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sleet_krkn [62]

3 years ago

9

Richard has a rectangular plot of land that is 525 feet long and y feet wide. He decides to build a fence around the plot. If th

e perimeter of the plot is 1,504 feet, find the value for y.

1 answer:

Naya [18.7K]3 years ago

3 0

Answer:

y = 227 feet

Step-by-step explanation:

Perimeter of a rectangle is P=2(L+B);

1504 = 2(525 + y)....... divide both sides by 2 we would have;

752 = 525 + y

y = 752 - 525

y = 227 feet

Kindly mark brainliest

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Classify each of the following as rational or irrational:

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Answer:

Rational:-5, 2/3, 0.5, sqrt 16

Irrational: sqrt 11, pi

Step-by-step explanation:

A rational number is a number which can be represented as a ratio or fraction and whose decimal is terminating or repeating. This includes all whole numbers positive and negative too.

Ex. -5, 2/3, 0.5, sqrt 16

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A tank contains 180 gallons of water and 15 oz of salt. water containing a salt concentration of 17(1+15sint) oz/gal flows into

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Let A(t) denote the amount of salt (in ounces, oz) in the tank at time t (in minutes, min).

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and flows out at a rate of

$\dfrac{dA}{dt}_{\rm out} = \left(\dfrac{A(t) \, \mathrm{oz}}{180 \,\mathrm{gal} + \left(8\frac{\rm gal}{\rm min} - 8\frac{\rm gal}{\rm min}\right) (t \, \mathrm{min})}\right) \left(8 \dfrac{\rm gal}{\rm min}\right) = \dfrac{A(t)}{180} \dfrac{\rm oz}{\rm min}$

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$\dfrac{dA}{dt} = \dfrac{dA}{dt}_{\rm in} - \dfrac{dA}{dt}_{\rm out} \iff \dfrac{dA}{dt} + \dfrac{A(t)}{180} = 136 (1 + 15 \sin(t))$

Multiply both sides by the integrating factor, $e^{t/180}$ , and rewrite the left side as the derivative of a product.

$e^{t/180} \dfrac{dA}{dt} + e^{t/180} \dfrac{A(t)}{180} = 136 e^{t/180} (1 + 15 \sin(t))$

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Integrate both sides with respect to t (integrate the right side by parts):

$\displaystyle \int \frac d{dt}\left[e^{t/180} A(t)\right] \, dt = 136 \int e^{t/180} (1 + 15 \sin(t)) \, dt$

$\displaystyle e^{t/180} A(t) = \left(24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t)\right) e^{t/180} + C$

Solve for A(t) :

$\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) + C e^{-t/180}$

The tank starts with A(0) = 15 oz of salt; use this to solve for the constant C.

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Recall the Pythagorean identity and definition of tangent,

$\cos^2(x) + \sin^2(x) = 1$

$\tan(x) = \dfrac{\sin(x)}{\cos(x)}$

Then

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so we can rewrite A(t) as

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which is to say, with amplitude

$2 \times \dfrac{267,200}{\sqrt{32,401}} \approx \mathbf{2,968.84 \,oz}$

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