You have just purchased a car and, to fund the purchase, you borrowed $32,000. If your monthly payments are $615.13 for the next 5 years, what is the APR of the loan?

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  5.76%

Step-by-step explanation:

There is no formula for APR. It must be found using an iterative calculation, as from a spreadsheet or financial calculator.

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The value can also be found graphically from the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where A is the monthly payment, P is the principal amount of the loan, r is the annual rate, and t is the number of years.

This can be put into a form that can be solved easily by a graphing calculator. We want it to find the x-intercept of f(x) = 0, so we define ...

  f(x) = A(P, x/100, t) -615.13

where A(P, r, t) is defined above, and we let r = x/100 so x is the APR. The graph shows us the APR is 5.763%.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

the awnser is visionary