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1 answer:
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Answer:6.3 in.
Step-by-step explanation:
Given
Radius of sphere
When ball is immersed in beaker, it causes the water to flowout of beaker which is collected in the conical vessel
Such that amount of water equivalent to sphere volume is collected in it.
volume of ball
Now volume of water collected is in shape of cone then volume of cone
and
Answer:
1. n = 40
2.
Step-by-step explanation:
The ordinary annuity formula can be written as ...
PV = PMT(1 -(1+r)^-n)/r
where PMT is the payment per period, r is the interest rate per period, and n is the number of periods.
This formula can be solved explicitly for n, but not for r. Iterative or other methods can be used to find r.
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1. Filling in the given information, we have ...
15000 = 650(1 -1.03^-n)/0.03
450/650 = 1 - 1.03^-n . . . . . divide by the coefficient of the stuff in parens
1.03^-n = 4/13 . . . . . . . . . . . solve for the exponential term
-n·log(1.03) = log(4/13) . . . . take logarithms
n = log(13/4)/log(1.03) ≈ 39.87 . . . . . solve for n
n ≈ 40
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2. We can rewrite the annuity formula to make it be a function of i that is zero at the desired value of i.
f(i) = PV -PMT(1 -(1+i)^-n)/i
If we want i as a percentage, then we can replace i with i/100 and fill in the given values to get ...
f(i) = 9000 -500(1 -(1 +i/100)^-35)/(i/100)
f(i) = 1000(9 -50(1 -(1 +i/100)^-35)/i) . . . . multiply the fraction by 100/100
Since we're seeking a value of f(r) that is zero, we can eliminate the factor of 1000.
f(i) = 9 -50(1 - (1+i/100)^-35)/i
The attached graph shows the solution to f(i)=0 is near i=4.27%. As a decimal rounded to 3 decimal places, this is ...
i ≈ 0.043
