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2 years ago

The radius of a semicircle is 4 miles. What is the semicircle's area?

Mathematics

1 answer:

adell [148]2 years ago

6 0

Answer:

8 $\pi$ miles or 25.133 miles

Step-by-step explanation:

your radius is 4 miles.

The area of a circle is A= $\pi r^{2}$

Therefore, the area of this circle is $4^{2} \pi$ , or 16 $\pi$

Half of this area, because what you're looking for is a semi-circle, is:

8 $\pi$ (exact) or 25.133 (rounded) miles.

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The table represents the observed number of leaves y on x branches of a tree. Calculate the rate of change between 3 and 4 branc

Dennis_Churaev [7]

Answer:

Step-by-step explanation:

The rate of change of number of tree y on x branches of a tree is expressed as shown;

m = Δy/Δx where;

m is the rate of change

Δy is the change in number of leaves between 3 and 4

Δx is change in number of branches between 3 and 4

m = Δy/Δx = y₂-y₁/x₂-x₁

From table between 3 and 4, y₂ = 100, y₁ = 75, x₂ = 4, x₁ = 3

m = 100-75/4-3

m = 25/1

m = 25

<em>Hence the rate of change between 3 and 4 branches is 25</em>

5 0

2 years ago

There is a bag filled with 5 blue and 6 red marbles.

Sidana [21]

Answer:

6/11

Step-by-step explanation:

probability

6+5=11

so 6/11

6 0

3 years ago

Read 2 more answers

Anyone ? Need help. Thanks

NNADVOKAT [17]

Answer:

$B.\:\: g(x)=4(2^x)$

Step-by-step explanation:

The given function is $f(x)=2^x$ .

If an exponential function is of the form; $F(x)=a(b^x)$ , then $0$ will vertically shrink the base function $f(x)=b^x$

and $a\:>\:1$ will vertically stretch the graph by $a$ units.

The correct answer is B.

7 0

3 years ago

Qasim and Alejandra both earn $15 an hour at their job. This week Alejandra worked three hours more than Qasim. If h represents

joja [24]

Answer:

Alejandra worked 8 hours and Qasim worked 5

Step-by-step explanation:

195/15 is 13. They worked 13 hours in total. 8 is 3 more than 5 and together they equal 13.

8 0

3 years ago

4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t

Klio2033 [76]

First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

$a_{n}=a_{1}r^{n-1}$

$a_{1}$ = the first term of the series

$r$ = the geometric ratio

$a_{1}$ would represent the height at which the ball is first dropped. Therefore:

$a_{1} = k$

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

$r=\frac{3}{4}$

Our general term would be:

$a_{n}=a_{1}r^{n-1}$

$a_{n}=k(\frac{3}{4}) ^{n-1}$

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

$k$ represents the initial height:

$k = 235\ ft$

$n$ represents the number of times the ball bounces:

$n = 6$

Plugging this back into our general term of the geometric series:

$a_{n}=k(\frac{3}{4}) ^{n-1}$

$a_{n}=235(\frac{3}{4}) ^{6-1}$

$a_{n}=235(\frac{3}{4}) ^{5}$

$a_{n}=55.8\ ft$

$a_{n}$ represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. 

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

$S_{n}=\frac{a_{1}(1-r^{n})}{1-r}$

We already know these variables:

$a_{1}= k = 235\ ft$

$r=\frac{3}{4}$

$n = 12$

Therefore:

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }$

$S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }$

$S_{n}=(4)(235)(1-\frac{3}{4} ^{12})$

$S_{n}=910.22\ ft$

8 0

2 years ago