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3 years ago

14

Jeff and his friends win a prize.

1 answer:

Anit [1.1K]3 years ago

8 0

Answer:

Prize, P = $352

Step-by-step explanation:

Let Jeff's share be J.
Let the value of the prize be P.

<u>Given the following data;</u>

J = $160
J = 5P/11

To find the value of the prize;

$\frac {5}{11} * P = 160$

$\frac {5P}{11} = 160$

Cross-multiplying, we have;

$5P = 160 * 11$

$5P = 1760$

$P = \frac {1760}{5}$

<em>Prize, P = $352</em>

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The general solution of 2 y ln(x)y' = (y^2 + 4)/x is

Sav [38]

Replace $y'$ with $\dfrac{\mathrm dy}{\mathrm dx}$ to see that this ODE is separable:

$2y\ln x\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{y^2+4}x\implies\dfrac{2y}{y^2+4}\,\mathrm dy=\dfrac{\mathrm dx}{x\ln x}$

Integrate both sides; on the left, set $u=y^2+4$ so that $\mathrm du=2y\,\mathrm dy$ ; on the right, set $v=\ln x$ so that $\mathrm dv=\dfrac{\mathrm dx}x$ . Then

$\displaystyle\int\frac{2y}{y^2+4}\,\mathrm dy=\int\dfrac{\mathrm dx}{x\ln x}\iff\int\frac{\mathrm du}u=\int\dfrac{\mathrm dv}v$

$\implies\ln|u|=\ln|v|+C$

$\implies\ln(y^2+4)=\ln|\ln x|+C$

$\implies y^2+4=e^{\ln|\ln x|+C}$

$\implies y^2=C|\ln x|-4$

$\implies y=\pm\sqrt{C|\ln x|-4}$

4 0

3 years ago

A stick 43 inches long is broken into two pieces, so that one piece is twice as long as the other. How long are the two pieces?

allsm [11]

Answer:

One piece is $\frac{43}{3}$ inches and another piece is $\frac{86}{3}$ inches

Step-by-step explanation:

Let smaller piece length be $s$

Let larger piece length be $l$

Since total of two pieces is 43, we can write:

$s+l=43$

Also, one piece is twice as long as the other (so longer piece is definitely twice as the short piece), we can write:

$l=2s$

<em>Substituting equation 2 into equation one, we can solve for s:</em>

$s+l=43\\s+(2s)=43\\3s=43\\s=\frac{43}{3}$

<em>Thus longer piece is:</em>

$l=2s=2(\frac{43}{3})=\frac{86}{3}$

3 0

4 years ago

Tell me how to do this please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1

alukav5142 [94]

Answer:

perimeter = 82 inches

Step-by-step explanation:

To find the perimeter, add all of the side lengths together

7 0

3 years ago

I NEED AN ANSWER PLEASE :(((

Alekssandra [29.7K]

Answer:

80 lemons

Step-by-step explanation:

Let x represent the amount of lemons that were on the tree.

We can use this to set up an equation:

$40\%x=32$

Note that percentages can also be written as that number over 100.

$\frac{40}{100}x=32$

Simplify the fraction.

$\frac{2}{5}x=32$

Multiply both sides by 5

$2x=160$

Divide both sides by 2

$x=80$

There were 80 lemons on the tree before he picked the lemons.

6 0

3 years ago

the perez family has a rectangle fish tank. How much water will the tank hold if its length is 3 feet, its width is 2 feet, and

myrzilka [38]

V = 3 x 2 x 3 = 18

answer

B) 18 cubic feet

7 0

3 years ago