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3 years ago

If f(x)=3^x+10 and g(x)=2x-4, find (f-g)(x)

Mathematics

1 answer:

nataly862011 [7]3 years ago

6 0

<h3>Answer: 3^x - 2x + 14</h3>

=====================================

Work Shown:

(f - g)(x) = f(x) - g(x)

(f - g)(x) = ( f(x) ) - ( g(x) )

(f - g)(x) = ( 3^x + 10 ) - ( 2x-4 )

(f - g)(x) = 3^x + 10 - 2x+4

(f - g)(x) = 3^x - 2x + (10+4)

(f - g)(x) = 3^x - 2x + 14

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3 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

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Required

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Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

<em>Using the volume formula of a cylinder</em>

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

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

Divide both sides by r

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

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

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3 years ago

Read 2 more answers

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BabaBlast [244]

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3 years ago

10ft*10ft of a circle What is the area, in ft2

alexgriva [62]

Answer:

Step-by-step explanation:

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2 years ago

(-2 + 1)² + 5(12 3) - 9.<br> The value of the expression is ?

Mumz [18]

Answer:

The total value of the given expression is 12.

Step-by-step explanation:

(-2 + 1)² + 5(12 ÷ 3) - 9

First, do the expressions within the parentheses.

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Next, simplify the exponents.

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Next, multiply 5 by 4.

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Add 1 and 20 together.

21 - 9

Subtract 9 from 21.

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3 years ago