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2 years ago

Jimmy invests $7,000 in an account that pays 3% interest compounded semi-annually. What is his balance after 8 years?

Mathematics

1 answer:

Bumek [7]2 years ago

7 0

Answer:

$8882.9

Step-by-step explanation:

A=p(1+(r/n))^nt

Given:P=7000, r=(3÷100%)=0.03 , n=2, t=8

A = 7000(1+(.03/2))^(2×8)

A = 7000 (1+0.015)^16

A = 7000 × 1.015^16

A = $8882.9

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Answer:iiii

Step-by-step explanation:iiiii

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3 years ago

A tank with a capacity of 1600 L is full of a mixture of water and chlorine with a concentration of 0.0125 g of chlorine per lit

Veronika [31]

Answer:

y(t) = 20 [1600^(-5/3)] x (1600-24t)^ (5/3)

Step-by-step explanation:

1) Identify the problem

This is a differential equation problem

On this case the amount of liquid in the tank at time t is 1600−24t. (When the process begin, t=0 ) The reason of this is because the liquid is entering at 16 litres per second and leaving at 40 litres per second.

2) Define notation

y = amount of chlorine in the tank at time t,

Based on this definition, the concentration of chlorine at time t is y/(1600−24t) g/ L.

Since liquid is leaving the tank at 40L/s, the rate at which chlorine is leaving at time t is 40y/(1600−24t) (g/s).

For this we can find the differential equation

dy/dt = - (40 y)/ (1600 -24 t)

The equation above is a separable Differential equation. For this case the initial condition is y(0)=(1600L )(0.0125 gr/L) = 20 gr

3) Solve the differential equation

We can rewrite the differential equation like this:

dy/40y = - (dt)/ (1600-24t)

And integrating on both sides we have:

(1/40) ln |y| = (1/24) ln (|1600-24t|) + C

Multiplying both sides by 40

ln |y| = (40/24) ln (|1600 -24t|) + C

And simplifying

ln |y| = (5/3) ln (|1600 -24t|) + C

Then exponentiating both sides:

e^ [ln |y|]= e^ [(5/3) ln (|1600-24t|) + C]

with e^c = C , we have this:

y(t) = C (1600-24t)^ (5/3)

4) Use the initial condition to find C

Since y(0) = 20 gr

20 = C (1600 -24x0)^ (5/3)

Solving for C we got

C = 20 / [1600^(5/3)] = 20 [1600^(-5/3)]

Finally the amount of chlorine in the tank as a function of time, would be given by this formula:

y(t) = 20 [1600^(-5/3)] x (1600-24t)^ (5/3)

7 0

3 years ago

Which ratio is higher 15:20 or 12:16. for 35 points

Margarita [4]

To find which ratio is higher, we can first convert the ratios into fractions (that makes it easier, at least for me) and then simplify the fractions and see which one is greater.

Since ratios are basically division, 15:20 = $\frac{15}{20}$ , and

12:16 = $\frac{12}{16}$

Now we simplify these fractions. 15 and 20 have a GCF of 5, so taking out the common number gives us the simplified fraction of $\frac{3}{4}$ .

12 and 16 have a GCF of 4, so taking out the common number gives us the simplified fraction of $\frac{3}{4}$ . Since $\frac{3}{4}$ = $\frac{3}{4}$ , these ratios are the same.

8 0

3 years ago

Use the law of sines to find what Angle R is:

stich3 [128]

Answer:

Step-by-step explanation:

So, according to the law of Sines, we have

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