What rate of interest compounded annually is required to triple an investment in 9 years? The rate of interest required is %.
(Round to two decimal places as needed.)

Answer :

13%

Step-by-step explanation:

Compound interest which is compounded annually calculated using the formula :

A = I( 1 + r/100)^t

Where I = invested amount

r = interest rate ; t = period ; A = final amount

If period = 9years, the rate required to triple the investment equals;

The final amount = 3 * invested amount = 3I

We now have ;

3I = I( 1 + r/100)^9

Divide both sides by I

3 = (1 + r/100)^9

Take the 9th root of both sides

3^(1/9) = (1 + r/100)^(9*1/9)

3^(1/9) = 1 + r/100

r/100 = 3^(1/9) - 1

r/100 = 1.1298309 - 1

r / 100 = 0.1298309

Multiply both sides by 100

r = 12.98309

r = 12.98 = 13%

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

step-by-step explanation:

it will be a cylinder. with a diameter of 8 and 4 single pieces high