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3 years ago

For the functions f(x)=4x−3 and g(x)=3x2+4x, find (f∘g)(x) and (g∘f)(x).

Mathematics

1 answer:

barxatty [35]3 years ago

7 0

Answer:

(16x + 21) and (16x - 6)

Step-by-step explanation:

f(g(x)) = f(6 + 4x)

Applying the f(x) function on (6 + 4x) gives

4(6 + 4x) - 3

Which equals 16x + 24 - 3

= 16x + 21

g(f(x)) = g(4x - 3)

Applying the g(x) function on (4x - 3) gives

6 + 4(4x - 3)

Which equals 6 + 16x - 12

= 16x - 6

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A sphere is inscribed in a cube with a surface area of 216 square centimeters. What is the volume of the sphere

pentagon [3]

Answer:

$V=298.5cm^3$

Step-by-step explanation:

To find the volume of the sphere we need to know its radius.

And the radius can be found with the information we have about the surface area.

The formula for the surface area is as follows:

$SA=4\pi r^2$

from this formula we clear the radius r:

$r^2=\frac{SA}{4\pi}\\ \\r=\sqrt{\frac{SA}{4\pi} }$

and we substitute the known value of the surface area, and also the value of $\pi$ :

$r=\sqrt{\frac{216cm^2}{4(3.1416)} }\\ \\r=\sqrt{\frac{216cm^2}{12.5664} }\\ \\r=\sqrt{17.1887cm^2}\\ \\r=4.146cm$

and now that we know the radius we find the volume:

$V=\frac{4\pi r^3}{3} \\\\V=\frac{4(3.1416)(4.146cm)^3}{3}\\ \\V=\frac{895.521cm^3}{3}\\ \\V=298.5cm^3$

the volume of the sphere is $298.5cm^3$

7 0

2 years ago

What value of x satisfies

LenaWriter [7]

Answer:

See explanation

Step-by-step explanation:

The given trigonometric equation is $cos(90-x)=-\frac{\sqrt{3} }{3}$ .

We take the inverse cosine of both sides to get:

$90-x=cos^{-1}(-\frac{\sqrt{3} }{3})$

$90-x=125$

$x=125-90$

$x=-35\degree=325\degree$ to the nearest degree

None of the options satisfies the given equation.

But if the question is actually;

$cos(90-x)=-\frac{\sqrt{3} }{2}$

Then;

$90-x=\cos^{-1}(-\frac{\sqrt{3} }{2})$ .

$90-x=210$ .

$x=-120\degree$ .

$x=360-120=240\degree$ .

In this case the answer will be B

5 0

3 years ago

Read 2 more answers

Determine the graph of the polar equation r=4/(1-1/2cosx(theta))

crimeas [40]

Answer:

see below

Step-by-step explanation:

We assume you want the graph of ...

$r=\dfrac{4}{1-\frac{1}{2}\cos{(\theta)}}$

A graphing calculator or spreadsheet is useful for this.

You know cos(θ) = cos(-θ), so the graph is symmetrical about the x-axis. You can evaluate the function at a few points to find the general outline.

r at 0° = 8

r at 30° ≈ 7.05

r at 45° ≈ 6.19

r at 60° ≈ 5.33

r at 90° = 4

r at 120° = 3.2

r at 135° ≈ 2.96

r at 150° ≈ 2.79

r at 180° ≈ 2.67

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Triangles always equal 180 degrees

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Nastasia [14]

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Step-by-step explanation: need more info

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