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Ksivusya [100]
3 years ago
7

to design the interior surface of a huge stainless-steel tank, you revolve the curve y=x^2 on the interval 0x4 about the y-axis.

the container, with dimensions in meter, is to be filled with sea water, which weighs 10,000 N/m3 . how much work will it take to empty the tank by pumping the water to the tank's top
Mathematics
1 answer:
Oksana_A [137]3 years ago
7 0

Answer:

W = 21.44*10⁶J

Step-by-step explanation:

Given

y = x²    (0 < x < 4)

γ = 10000 N/m³

W = ?

If we apply

y = 4² = 16 = h

y =  x²  ⇒  x = √y

then

V = π*(√y)²*dy = π*y*dy

W = (γ*V) *(16-y) = γ*π*y*dy*(16-y)

⇒  W = γ*π*∫y*(16-y)dy = γ*π*(8y²-(y³/3))

finally we obtain  (0 < y < 16)

W = γ*π*(8y²-(y³/3)) = 10000*π*(8*16²-(16³/3)) = 21.44*10⁶J

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Step-by-step explanation:

3 0
3 years ago
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Use the quadratic formula to solve the equation. If necessary, round answers to the nearest hundredth. 5x2 + 16x – 84 = 0
Anni [7]
Hello!!

x + 6 = 0 or 5x - 14 = 0

x = -6 or 5x - 14 = 0

x = -6 or 5x = 14

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3 years ago
How to do equations with a variable on both sides x+3= -x - 5
ss7ja [257]
Explanation: 
When we have variables on both sides we look for the coefficient that is lower than the two and reverse the sign. 

Example: 

1x+ 4 = 2x+3 

We reverse 1x sign because it is lower so we will be subtracting

2x-1x = 1x

1x+3=4 

We would then solve for x.

<span> 

Let's begin to solve! </span>
Step 1:

You would look for the coefficient or variable that is less and reverse the sign. 

In this question the lower number is -x and so we would reverse the sign to add. 

x+x= 2

Step 2: 
We now have

2x+3 = -5

Step 3: 
We will subtract 3 to -5 to find X

-3+-5= -8

Step 4:
2x = -8

Divide both sides by two fo find x 

Our answer:

\boxed{x = -4}

-


Summary:

We first looked for the lower coefficient (in this case variable). We then flipped the sign and solved for x. 




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