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3 years ago

What is the volume of the cylinder?

Mathematics

1 answer:

Anna007 [38]3 years ago

7 0

Answer:

B. 2010.62 ft³

Step-by-step explanation:

The formula for the volume of a cylinder is ...

V = πr²h . . . . . where r is the radius and h is the height

Filling in the numbers and doing the arithmetic, we get ...

V = π(8 ft)²(10 ft) = 640π ft³ ≈ 2010.6193 ft³ ≈ 2010.62 ft³

The volume of the cylinder is about 2010.62 ft³.

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30 POINTS! PLEASE HELP!

nikklg [1K]

Triangle ABC is similar to triangle JKL. They both have the same angle amounts.

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2 years ago

I NEED HELP WITH QUESTION PLEASE!! What is the inverse of f(x) (x) = (x-4)² for x ≥ 4?

goblinko [34]

Answer:

4th choice $\bold{f^{-1}(x) = \sqrt{x} + 4}$

Step-by-step explanation:

Definition of the inverse of a function

A function g is the inverse of a function f if whenever y=f(x) then x=g(y). In other words, applying f and then g is the same thing as doing nothing. We can write this in terms of the composition of f and g as g(f(x))=x. The domain of f becomes the range of g and the range of f becomes the domain of g

To solve for the inverse of the function $f(x) =\left(x-4\right)^2$

Let $y=\left(x-4\right)^2$

$\mathrm{Replace}\:x\:\mathrm{with}\:y$ $\text{ and replace }\:y\:\mathrm{with}\:x$

$x=\left(y-4\right)^2$

Switch sides
$\left(y-4\right)^2=x$

Take square roots on both sides
$y-4=\pm\sqrt{x}$

Add 4 on both sides to solve for y

$y = \pm\sqrt{x} + 4$

We have two solutions

$y=\sqrt{x}+4,\:y=-\sqrt{x}+4$

To determine which one of these to be chosen not that in the given choices we can eliminate the first two since x cannot be negative

The third choice can also be eliminated since
$-\sqrt{x} + 4$ is a decreasing function for $x \ge 0$

So the last answer choice is correct and the inverse of $f(x) = (x-4)^2$

is given by $f^{-1}(x) = \sqrt{x} + 4$

Answer:4th choice $\bold{f^{-1}(x) = \sqrt{x} + 4}$

Note

Domain of (x-4)² is [4, ∞) since x ≥ 4 and (x-4)² cannot be negative

Range of (x-4)² is [0, ∞)

Domain of $\sqrt{x}\:+\:4$ is [0, ∞)

Range of $\sqrt{x}\:+\:4$ is [4, ∞)

so indeed the domain of (x-4)² has become the range of $\sqrt{x}\:+\:4$ and the range of (x-4)² has become the domain of $\sqrt{x}\:+\:4$

5 0

6 months ago

Write an equation of the line that passes through (7,10) and is perpendicular to the line y=12x−9.

Ulleksa [173]

Answer:

y = - $\frac{1}{12}$ x + $\frac{127}{12}$

Step-by-step explanation:

y = 12x - 9

Slope of line perpendicular to given is m = - $\frac{1}{12}$

P(7, 10)

y - 10 = - $\frac{1}{12}$ (x - 7)

y = -  $\frac{1}{12}$  x +  $\frac{127}{12}$  

8 0

2 years ago

You have 3/4 of a pie leftover after your party. Each guest takes home 1/6 of the leftover pie. What fraction of the original pi

Mazyrski [523]

What are you looking for how many they took or how many in total is left

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2 years ago

Mr Frank purchased 5_1/4 pounds of rocks. He used 3/5 of a pound on one aquarium. He then split the rest of the rocks between hi

riadik2000 [5.3K]

Answer:

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Step-by-step explanation:

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6 0

2 years ago