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3 years ago

15

Marge puts $800 in a bank account that earns 3% annual interest. If she leaves the money in the bank but does not add to it, how

much will she have at the end of the first year?

1 answer:

yanalaym [24]3 years ago

7 0

Multiply 800$ by telephone annual interest which is, 0.03% and you get 24$. Add 24 to the 800 and 824 is your answer.

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1. Consider an athlete running a 40-m dash. The position of the athlete is given by , where d is the position in meters and t is

sasho [114]

There is some information missing in the question, since we need to know what the position function is. The whole problem should look like this:

Consider an athlete running a 40-m dash. The position of the athlete is given by $d(t)=\frac{t^{2}}{6}+4t$ where d is the position in meters and t is the time elapsed, measured in seconds.

Compute the average velocity of the runner over the intervals:

(a) [1.95, 2.05]

(b) [1.995, 2.005]

(c) [1.9995, 2.0005]

(d) [2, 2.00001]

Answer

(a) 6.00041667m/s

(b) 6.00000417 m/s

(c) 6.00000004 m/s

(d) 6.00001 m/s

The instantaneous velocity of the athlete at t=2s is 6m/s

Step by step Explanation:

In order to find the average velocity on the given intervals, we will need to use the averate velocity formula:

$V_{average}=\frac{d(t_{2})-d(t_{1})}{t_{2}-t_{1}}$

so let's take the first interval:

(a) [1.95, 2.05]

$V_{average}=\frac{d(2.05)-d(1.95)}{2.05-1.95}$

we get that:

$d(1.95)=\frac{(1.95)^{3}}{6}+4(1.95)=9.0358125$

$d(2.05)=\frac{(2.05)^{3}}{6}+4(2.05)=9.635854167$

so:

$V_{average}=\frac{9.6358854167-9.0358125}{2.05-1.95}=6.00041667m/s$

(b) [1.995, 2.005]

$V_{average}=\frac{d(2.005)-d(1.995)}{2.005-1.995}$

we get that:

$d(1.995)=\frac{(1.995)^{3}}{6}+4(1.995)=9.30335831$

$d(2.005)=\frac{(2.005)^{3}}{6}+4(2.005)=9.363335835$

so:

$V_{average}=\frac{9.363335835-9.30335831}{2.005-1.995}=6.00000417m/s$

(c) [1.9995, 2.0005]

$V_{average}=\frac{d(2.0005)-d(1.9995)}{2.0005-1.9995}$

we get that:

$d(1.9995)=\frac{(1.9995)^{3}}{6}+4(1.9995)=9.33033358$

$d(2.0005)=\frac{(2.0005)^{3}}{6}+4(2.0005)=9.33633358$

so:

$V_{average}=\frac{9.33633358-9.33033358}{2.0005-1.9995}=6.00000004m/s$

(d) [2, 2.00001]

$V_{average}=\frac{d(2.00001)-d(2)}{2.00001-2}$

we get that:

$d(2)=\frac{(2)^{3}}{6}+4(2)=9.33333333$

$d(2.00001)=\frac{(2.00001)^{3}}{6}+4(2.00001)=9.33339333$

so:

$V_{average}=\frac{9.33339333-9.33333333}{2.00001-2}=6.00001m/s$

Since the closer the interval is to 2 the more it approaches to 6m/s, then the instantaneous velocity of the athlete at t=2s is 6m/s

8 0

3 years ago

You are selling tickets for the school play "13". Student tickets cost $4 and general admission tickets cost $6. You sell 525 ti

Scilla [17]

Answer:

Step-by-step explanation:

s= student ticket

g= general admisson ticket

4s+6g=2876

s+g=525

4s+6g=2876

-4s-4g=-2100

add both equations

2g=776

g=388

s+g=525

s+388=525

s=137

6 0

3 years ago

Is it true that (x + 3)2 = x2 + 9? Justify your answer.

Katena32 [7]

Answer:

No

Step-by-step explanation:

3 times 2 is 6 and 2 times x is 2x so therefore 2x+6 does not equal 2x+9. Hope this helps!

3 0

3 years ago

Read 2 more answers

John had some money in his savings account. He donated 1/6 of his money to charity. If he donated $75 dollars to charity, how mu

kirill115 [55]

He had $450 dollars in his savings account. If 1/6 is equal to 75, you will multiply 75 by 6 to get the full amount, which is $450. I hope this helps!

7 0

4 years ago

Radius of a circle with an area of 907.9 centimeters

Roman55 [17]

$\bf \textit{area of a circle}\\\\
A=\pi r^2~~
\begin{cases}
r=radius\\
-----\\
A=907.9
\end{cases}\implies 907.9=\pi r^2
\\\\\\
\cfrac{907.9}{\pi }=r^2\implies \sqrt{\cfrac{907.9}{\pi }}=r$

3 0

3 years ago