8 : sand pouring from a chute forms a conical pile whose height is always equal to the diameter. if the height increases at a co
1 answer:
When the pile is 10 feet high, the rate at which sand is released from the chute is 125 ft^3/min
Let x denote the cone's height.
We've been told that when sand is poured down a chute, it always creates a conical pile whose height is equal to its diameter.
Since radius is known to be equal to half of diameter, the radius of a cone would be x/2.
To resolve the issue at hand, we shall use the volume of cone formula.
v=1/3
v= 1/3(x/2)^2(x/2)
v= 1/3(x^2/4)(x/2)
v= x^3/12
When we translate the height and radius values into terms of x, we obtain:
dv/dt =1/3 (3x^2)dx/dt
By solving the equation,
dv/dt =125
Consequently, 125ft^3/min of sand per minute are being released from the chute.
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Answer: Can I get brainliest and 5 stars? thank you.
a)
b)
c)
Step-by-step explanation:
a) I can't put line above it, but the line expresses that 6 and 5 and repeating infinitely. Let X equal the decimal number.
First multiply by 1 followed by as many zeros as repeating numbers there are. In this case since 6 and 5 are the repeating numbers, we have to add 2 zeros which is basically multiplying by 100
0.65*100=65.65 (another 65 remains on the right because they're infinite.)
Now substract from the original number. Now we have a new equation that says: .
Substract equation 1 from equation 2.
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Solve just like any other equation. Divide by 99 to isolate x.
This is the fraction.
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b) This one is a little bit different because we only have 1 repeating number.
In this case we have to multiply by 10.
Equation 1:
Equation 2:
Substract.
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divide by 9 to isolate x
To get rid of the decimal in the numerator, multiply both numerator and denominator by 10 so that we don't change the fraction.
and this is your fraction.
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c) 0.65 this one has no repeating number. It's a finite decimal number.
I assume you already know that; , so, we can do the same here to have a fraction.
Now, in order to get rid of the decimal, multiply by 1 followed by as many zeros as decimal numbers are. In this case 2 zeros because there are 2 decimal numbers, so it's 100. Remember that if you do it in the numerator, you have to do it in the denominator as well to not change the fraction.
Simplify if possible.
This is your fraction.