Taylor has $32000 a part of which he invested at 5% and the remainder at 3%. His annual return on each investment is the same. At what rate would he have to invest all her money to get the same interest?

Taylor have to invest the total money at 3.75%

Step-by-step explanation:

Let the part of money invested at 5% be 'a' and the part of money invested at 3% be (32000-a).

To find (a) :

The annual income for both the 5% and 3% investment is equal.

Interest= (amount x rate of interest x time) /100

Interest for 5% rate on investment

Interest = (a x 5 x 1) /100

Interest for 3% rate on investment

Interest = [(32000-a) x 3 x 1]/100

Both the interests are equal so equate both the equations.

(a x 5 x 1) /100 = [(32000-a) x 3 x 1] /100

5a = (32000-a) 3

5a = 96000-3a

8a = 96000

a = 96000/8

a = 12000

32000-a = 32000-12000

= 20000

The amount invested at 5% is $12000 and invested $20000 at 3%

Interest = (12000 x 5 x 1) /100

= 60000/100

= $600

Interest = (20000 x 3 x 1) /100

= 60000/100

= $600

Total interest = $1200

To find the rate at which the total money is to be invested to get the same annual income.

1200 = (32000 x rate x 1) /100

1200 x 100 = 32000 x rate x 1

120000 = 32000 x rate

120000/32000 = rate

Rate = 3.75%

Taylor have to invest the total money at 3.75% to get the same annual income

if he has no friends he cant give them out to his friends

step-by-step explanation:

no friends = cant give anything out

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.