Geometry question plz help

KengaRu [80]

Answer with Step-by-step explanation:

The given differential euation is

$\frac{dy}{dx}=(y-5)(y+5)\\\\\frac{dy}{(y-5)(y+5)}=dx\\\\(\frac{A}{y-5}+\frac{B}{y+5})dy=dx\\\\\frac{1}{100}\cdot (\frac{10}{y-5}-\frac{10}{y+5})dy=dx\\\\\frac{1}{100}\cdot \int (\frac{10}{y-5}-\frac{10}{y+5})dy=\int dx\\\\10[ln(y-5)-ln(y+5)]=100x+10c\\\\ln(\frac{y-5}{y+5})=10x+c\\\\\frac{y-5}{y+5}=ke^{10x}$

where

'k' is constant of integration whose value is obtained by the given condition that y(2)=0\\

$\frac{0-5}{0+5}=ke^{20}\\\\k=\frac{-1}{e^{20}}\\\\\therefore k=-e^{-20}$

Thus the solution of the differential becomes

$\frac{y-5}{y+5}=e^{10x-20}$

5 0

3 years ago

Read 2 more answers

A piece of pipe is 303/4 inches long. If five pieces, each 41/3 inches long, are cut from the pipe, how many inches of pipe rema

galina1969 [7]

So, what is the total lenght of the pieces that wer cut off?

we multiply the lenght by the number:

4 $\frac{1}{3}$ *5=20+ $\frac{5}{3}$ =21 $\frac{2}{3}$

and we subtract this from the original pipe, that is

30 $\frac{3}{4}$ -21 $\frac{2}{3}$

we need to bring the two fractions to the same denominator (by multiplying the fraction art in the first by 3 and 4 the second):

30 $\frac{9}{12}$ -21 $\frac{8}{12}$ =9 $\frac{1}{12}$

so the correct answer is D!

3 0

2 years ago

(PLEASE ANSWER ASAP) Which number is between 1/6 and 0.25?

serg [7]

If you change both to a fraction you would see that you have 1/6 and 1/4 (.25 as a fraction). So 1/5 would be in between them.

You could also change both as a decimal. 1/6 =.166666 and .25 so any number in between them would be correct such as .2 which is the same as 1/5.

8 0

3 years ago

PLEASE HELP! 15 POINTS! whats the value of b?

Zarrin [17]

Answer:

66.6

Step-by-step explanation:

180-113.4=66.6

5 0

2 years ago

Read 2 more answers

3. You want to have $4000 in your savings account after 2 years. Find the amount you should deposit for each of the situations d

pychu [463]

Answer:

Part A)

About $3767.34.

Part B)

About $3692.47.

Step-by-step explanation:

Part A)

Recall that compound interest is given by the formula:
$\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}$

Where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years.

To obtain $4000 after two years, let A = 4000 and t = 2.

Because the account pays 3% interest compounded monthly, r = 0.03 and n = 12.

Substitute and solve for P:

$\displaystyle \begin{aligned} (4000) & = P\left(1+\frac{(0.03)}{(12)}\right)^{(12)(2)} \\ \\ P & = \frac{4000}{\left(1+\dfrac{(0.03)}{(12)}\right)^{(12)(2)}} \\ \\ & \approx \$3767.34\end{aligned}$

In concluion, about $3767.34 should be deposited.

Part B)

Recall the formula for continuous compound:

$\displaystyle A = Pe^{rt}$

Where e is Euler's number.

Hence, let A = 4000, r = 0.04 and t = 2. Substitute and solve for P:

$\displaystyle \begin{aligned}(4000) & = Pe^{(0.04)(2)} \\ \\ P & = \frac{4000}{e^{(0.02)(4)}} \\ \\ & \approx \$3692.47 \end{aligned}$

In conclusion, about $3692.47 should be deposited.

8 0

2 years ago