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3 years ago

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

Verify each case

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.

Goshia [24]

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;

Using the volume formula of a cylinder

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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