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2 years ago

Find the circumference of a circular window if the area is 100pi sq units

Mathematics

2 answers:

padilas [110]2 years ago

7 0

20pi sq units
.............

-BARSIC- [3]2 years ago

6 0

For this problem, using the area of the circle, we have to work backwards to find the radius to find the circumference

The area of the circle (A) = 100π units

A = 100π

The formula for area of a circle

A = πr²

Since we know what A is, lets plug it into the equation for area of a circle to solve for r

100π = πr²

Divide π from both sides to cancel them out

100 = r²

Take the square root of both sides to isolate r, the radius

r = 10

Now that we know what r is, let's plug it into the equation for the circumference of a circle

Circumference = 2πr

= 2π(10)

Multiply 2 and 10, because both are like terms

Circumference of the window = 20π

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A certain ball is dropped from a height of x feet. It always bounces up to 2/3 x feet. Suppose the ball is dropped from 10 feet

galina1969 [7]

Given that if a ball is dropped from x feet, it bounces up to 2/3 x feet.

And the ball is dropped from 10 feet, that is x=10 feet,

So,before the first bounce it travels 10 feet distance.

Between first and second bounce it travels $\frac{2}{3}* 10 + \frac{2}{3} * 10 = 20*(\frac{2}{3})$

Between second and third bounce, it travels $20*(\frac{2}{3})^{2}$

Between third and fourth bounce, it travels $20*(\frac{2}{3}) ^{3}$

Like that between 29th and 30th bounce, it travels $20*(\frac{2}{3} )^{29}$

Hence total distance traveled is

$10+20*(\frac{2}{3} )+20*(\frac{2}{3})^{2} + 20*(\frac{2}{3}) ^{3}+......+20*(\frac{2}{3})^{29}$

= $10+20[(\frac{2}{3}) +(\frac{2}{3}) ^{2} +(\frac{2}{3}) ^{3} +.....+(\frac{2}{3} )^{29} ]$

= $10+20[\frac{\frac{2}{3}*(1-(\frac{2}{3})^{29}) }{1-\frac{2}{3} }]$

= 10+20*2*(1- $(\frac{2}{3}) ^{29}$ )

= 49.9997 feet ≈ 50 feet approximately.

7 0

2 years ago

Read 2 more answers

which of the three sets could not be the lengths of the sides of a triangle {6,10,12} {5,7,10} {4,4,9} {2,3,3}

Phoenix [80]

So for this, we will be applying the Triangle Inequality Theorem, which states that the sum of 2 sides must be greater than the third side for it to be a triangle. If any inequality turns out to be false, then the set cannot be a triangle.

$A+B>C\\A+C>B\\B+C>A$

<h2>First Option: {6, 10, 12}</h2>

Let A = 6, B = 10, and C = 12:

$6+10>12\\16>12\ \textsf{true}\\\\6+12>10\\18>10\ \textsf{true}\\\\12+10>6\\22>6\ \textsf{true}$

<h2>Second Option: {5, 7, 10}</h2>

Let A = 5, B = 7, and C = 10

$5+7>10\\12>10\ \textsf{true}\\\\5+10>7\\15>7\ \textsf{true}\\\\10+7>5\\17>5\ \textsf{true}$

<h2>Third Option: {4, 4, 9}</h2>

Let A = 4, B = 4, and C = 9

$4+4>9\\8>9\ \textsf{false}\\\\4+9>4\\13>4\ \textsf{true}\\\\4+9>4\\13>4\ \textsf{true}$

<h2>Fourth Option: {2, 3, 3}</h2>

Let A = 2, B = 3, and C = 3

$2+3>3\\5>3\ \textsf{true}\\\\2+3>3\\5>3\ \textsf{true}\\\\3+3>2\\6>2\ \textsf{true}$

<h2>Conclusion:</h2>

Since the third option had an inequality that was false, <u>the third option cannot be a triangle.</u>

5 0

2 years ago

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How many inches are in 125<br> 1<br> 2<br> 5<br> groups of 123<br> 1<br> 2<br> 3<br> inches?

Sveta_85 [38]

Answer: 15,375 inches

Step-by-step explanation: If there are 123 inches in each group, and there are 125 groups, it is a multiplication operation.

123 × 125 = 15375

<em>The format of the question makes it a bit confusing. I hope this helps.</em>

<em />

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2 years ago

Required<br> What effect does the sales tax or tip have on the final price? *

Montano1993 [528]

Answer:

Percentages: Price before and after sales tax

Step-by-step explanation:

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2 years ago

Find the distance between the points (-7, -6) and (-3, 0).

FrozenT [24]

Answer:

7.21 unit

Step-by-step explanation:

distance= √[(-7+3)^2 + (-6-0)^2]

= 7.21 unit

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2 years ago