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3 years ago

Evaluate the function rule for the given value.

Mathematics

2 answers:

igor_vitrenko [27]3 years ago

5 0

the answer is 25

raise 5 to the power of 2 and you get 25

Lena [83]3 years ago

3 0

Answer:

Option C - 10

Step-by-step explanation:

Given : Function $f(x)=5x$

To find : Evaluate the function for the value x=2

Solution :

We have given the function $f(x)=5x$

We have to find the value of f(x) at x=2

Substitute x=2 in the given function f(x)

$f(x)=5x$

$f(2)=5(2)$

$f(2)=10$

Therefore, Option C is correct.

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1. Given the points P (1, - 4). Q (3,-2), R (-3,5), find the coordinates of the mid-points A and B of PO and PR respectively and

aleksandrvk [35]

1583.34 there you go

5 0

2 years ago

If Fran has 7 sheets of paper for a coloring project. If she only uses 1/3 of a sheet of paper per drawing how man drawings can

Ymorist [56]

1 sheet can contain 3 drawings. So 7 x 3 = 21.

21 drawings in total.

4 0

3 years ago

Read 2 more answers

The circular opening of an ice cream cone has a diameter of 7 centimeters. The height of the cone is 10 centimeters. What is the

Nataly [62]

We have been given that the circular opening of an ice cream cone has a diameter of 7 centimeters. The height of the cone is 10 centimeters. We are asked to find the volume of the ice cream cone in cubic centimeters.

We will use volume of cone formula to solve our given problem.

$V=\frac{1}{3}\pi r^2h$ , where,

r = Radius

h = Height.

We know that diameter is two times the radius, so radius of cone would be half the diameter that is $\frac{7}{2}$ cm.

$V=\frac{1}{3}\pi\cdot (\frac{7}{2}\text{ cm})^2\cdot 10\text{ cm}$

$V=\frac{1}{3}\pi\cdot \frac{49}{4}\text{ cm}^2\cdot 10\text{ cm}$

$V=\frac{490\pi }{12}\text{ cm}^3$

$V=128.2817\text{ cm}^3$

Upon rounding to nearest tenth, we will get:

$V\approx 128.3\text{ cm}^3$

Therefore, the volume of the cone would be approximately 128.3 cubic cm.

8 0

3 years ago

The transformation T = [0 1 -1 0] is applied the figure below.

Margaret [11]

Answer:

<h2>a.) reflect across x-axis</h2>

Step-by-step explanation:

The transformation described is about multiplying the vertical value by -1:

$(x,y) \implies (x,-y)$

That means all vertical coordinates will change to the opposite side, but all horizontal coordinates will maintain at the same coordinate.

As a result, we'll have a reflection across the x-axis, because the y coordinates were transformed.

Therefore, the right answer is A.

4 0

3 years ago

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

3 years ago