How many times larger is 3 x 10 to the negative fifth power than 6 x 10 to the negative twelfth power?

35 POINTS AVAILABLE

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

Refer to the isosceles trapezoid shown. Find m(BC)

patriot [66]

Answer:

answer is 9cm

opposite side of trapezium are equal

hopes this helps u

5 0

2 years ago

Plz plz answer this question NO LINKS :)

masya89 [10]

Answer:

did you forget a picture?

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Plane traveled 1120 miles each way to Munich and back. The trip there was with the wind. It took 10 hours. The trip back was int

kotegsom [21]

Answer:

84 mph and 28 mph

Step-by-step explanation:

Let the speed of plane is p and speed of the wind is w.

Then we have:

10*(p + w) = 1120 ⇒ p + w = 112
20*(p - w) = 1120 ⇒ p - w = 56

Sum the two equations and solve for p:

p + w + p - w = 112 + 56
2p = 168
p = 84

Find w:

84 + w = 112
w = 112 - 84
w = 28

6 0

2 years ago

Will give brainliest to correct answer !

jarptica [38.1K]

lmk if you're looking for point slope form but it's y = 2/5x - 3

7 0

2 years ago