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Yuliya22 [10]
3 years ago
11

The rate of depreciation dv / dt of a machine is inversely proportional to the square of t + 1, where v is the value of the mach

ine t years after it was purchased. the initial value of the machine was $500,000, and its value decreased $200,000 in the first year. estimate its value to the nearest whole number after 6 years.
Mathematics
1 answer:
lukranit [14]3 years ago
6 0
The solution for this problem is:
dV/dt = r/(t + 1)², V(0) = $500000, V(1) = $500000 - $200000 = $300000 
∫dV = r∫ 1/(t + 1)² dt 
V(t) = -r/(t + 1) + C 
500000 = -r/(0 + 1) + C 
400000 = -r/(1 + 1) + C 
C = 300000, r = -100000 
V(t) = 100000/(t + 1) + 300000 
V(6) = 100000/(6+ 1) + 300000 
V(6) = 14285.7143 + 300000

V(6) = $314285.71
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3 years ago
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You deposit $3000 into an account that pays 4.8% interest, compounded monthly. A) What is the value of the account after 5 years
Snezhnost [94]

Answer:

14.4 years (about 14 years 6 months)

Step-by-step explanation:

Given data

Principal= $3000

Rate= 4.8%

A. Time= 5 years

The expression for compound interest is

A=P(1+r)^t

Substitute

A= 3000(1+0.048)^5

A= 3000(1.048)^5

A=3000*1.264

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Hence the balance will be $3792

B. Final Amount A = $6000

The expression to find time is given ast

t= ln(A/P) / r

substitute

t= ln(6000/3000)/0.048

t= ln2/0.048

t= 0.6931/0.048

t=14.43

Hence the time is 14.4 years (about 14 years 6 months)approx

8 0
3 years ago
What is the sum of 62/100
andrey2020 [161]
If you were to add these both you would get 162 

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3 years ago
A scooter travels 30 feet in 2 seconds at a constant speed.
Sever21 [200]

Answer:

The scooter travels 15 feet in 1 second

The scooter travels 45 feet in 3 seconds

The scooter travels 60 feet in 4 seconds

The scooter travels 75 feet in 5 seconds

Step-by-step explanation:

First, let's find the number of feet the scooter travels in 1 second

(30 : 2) ÷ 2 = 15 : 1

Now that we have the unit rate, we can easily find the answers to the other questions.

(15 : 1) x 3 = 45 : 3

(15 : 1) x 4 = 60 : 4

(15 : 1) x 5 = 75 : 5

I Hope That This Helps! :)

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