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3 years ago

A family purchases a light sphere to be used out on their patio. The diameter of the sphere is 20 in.

Mathematics

2 answers:

NeX [460]3 years ago

7 0

Answer:

Volume of the sphere is 41866.67 in³ .

Step-by-step explanation:

Formula

$Volume\ of\ a\ sphere = \frac{4}{3}\pi\ r^{3}$

Where r is the radius of the sphere .

As given

The diameter of the sphere is 20 in.

$Radius = \frac{Diameter}{2}$

$Radius = \frac{20}{2}$

Radius = 10 in

$\pi = 3.14$

Putting all the values in the formula

$Volume\ of\ a\ sphere = \frac{4\times 3.14\times 10\times 10\times 10}{3}$

$Volume\ of\ a\ sphere = \frac{4\times 314\times 10\times 10\times 10}{3\times 10}$

$Volume\ of\ a\ sphere = \frac{4\times 314\times 10\times 10}{3}$

$Volume\ of\ a\ sphere = \frac{125600}{3}$

Volume of a sphere = 41866.67 in³ (Approx)

Therefore the volume of the sphere is 41866.67 in³ .

mixer [17]3 years ago

5 0

Radius = 10 inches
Volume = (4/3) * PI * radius ^ 3
Volume = (4/3) * 3.14 * 10^3
Volume = 4,186.6666666667 
Volume = 4,186.67

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For the function y=3x2: (a) Find the average rate of change of y with respect to x over the interval [3,6]. (b) Find the instant

nirvana33 [79]

Answer:

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

Step-by-step explanation:

a) Geometrically speaking, the average rate of change of $y$ with respect to $x$ over the interval by definition of secant line:

$r = \frac{y(b) -y(a)}{b-a}$ (1)

Where:

$a$ , $b$ - Lower and upper bounds of the interval.

$y(a)$ , $y(b)$ - Function exaluated at lower and upper bounds of the interval.

If we know that $y = 3\cdot x^{2}$ , $a = 3$ and $b = 6$ , then the average rate of change of $y$ with respect to $x$ over the interval is:

$r = \frac{3\cdot (6)^{2}-3\cdot (3)^{2}}{6-3}$

$r = 27$

The average rate of change of $y$ with respect to $x$ over the interval $[3,6]$ is 27.

b) The instantaneous rate of change can be determined by the following definition:

$y' = \lim_{h \to 0}\frac{y(x+h)-y(x)}{h}$ (2)

Where:

$h$ - Change rate.

$y(x)$ , $y(x+h)$ - Function evaluated at $x$ and $x+h$ .

If we know that $x = 3$ and $y = 3\cdot x^{2}$ , then the instantaneous rate of change of $y$ with respect to $x$ is:

$y' = \lim_{h \to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{(x+h)^{2}-x^{2}}{h}$

$y' = 3\cdot \lim_{h \to 0} \frac{2\cdot h\cdot x +h^{2}}{h}$

$y' = 6\cdot \lim_{h \to 0} x +3\cdot \lim_{h \to 0} h$

$y' = 6\cdot x$

$y' = 6\cdot (3)$

$y' = 18$

The instantaneous rate of change of $y$ with respect to $x$ at the value $x = 3$ is 18.

5 0

2 years ago

B is the midpoint of AC. C is the midpoint of AD. Find the coordinates of B and D given the coordinates of A (-2,5) and the coor

GalinKa [24]

B= (3,6) and D= (18,9)

Step-by-step explanation:

To find the midpoint of two given points add X1 and X2 together, then divide by 2 to get the X value of the midpoint and do the same thing for the Y value. That will get you B. From there you can see to get from point A to point C you add 10 to the x value and add 2 to the y value. Because C is the midpoint just double what you had to add to get point D (add 20 to x and add 4 to y)

4 0

2 years ago

Can Someone help me plz????

bearhunter [10]

Answer:

4. C

5. 7

6. 3

Step-by-step explanation:

Four:

You have to multiply both of them. Just easy math!

Five:

This one is more complicated. You can see that it is asking you to plug in for a,

F(3):

$f(3)= 4(3)-5$

$f(3)=12-5$

$f(3)=7$

F(1.25):

$f(1.25)=4(1.25)-5$

$f(1.25)=5-5$ $f(1.25)=0$

So now just subtract the answers. 7-0 equals 7.

Six:

Just look at the graph and see what number corresponds with y(6), or the 6 on the y axis. It appears to be three.

Have a nice day! Hope this helps. Don't forget to mark brainliest!

4 0

3 years ago

Read 2 more answers

What is 25 percent of 32?

vitfil [10]

Answer:

1.28 or 128

Step-by-step explanation:

you would take 32 and divide it by.25

6 0

3 years ago

Daniel spent $4.75 for lunch and $1.85 for a snack. Kyle spent $5.75 for lunch and $1.00 for a snack. How much more money did Ky

Katena32 [7]

Daniel spent $4.75 for a lunch and $1.85 for a snack
$4.75+$1.85=$6.6, so Daniel spent $6.6 total

Kyle spent $5.75 for lunch and $1.00 for a snack
$5.75+$1.00=$6.75, so Kyle spend total $6.75.

Final step:
$6.75-$6.6=$0.15. As a result, Kyle spent $0.15 or 15 cent more than Daniel. Hope it help!

3 0

3 years ago