Mathematics, 18.03.2021 01:50 EllaLovesAnime

Rich is comparing the cost of maintaining his car with the depreciation value of the car. The value starts at $20,000 and decreases by 15% each year.
The maintanance cost is $500 the first year and increases by 28% per year.
When will the maintenance cost and the value be the same.
Please explain step by step

Answers: 2

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Answer from: MrKrinkle77

The maintance cost and the value will be the same in 9 years.

Step-by-step explanation:

Exponential function:

An exponential function has the following format:

y(t) = y(0)(1 + r)^t

In which r is the rate of change.

The value starts at $20,000 and decreases by 15% each year.

This means that V(0) = 20000, r = -0.15

V(t) = V(0)(1 + r)^t

V(t) = 20000(1 - 0.15)^t

V(t) = 20000(0.85)^t

The maintance cost is $500 the first year and increases by 28% per year.

This means that M(0) = 500, r = 0.28 . So

M(t) = M(0)(1 + r)^t

M(t) = 500(1 + 0.28)^t

M(t) = 500(1.28)^t

When will the maintenance cost and the value be the same.

This is t for which:

V(t) = M(t)

20000(0.85)^t = 500(1.28)^t

$\frac{(1.28)^t}{(0.85)^t} = \frac{20000}{500}$

$(\frac{1.28}{0.85})^t = 40$

$\log{(\frac{1.28}{0.85})^t} = \log{40}$

$t\log{(\frac{1.28}{0.85})} = \log{40}$

$t = \frac{\log{40}}{\log{(\frac{1.28}{0.85})}}$

t = 9

The maintance cost and the value will be the same in 9 years.

Answer from: Quest

Answer: 10pi

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.

Find the length of ac express your answer in terms of pi

Answer from: Quest

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

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