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FromTheMoon [43]
3 years ago
6

The figure below shows part of a stained-glass window depicting the rising sun. Which function can be used to find the area of t

he region outside the semicircle but inside the rectangle?

Mathematics
1 answer:
Kryger [21]3 years ago
3 0

Answer:

A(w) = w^2 + 5w - \frac{1}{8}\pi w^2

Step-by-step explanation:

A = the area of the region outside the semicircle but inside the rectangle

w = the width of the rectangle or diameter of the semicircle

Since "A" is determined by "w", therefore, "A" is a function of "w" = A(w).

A(w) = (area of rectangle) - (area of semicircle)

A(w) = (l*w) - (\frac{1}{2} \pi r^2)

Where,

lenght of rectangle (l) = w + 5

width of rectangle (w) = w

r = ½*w = \frac{w}{2}

Plug in the values:

A(w) = ((w + 5)*w) - (\frac{1}{2} \pi (\frac{w}{2})^2)

A(w) = ((w + 5)*w) - (\frac{1}{2} \pi (\frac{w}{2})^2)

Simplify

A(w) = (w^2 + 5w) - (\frac{1}{2} \pi (\frac{w^2}{4})

A(w) = w^2 + 5w - \frac{1}{2}*\pi*\frac{w^2}{4}* \pi

A(w) = w^2 + 5w - \frac{1*\pi*w^2}{2*4}

A(w) = w^2 + 5w - \frac{1*\pi w^2}{8}

A(w) = w^2 + 5w - \frac{1}{8}\pi w^2

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Subtract. write your answer in simplest form
xeze [42]

Answer:

6 \frac{11}{15}

Step-by-step explanation:

OK because 9 is less than 13 we have to add to nine using the whole number.

9 turns into 8  and 9 turns into 24. (15 makes a whole so we must add 15 to 9)

now we can subtract.

8\frac{24}{15} - 2\frac{13}{15} = 6 \frac{11}{15}

5 0
3 years ago
Read 2 more answers
Confused on what do do first . Can anyone help ?
kirza4 [7]
So solve for q

first factor q out of the summationq \sum^{\inf}_{k=2} (\frac{2}{3})^k=8

now, determine what the summation is
\sum^{\inf}_{k=2} (\frac{2}{3})^k =?

its been a while since ive done summations so i dont remember any tricks but that summation is essentially equal to
\frac{2}{3} ^2 +\frac{2}{3}^3+\frac{2}{3}^4+\frac{2}{3}^5+...

or factored to be something like this
\frac{2}{3}^2 *(1+\frac{2}{3}+\frac{2}{3}^2+\frac{2}{3}^3+...)
which i believe there's a formula for

regardless using a calculator, the summation turns out to be 4/3 i think

you should definitely double check this step

so replacing the summation for 4/3, the equation is now
q*(4/3) =8

pretty easy to solve from here
divide 4/3 to both sides to get q


any questions?
5 0
3 years ago
Type a digit that makes this statement true.<br><br> 908,08<br> is divisible by 2.
galben [10]

Answer:

So we have to start with the rules of two and the rules of two are

The divisibility rule for 2 states that any number with the last digit of 0, 2, 4, 6, or 8 will be divisible by 2.  So that's how we know

4 0
3 years ago
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An isosceles triangle has an angle that measures 94º. Which other angles could be in that
Nataly [62]

Answer:

43°

Step-by-step explanation:

In a isosceles triangle, two angles HAVE to be equal.

This means that 94 can be one of the angles that are equal, or the angle that is not equal to another angle.

Let's start with the fact that 94 can be one of the angles that are equal. (Note: angles in a triangle add up to 180)

94+94+x=180

188+x=180

There is NOT a possible value for x in this situation, as you cannot have a negative value of an angle. Therefore we must try the other situation where 94 is the angle that is not equal to another angle.

x+x+94=180

2x+94=180

Subtract 94 from both sides

2x=86


Divide both sides by 2

x=43

Therefore the answer is 43°

4 0
2 years ago
WILL GIVE BRAINLIEST, SUPERB RATING, AND THANKS!
Vaselesa [24]

A line on this coordinate plane is horizontal when every input (x) has the same output y).

This function always gives the same output with no matter what input you put it in.

8 0
3 years ago
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