Jamal placed two orders with an internet clothing store. The first order was 13 ties (t) and 4 pairs of suspenders (s), and totaled $487. The second order was for 6 ties and 2 pairs of suspenders, and totaled $232. The bill does not list per-term price, but all ties have the same price and all suspenders have the same price

t = $23

s= $47

Step-by-step explanation:

First order =

13t + 4s = 487

Second order

6t + 2s = 232

13t + 4s = 487 (1)

6t + 2s = 232 (2)

Multiply (2) by 2

12t + 4s = 464 (2b)

13t + 4s = 487

12t + 4s = 464

Subtract

12t - 10t = 487 - 464

t = $23

Substitute t = 23

13t + 4s = 487

13(23) + 4s = 487

299 + 4s = 487

4s = 487 -299

4s = 188

s = 188 / 4

= 47

s= $47

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.