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konstantin123 [22]
3 years ago
6

Please help Will mark the Brainlest ASAP

Mathematics
1 answer:
Natalija [7]3 years ago
3 0

Problem 1

Part (a)

V1 = volume of sink = (4000/3)*pi = (4000pi)/3

V2 = volume of cup A

V2 = volume of cylinder with diameter 4 in, height 8 in

V2 = pi*r^2*h

V2 = pi*2^2*8 ... radius r = 2 is half the diameter d = 4

V2 = 32pi

x = number of cups of water needed to empty sink

x*V2 = V1

x = V1/V2

x = V1 divided by V2

x = (4000pi/3) divided by (32pi)

x = 41.667 approximately

Round up to the nearest whole number to get 42. It will take 42 scoops to empty the sink if you use cup A. The last scoop (the 42nd scoop) isn't a full cup, but it is needed or else the sink will still be full. Put another way, 41 scoops is not enough.

<h3>Answer: 42 cups</h3>

----------------

Part (b)

V3 = volume of cup B

V3 = volume of cylinder with diameter 8 in, height 8 in

V3 = pi*r^2*h

V3 = pi*4^2*8 ... radius r = 4 is half the diameter d = 8

V3 = 128pi

y = number of cups of water needed to empty sink if you use cup B

y*V3 = V1

y = V1/V3

y = V1 divided by V3

y = (4000pi/3) divided by (128pi)

y = 10.4167 approximately

Round up to the nearest whole number to get 11

You need 11 scoops of cup B to empty the sink. Ten cups won't be enough.

<h3>Answer: 11 cups</h3>

==================================================

Problem 2

Part (a)

V1 = volume of sink = (4000/3)*pi = (4000pi)/3

V2 = volume of cup A

V2 = volume of cone with diameter 4, height 8

V2 = (1/3)*pi*r^2*h

V2 = (1/3)*pi*4^2*8

V2 = (32/3)*pi ..... note how we multiply problem 1's V2 value by 1/3

V2 = 32pi/3

x = number of cups of water needed to empty sink

x*V2 = V1

x = V1/V2

x = V1 divided by V2

x = (4000pi/3) divided by (32pi/3)

x = 125

<h3>Answer: 125 cups</h3>

---------------

Part (b)

V3 = volume of cup B

V3 = volume of cone with diameter 8 in, height 8 in

V3 = (1/3)*pi*r^2*h

V3 = (1/3)*pi*4^2*8 ... radius r = 4 is half the diameter d = 8

V3 = (128/3)pi ..... this is 1/3 of the V3 value in problem 1 above

V3 = 128pi/3

y = number of cups of water needed to empty sink if you use cup B

y*V3 = V1

y = V1/V3

y = V1 divided by V3

y = (4000pi/3) divided by (128pi/3)

y = 31.25

Round up to the nearest whole number to get 32. Using 31 cups won't be enough.

<h3>Answer: 32 cups</h3>

==================================================

Problem 3

A = volume of cone at the bottom

A = (1/3)*pi*r^2*h

A = (1/3)*pi*8^2*12

A = (1/3)*pi*768

A = (1/3)*768*pi

A = 256pi

B = volume of hemisphere on top

B = half of the volume of a sphere

B = (1/2)*(volume of sphere)

B = (1/2)*( (4/3)*pi*r^3 )

B = (2/3)*pi*r^3

B = (2/3)*pi*8^3

B = (2/3)*pi*512

B = (2/3)*512*pi

B = (1024/3)*pi

B = 1024pi/3

C = volume of entire 3D solid

C = A+B

C = 256pi + 1024pi/3

C = 256pi*(3/3) + 1024pi/3

C = 768pi/3 + 1024pi/3

C = (768pi+1024pi)/3

C = 1792pi/3 ... is the exact total volume

C = 1792*3.14/3

C = 1875.62666666667 ... is the approximate total volume

C = 1875.6

<h3>Answer: 1875.6 cubic inches</h3>
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3 years ago
A surveyor holds a laser range finder 3 feet above the ground and determines that the range finder is 92 feet from a building an
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8 0
3 years ago
How do I do this?? Help!
Shkiper50 [21]

Hi there!

In order to use the elimination method, you have to create one variable that has the same coefficient. This is to be able to eliminate one variable and have a one variable equation (which you can then solve).

In your case, we'll have the "x" have the same coefficient by multiplying the top equation by 4 and the bottom equation by 2 :

4( -2x + 3y = -4) → -8x + 12y = -16

2( 4x - 2y = 16) → 8x - 4y = 32


Now that both of your equation have a variable with the same coefficient, you need to choose rather you need to add or subtract the equations in order to get rid of the variable (in this case we want to get rid of the "x").

In your case, you want to add both equation together which will give you :

8y = 16


Now that you only have one variable, all you need to do now is solve the equation for "y" :

8y = 16

Divide each side of the equation by 8

y = 2 → Your answer


There you go! I really hope this helped, if there's anything just let me know! :)


7 0
3 years ago
Read 2 more answers
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