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3 years ago

The diameter of a sphere is 4 centimeters. Which represents the volume of the sphere? π cm3 8π cm3 π cm3 16π cm3

Mathematics

2 answers:

BartSMP [9]3 years ago

7 0

ФThe Answer is A).32/3π cm3 Ф

ICE Princess25 [194]3 years ago

6 0

we know that

the volume of the sphere is equal to

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

where

r is the radius of the sphere

In this problem

we have the diameter

$D=4\ cm\\\\ r=\frac{D}{2}\\\\r=2\ cm$

substitute the value of the radius in the formula above

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

$V=\frac{32}{3}\pi\ cm^{3}$

therefore

the answer is

the volume of the sphere is equal to

$V=\frac{32}{3}\pi\ cm^{3}$

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3 years ago

Steven Kellogg, a machine operator, works at an hourly rate of $10.60 and

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Answer:

$Straight\ Time\ Pay = \$392.2$

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Step-by-step explanation:

Given

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$Overtime\ Pay = Overtime\ Rate * Overtime\ Hours$

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$Overtime\ Pay = \frac{\$10.6}{2} * 8$

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3 years ago

Heyo, could you help me? thank you

devlian [24]

Answer:

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Step-by-step explanation:

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3 years ago

Graph the following piecewise function on a separate piece of graph paper and upload your graph below.

Alecsey [184]

ANSWER

To graph the function

$f(x)=\left \{ {{x+4\:\:if\:\:-4\leq x$

follow the steps below.

1. Find y- intercept by plugging in $x=0$ .

$x=0$ is on the interval, $-4\leq x$ , so we substitute in to

$f(x)=x+4$

$\Rightarrow f(0)=0+4$

$\Rightarrow f(0)=4$

Hence the y-intercept is $(0,4)$

2. Find x-intercept by setting $f(x)=0$

This implies that

$x+4=0,$ on $-4\leq x$

or

$2x-1=0$ on $3\leq x$

We now solve for $x$ on each interval,

$x=-4,$ on $-4\leq x$

or

$x=\frac{1}{2}$ on $3\leq x$

But observe that

$x=\frac{1}{2}$ does not belong to $3\leq x$

This means it can never be an intercept for this piece-wise function.

Hence our x-intercept is $(-4,0)$

3. Plotting the boundaries of the interval.

For $f(x)=x+4$ on $-4\leq x$

$f(-4)=-4+4$

$\Rightarrow f(-4)=0$ .

This point $(-4,0)$ coincides with the x-intercept.

$f(3)=3+4$

$f(3)=7$

So we have the point $(3,7)$ . But note that $x=3$ does not belong to this interval so we plot this point as a hole.

For $f(x)=2x-1$ on $3\leq x$

$f(3)=2(3)-1$

$\Rightarrow f(3)=5$

So we plot $(3,5)$

$f(6)=2(6)-1$

$\Rightarrow f(6)=11$

So we plot $(6,11)$ also as a hole.

Plotting all these points we can now graph the function,

$f(x)=\left \{ {{x+4\:\:if\:\:-4\leq x$

See attachment for graph.