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3 years ago

60 POINTS!! Please help me out with these 2 questions

Mathematics

1 answer:

arsen [322]3 years ago

4 0

Answer:

1. money in the account = 400 + 6t where t is the number of years

2. Total cost = principal ( 1+ rate* time)

Step-by-step explanation:

1. The formula for simple interest is I = PRT where

P = principal

R is the interest rate

T is the time in years

I = 400 * .015 * t

I = 6t where t is the number of year

The amount of money in the account is the principal plus the interest

money in the account = 400 + 6t

Since we were not given the time period, I will leave it here.

2. Since we are paying simple interest

The formula for simple interest is I = PRT where

P = principal

R is the interest rate

T is the time in years

We can figure out what the total interest is

Add it to the amount of the principal

The total amount you will pay on the loan is

Total cost = Principal + interest

= principal + principal * rate * time

= principal ( 1+ rate* time)

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2. At 1 pm, you leave Ellensburg at a constant speed of 75 miles per hour. At 2:30 pm, your

MA_775_DIABLO [31]

Here, we are required to determine how many hours your friend will drive in order to catch you.

(a) Your friend will have to drive 7 and a half hours inorder to catch you.

(b) You both will be 675 miles away from Ellensburg at that time.

If you leave at 1 pm; At 2:30pm;

That is; 1 and a half hours after leaving; you must have covered a distance, d = 75 × 1.5
d = 112.5miles.

Therefore, your position; S after 2:30pm is given by;

S(a) = 75t + 112.5 miles from Ellensburg.

For your friend; travelling at 90miles/hr;

His position is given as; S(b) = 90 × t

(a) For your friend to catch you, you both must be in the same position;

i.e S(a) = S(b)

75t + 112.5 = 90t

90t -75t = 112.5

t = 112.5/15

t = 7.5hours

(b) To determine how far you both are from Ellensburg; we can either evaluate:

S(b) = 90t or S(a) = 75t + 112.5

Therefore, By evaluating S(b) = 90t.

S(b) = 90 × 7.5

S(b) = 675miles from Ellensburg.

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3(p+5)-3(p+2) expand and simplify

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This equation is separable,

$\dfrac{dA}{dt} = -6A \implies \dfrac{dA}A = -6\,dt$

Integrate both sides and solve for $A$ :

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$\ln|A| = -6t + C$

$e^{\ln|A|} + e^{-6t+C}$

$\implies A(t) = Ce^{-6t}$

Solve for $C$ using the initial value.

$A(0) = 6 \implies 6 = Ce^0 \implies C=6$

Then the particular solution is

$\boxed{A(t) = 6e^{-6t}}$

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3x+8=5x-20 what is x ?

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