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2 years ago

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A one year member ship to your local gym costs $539. there is an initial fee of $35. write an equation tou can use to fund out h

ow much you pay per month

1 answer:

stich3 [128]2 years ago

4 0

$539 - $35 = $504

$504 : 12 = $42

Per month you pay $42.

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A quarter is 1/5 of an inch thick and 5 quarters weigh one ounce. Stephanie built a toothpick bridge that could safely hold 3 po

AleksandrR [38]

Answer:

Maximum height of quarter tower = 9.6 inches.

Step-by-step explanation:

The thickness of a quarter = $\frac{1}{5}$ inches

Weight of a quarter = 1 ounce

The maximum weight that could safely hold = 3 pounds.

<u>The conversion factor for ounce to pound is 1 ounce = 0.0625 pound</u>

The number of quarter used in the tower = no of ounces equivalent to 3 pounds.

No of ounces equivalent to 3 pounds = $\frac{3}{0.0625}$

No of ounces equivalent to 3 pounds = 48

So the height of quarter tower = 48 \times $\frac{1}{5}$ inches

= 9.6 inches.

4 0

3 years ago

Solution for dy/dx+xsin 2 y=x^3 cos^2y

vichka [17]

Rearrange the ODE as

$\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y=x^3\cos^2y$
$\sec^2y\dfrac{\mathrm dy}{\mathrm dx}+x\sin2y\sec^2y=x^3$

Take $u=\tan y$ , so that $\dfrac{\mathrm du}{\mathrm dx}=\sec^2y\dfrac{\mathrm dy}{\mathrm dx}$ .

Supposing that $|y|$ , we have $\tan^{-1}u=y$ , from which it follows that

$\sin2y=2\sin y\cos y=2\dfrac u{\sqrt{u^2+1}}\dfrac1{\sqrt{u^2+1}}=\dfrac{2u}{u^2+1}$
$\sec^2y=1+\tan^2y=1+u^2$

So we can write the ODE as

$\dfrac{\mathrm du}{\mathrm dx}+2xu=x^3$

which is linear in $u$ . Multiplying both sides by $e^{x^2}$ , we have

$e^{x^2}\dfrac{\mathrm du}{\mathrm dx}+2xe^{x^2}u=x^3e^{x^2}$
$\dfrac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]=x^3e^{x^2}$

Integrate both sides with respect to $x$ :

$\displaystyle\int\frac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]\,\mathrm dx=\int x^3e^{x^2}\,\mathrm dx$
$e^{x^2}u=\displaystyle\int x^3e^{x^2}\,\mathrm dx$

Substitute $t=x^2$ , so that $\mathrm dt=2x\,\mathrm dx$ . Then

$\displaystyle\int x^3e^{x^2}\,\mathrm dx=\frac12\int 2xx^2e^{x^2}\,\mathrm dx=\frac12\int te^t\,\mathrm dt$

Integrate the right hand side by parts using

$f=t\implies\mathrm df=\mathrm dt$
$\mathrm dg=e^t\,\mathrm dt\implies g=e^t$
$\displaystyle\frac12\int te^t\,\mathrm dt=\frac12\left(te^t-\int e^t\,\mathrm dt\right)$

You should end up with

$e^{x^2}u=\dfrac12e^{x^2}(x^2-1)+C$
$u=\dfrac{x^2-1}2+Ce^{-x^2}$
$\tan y=\dfrac{x^2-1}2+Ce^{-x^2}$

and provided that we restrict $|y|$ , we can write

$y=\tan^{-1}\left(\dfrac{x^2-1}2+Ce^{-x^2}\right)$

5 0

3 years ago

A container can hold quarts of 8 3/5cooking oil. It contains 1 1/3 quarts of cooking oil. How much more cooking oil is needed to

Mamont248 [21]

Answer:

4 14/15

Step-by-step explanation:

8 3/5 - 11/3

8 9/15 - 55/15

8 9/15 - 3 10/15

7 24/15 - 3 10/15

4 14/15

6 0

2 years ago

Please explain me I can’t understand

valina [46]

Step-by-step explanation:

They are asking, like units are in the sum

3 0

3 years ago

Help I don’t know the steps

Korvikt [17]

Answer:

down below

Step-by-step explanation:

straight lines are 180 degrees and you have 2 angles on a line. one of which is 72 and the other is unknown. It is solved for below.

$180=72+x\\180-72=72+x-72\\108=x$

your missing degree is 108.

i may not be right, if i'm not i am very sorry.

7 0

2 years ago