2

Step-by-step explanation:

2 ( x + 5 ) = 3x + 1

2x +10 = 3x + 1

10 = 1x + 1

- 1       -1

9 = 1x

9 = x

3y - 4 = 6 - 2y

5y -4 =6

5y = 10

y = 2

3 (n + 2) = 9 ( 6-n)

3n + 6 = 54 -9n

3n +9n = 54 - 6

12n =54 -6

12n =48

n = 4

Answer:

I have solved this on Paper and attached an image in the explanation part!

Step-by-step explanation:

Answer:

2.4 would be the answer i took this before

Step-by-step explanation:

The volume of the given solid, with the boundaries, is given as follows:

661.5 cubic units.

The volume of the solid is obtained using a double integral.

The equation for the solid is given as follows:

7x + 9y + z = 63.

z = 63 - 7x - 9y.

The coordinate planes bound the plane, hence:

Hence the double integral that is used to obtain the volume of the solid is given as follows:

[tex]V = \int_{0}^{9}\int_{0}^{7 - \frac{7x}{9}} 63 - 7x - 9y dydx[/tex]

The inner integral is given as follows:

[tex]I = \int_{0}^{7 - \frac{7x}{9}} 63 - 7x - 9y dy[/tex]

Which, applying the Fundamental Theorem of Calculus, has the result given as follows:

[tex]I = -98x + \frac{49x^2}{9} - \frac{(7x + 63)^2}{18} + 441[/tex]

Then the volume of the solid is given by the outer integral as follows:

[tex]V = \int_{0}^{9} \left(-98x + \frac{49x^2}{9} - \frac{(7x + 63)^2}{18} + 441\right) dx[/tex]

Which has a numeric value of:

661.5 cubic units.

More can be learned about integrals and volumes at https://brainly.com/question/25870210

#SPJ1

The equation that can be used to determine the pounds of laundry the customer brought in to be washed and folded that month is;

D. 0.53x + 26.00 = 37.66

We are given that;

Monthly service fee for Lundromat = $26

They wash and fold clothes at $0.53 per pound  for those customers with a laundry service.

Now, we are told that a customer paid $37.66 total for the month.

If the number of pounds of clothes is denoted as x, then it means that the equation for this will be;

0.53x + 26.00 = 37.66

Read more about Linear equation word problem at; https://brainly.com/question/21405634

#SPJ1

An analyst makes a statistical error known as a sampling error when they choose a sample that does not accurately represent the complete population of data.

In statistics, a truly random sample involves selecting people from a population with an equivalent probability; in other words, picking individuals from a group without bias.

Failing to accomplish this appropriately will result in a sampling bias, which can dramatically increase the sample error in a systematic fashion. For instance, using a sample from just one nation to estimate the average height of all people on Earth could lead to a significant over- or underestimation.

In practice, it might be challenging to select an impartial sample because various criteria (for instance, nation, age, gender, and so on) may substantially bias the estimator. It is important to make sure that none of these aspects are taken into consideration when choosing the sample.

Hence, An analyst makes a statistical error known as a sampling error when they choose a sample that does not accurately represent the complete population of data.

learn more about sampling error:

https://brainly.com/question/28108200

#SPJ4