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Lelu [443]
3 years ago
8

Please help I have a quiz soon

Mathematics
1 answer:
Novay_Z [31]3 years ago
3 0

Answer:

The option that no represent a linear function is f(x)=3^x

Step-by-step explanation:

we know that

The graph of a linear function is a straight line

The equation of a linear function in slope intercept form is equal to

f(x)=mx+b

where

m is the slope

b is the y-intercept

<u><em>Verify each case</em></u>

option 1) we have

f(x)=3x-2

This option represent a linear function

where

m=3

b=-2

option 2) we have

f(x)=x

This option represent a linear function

where

m=1

b=0

This option represent a linear direct variation function

option 3) we have

f(x)=3^x

This option not represent a linear function

This option represent a exponential function

option 4) we have

f(x)=3x

This option represent a linear function

where

m=3

b=0

This option represent a linear direct variation function

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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.​
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Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = 21m^3

Required

Volume of the sphere

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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4. Use you straight edge and connect the points.

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