WILL GIVE BRAINLIEST, THANKS, AND 5STARS!<br> PLEASE HELP ME ANSWER THIS QUESTION

A giant scoop, operated by a crane, is in the shape of a hemisphere of radius 21 inches. The scoop is used to transfer molten st

eduard

Answer:

31.5 in

Step-by-step explanation:

Volume of a hemisphere = (2/3) $\pi$ r³
(where r is the radius)
Volume of a cylinder = $\pi$ r²h
(where r is the radius and h is the height)
radius r = (1/2) diameter

First, find the volume of the scoop using the volume of a hemisphere formula with r = 21:

Volume = (2/3) $\pi$ x 21³ = 6174 $\pi$ in³

Now equate the found volume of the scoop to the equation of the volume of a cylinder with r = 14, and solve for h:

$\pi$ 14²h = 6174 $\pi$

196 $\pi$ h = 6174 $\pi$

Divide both sides by $\pi$ : 196h = 6174

Divide both sides by 196: h = 31.5

Therefore, the height of the molten steel in the storage tank is 31.5 in

3 0

2 years ago

Solve the following equations: (a) x^11=13 mod 35 (b) x^5=3 mod 64

tino4ka555 [31]

a.

$x^{11}=13\pmod{35}\implies\begin{cases}x^{11}\equiv13\equiv3\pmod5\\x^{11}\equiv13\equiv6\pmod7\end{cases}$

By Fermat's little theorem, we have

$x^{11}\equiv (x^5)^2x\equiv x^3\equiv3\pmod5$

$x^{11}\equiv x^7x^4\equiv x^5\equiv6\pmod 7$

5 and 7 are both prime, so $\varphi(5)=4$ and $\varphi(7)=6$ . By Euler's theorem, we get

$x^4\equiv1\pmod5\implies x\equiv3^{-1}\equiv2\pmod5$

$x^6\equiv1\pmod7\impleis x\equiv6^{-1}\equiv6\pmod7$

Now we can use the Chinese remainder theorem to solve for $x$ . Start with

$x=2\cdot7+5\cdot6$

Taken mod 5, the second term vanishes and $14\equiv4\pmod5$ . Multiply by the inverse of 4 mod 5 (4), then by 2.

$x=2\cdot7\cdot4\cdot2+5\cdot6$

Taken mod 7, the first term vanishes and $30\equiv2\pmod7$ . Multiply by the inverse of 2 mod 7 (4), then by 6.

$x=2\cdot7\cdot4\cdot2+5\cdot6\cdot4\cdot6$

$\implies x\equiv832\pmod{5\cdot7}\implies\boxed{x\equiv27\pmod{35}}$

b.

$x^5\equiv3\pmod{64}$

We have $\varphi(64)=32$ , so by Euler's theorem,

$x^{32}\equiv1\pmod{64}$

Now, raising both sides of the original congruence to the power of 6 gives

$x^{30}\equiv3^6\equiv729\equiv25\pmod{64}$

Then multiplying both sides by $x^2$ gives

$x^{32}\equiv25x^2\equiv1\pmod{64}$

so that $x^2$ is the inverse of 25 mod 64. To find this inverse, solve for $y$ in $25y\equiv1\pmod{64}$ . Using the Euclidean algorithm, we have

64 = 2*25 + 14

25 = 1*14 + 11

14 = 1*11 + 3

11 = 3*3 + 2

3 = 1*2 + 1

=> 1 = 9*64 - 23*25

so that $(-23)\cdot25\equiv1\pmod{64}\implies y=25^{-1}\equiv-23\equiv41\pmod{64}$ .

So we know

$25x^2\equiv1\pmod{64}\implies x^2\equiv41\pmod{64}$

Squaring both sides of this gives

$x^4\equiv1681\equiv17\pmod{64}$

and multiplying both sides by $x$ tells us

$x^5\equiv17x\equiv3\pmod{64}$

Use the Euclidean algorithm to solve for $x$ .

64 = 3*17 + 13

17 = 1*13 + 4

13 = 3*4 + 1

=> 1 = 4*64 - 15*17

so that $(-15)\cdot17\equiv1\pmod{64}\implies17^{-1}\equiv-15\equiv49\pmod{64}$ , and so $x\equiv147\pmod{64}\implies\boxed{x\equiv19\pmod{64}}$

5 0

3 years ago

Today, both the soccer team and the basket ball team had games (starting on Monday). The soccer team plays every 3 days and the

yarga [219]

I think eight because if you add those days together they will play again in eight days so that they play on the same day.

Sorry if I got it wrong I tried and that's what counts, right?

3 0

3 years ago

Solve the equation 4n = 9

aliina [53]

Answer:

n = 9/4 = 2.250

Step-by-step explanation:

Rearrange: 4*n-(9)=0

Solve: 4n-9 = 0

4n = 9

n = 9/4 = 2.250

answer: n = 9/4 = 2.250

6 0

3 years ago

Read 2 more answers

3 + (5 + 7) = (3 + 5) + 7

Ivahew [28]

Answer:

true

Step-by-step explanation:

3 + (5 + 7) = (3 + 5) + 7

3 + (12) = (8) + 7

15 = 15

4 0

3 years ago

WILL GIVE BRAINLIEST, THANKS, AND 5STARS! PLEASE HELP ME ANSWER THIS QUESTION