PLEASE HELP ASAP, the distance between the gears is 36 and the radius of the larger circle is 17.

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aliina [53]

Answer:

Part 1) The length of each side of square AQUA is $3.54\ cm$

Part 2) The area of the shaded region is $(486\pi-648)\ units^{2}$

Step-by-step explanation:

Part 1)

step 1

Find the radius of the circle S

The area of the circle is equal to

$A=\pi r^{2}$

we have

$A=25\pi\ cm^{2}$

substitute in the formula and solve for r

$25\pi=\pi r^{2}$

simplify

$25=r^{2}$

$r=5\ cm$

step 2

Find the length of each side of square SQUA

In the square SQUA

we have that

SQ=QU=UA=AS

$SU=r=5\ cm$

Let

x------> the length side of the square

Applying the Pythagoras Theorem

$5^{2}=x^{2} +x^{2}$

$5^{2}=2x^{2}$

$x^{2}=\frac{25}{2}\\ \\x=\sqrt{\frac{25}{2}}\ cm\\ \\ x=3.54\ cm$

Part 2) we know that

The area of the shaded region is equal to the area of the larger circle minus the area of the square plus the area of the smaller circle

Find the area of the larger circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=AB=18\ units$

substitute in the formula

$A=\pi (18)^{2}=324\pi\ units^{2}$

step 2

Find the length of each side of square BCDE

we have that

$AB=18\ units$

The diagonal DB is equal to

$DB=(2)18=36\ units$

Let

x------> the length side of the square BCDE

Applying the Pythagoras Theorem

$36^{2}=x^{2} +x^{2}$

$1,296=2x^{2}$

$648=x^{2}$

$x=\sqrt{648}\ units$

step 3

Find the area of the square BCDE

The area of the square is

$A=(\sqrt{648})^{2}=648\ units^{2}$

step 4

Find the area of the smaller circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=(\sqrt{648})/2\ units$

substitute in the formula

$A=\pi ((\sqrt{648})/2)^{2}=162\pi\ units^{2}$

step 5

Find the area of the shaded region

$324\pi\ units^{2}-648\ units^{2}+162\pi\ units^{2}=(486\pi-648)\ units^{2}$

7 0

3 years ago

Libby earns $10 each hour for babysitting. Let m = the money she earns, and t = the time in hours she is babysitting. What equat

elena55 [62]

Answer:

$10t=m

Step-by-step explanation:

If for each hour is $10.

She would earn the number of hours times $10.

Example: She did babysitting for 4 hours this weekend. The equation is $10(4)=m or $10 x 4 = m. m=40

8 0

3 years ago

Kiran said that this diagram can show the solution to 16÷8=? or 16÷2=?, depending on how we think about the equations and the “?

nignag [31]

Answer:

16÷2

Step-by-step explanation:

It would be 16 divided by 2. This is because in the diagram they are splitting 16 by 2. Splitting 16 by 2 gets you two 8's.

8 0

3 years ago

Can someone help me understand this question?

JulijaS [17]

Hey there!

For Part A, because the amount earned on Sunday isn't specified, we can call this additional income x. Because we're writing an expression, we don't need an equal sign. The expression will be (x + 14).

For Part B, "2 less than" will mean "– 2" and "twice than" will mean the amount of dogs that Alicia walked times 2. We can call the amount that Alicia walked y to avoid confusion with the last expression (though you could use whatever variable here) and your expression will be (2y – 2).

Hope this helped you out! :-)

3 0

3 years ago

Kim purchased 6 small containers of potato salad and Seth purchased 2 extra large containers of potato salad. What is the differ

icang [17]

I am assuming that the attached is the complete question and we need to get the information from the table.

From the table we know the below fact:

$1 \; small \; container \; of \; potato \; salad \; Weighs \; \frac{2}{8} \; pounds\\\\1 \; extra \; large \; container \; of \; potato \; salad \; Weighs \; \frac{9}{8} \; pounds$

$Weight \; of \; 6 \; small \; container = 6 \times \frac{2}{8} = \frac{12}{8} \; pounds\\\\Weight \; of \; 2 \; Extra \; large \; container = 2 \times \frac{9}{8} \; = \; \frac{18}{8} \; pounds$

Conclusion:

The difference in weights, in pounds of Kim’s and Seth’s purchases is given below:

$\frac{18}{8} - \frac{12}{8} = \frac{18-12}{8} = \frac{6}{8} \\\\Simplifying \; the \; fraction \; dividing \; by \; 2 \; on \; both \; numerator \; and \; denominator\\\\ \frac{6 \div 2}{8 \div 2} = \frac{3}{4}$

Final answer : 0.75 pounds

6 0

4 years ago

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