Questions 3 and 4, no work required……………………………………

marissa [1.9K]

Answer:

(D) 30pi inches

Step-by-step explanation:

First, we use the given volume, the given height, and the formula of the volume of a cylinder to find the radius of the base. Then we use the radius of the base to find the circumference of the base.

$volume = \pi r^2 h$

$volume = 6750 \pi~in.^3$

We set the formula equal to the volume and replace h with 30 in.

$\pi r^2 h = 6750 \pi~in.^3$

$\pi r^2 \times 30 ~in. = 6750 \pi~in.^3$

Divide both sides by 30pi in.

$r^2 = 225 ~in.^2$

Take the square root of each side.

$\sqrt{r^2} = \sqrt{225 ~in.^2}$

$r = 15~in.$

The radius of the base is 15 in.

Now we use the radius of the base and the formula of the circumference of a circle to find the answer.

$circumference = 2 \pi r$

$circumference = 2 \pi \times 15~in.$

$circumference = 30 \pi ~in.$

6 0

3 years ago

Find a cartesian equation for the curve and identify it. r = 10 tan(θ) sec(θ)

Vilka [71]

For a cartesian equation
$x=r\cos\theta \ and \ y=r\sin\theta \\ \\ \cos\theta=\frac{x}{r} \ and \ \sin\theta=\frac{y}{r} \\ \\ \tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{y}{r}\cdot\frac{r}{x}=\frac{y}{x} \\ \\ \sec\theta=\frac{1}{\cos\theta}=\frac{r}{x}$

Given r = <span>10 tan(θ) sec(θ)
$r=10\tan\theta\sec\theta=10\cdot\frac{y}{x}\cdot\frac{r}{x} \\ \\ \Rightarrow10y=x^2 \\ \\ \Rightarrow y= \frac{1}{10} x^2$

Therefore,</span>the curve is a parabola opening upward with vertex (0, 0).

3 0

3 years ago

180% if what number is 36

elena-s [515]

Answer:

64.8

Step-by-step explanation:

7 0

2 years ago

Functions and Transformations

DaniilM [7]

The new translated function will be more towards the origin , as the value of length is decreased , Option C is the right answer.

<h3>What is a Function ?</h3>

A function is a mathematical statement used to relate a dependent and an independent variable.

It is given that

Area of a Rectangle is 10 sq. unit

Width of the Rectangle is x unit

Length is given by

l(x) = 10 / x

When the length of the Rectangle is increased by 1 ,

The new function will be

l(x) = 10 /(x+1)

The new translated function will be more towards the origin , as the value of length is decreased ,

This is represented by Graph 3 ,

This can be proved by keeping the value of x

let x = 2

y = 10 /3 = 3.333

This is only in the graph 3 , Therefore Option C is the right answer.

To know more about Function

brainly.com/question/12431044

#SPJ1

6 0

1 year ago

The interior angles formed by the sides of a pentagon have measures that sum to 540°. What is the measure of angle B?

patriot [66]

Answer:

m∠B = 110°

Step-by-step explanation:

We know that,

The sum of the measures of the angles in a pentagon is 540°.

So, we get,

130 + (x-5) + (x+30) + 75 + (x-35) = 540

i.e. 3x + (130+30+75) - (5+35) = 540

i.e. 3x + 235 - 40 = 540

i.e. 3x + 195 = 540

i.e. 3x = 540 - 195

i.e. 3x = 345

i.e. x= 115°

Now, as m∠B = (x-5)° = (115-5)° = 110°

Hence, the measure of angle B is 110°.

4 0

3 years ago

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