The value of a stock share in a new technology company has been increasing at a rate of 8.6% quarterly. the initial price of one share was $102.15. an investor plans to sell once the value of one share reaches $233.10. if t is the number of quarters since the initial price of one share was set, which equation could be used to determine how long it will take the share to reach $233.10, assuming it continues to grow at the same rate? 102.15 = 233.10(0.086)t

The equation is :

Step-by-step explanation:

The given rate of interest = 8.6% or 0.086

The initial price of one share was $102.15. An investor plans to sell once the value of one share reaches $233.10.

No, if 't' is the number of quarters since the initial price of one share was set, then the equation that could be used to determine how long it will take the share to reach $233.10 is :

a negative exponent is translated as follows:

so, we have

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.