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3 years ago

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to make a backyard ice rink, a company developed Ice Rink Layers which are like giant plastic bags that can be filled with water

once the water freezes the top plastic layers is removed to expose the ice. the company manufactures the bags with high strength plastic in two designs shown below?

1 answer:

notsponge [240]3 years ago

4 0

You need a perfectly level, large area

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Consider the differential equation:

Wewaii [24]

(a) Take the Laplace transform of both sides:

$2y''(t)+ty'(t)-2y(t)=14$

$\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s$

where the transform of $ty'(t)$ comes from

$L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)$

This yields the linear ODE,

$-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s$

Divides both sides by $-s$ :

$Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}$

Find the integrating factor:

$\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C$

Multiply both sides of the ODE by $e^{3\ln|s|-s^2}=s^3e^{-s^2}$ :

$s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}$

The left side condenses into the derivative of a product:

$\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}$

Integrate both sides and solve for $Y(s)$ :

$s^3e^{-s^2}Y(s)=7e^{-s^2}+C$

$Y(s)=\dfrac{7+Ce^{s^2}}{s^3}$

(b) Taking the inverse transform of both sides gives

$y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]$

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that $\frac{7t^2}2$ is one solution to the original ODE.

$y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7$

Substitute these into the ODE to see everything checks out:

$2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14$

5 0

3 years ago

What is the value of 3/4 increased by 2 1/6?

Mashutka [201]

Answer:

2 11/12

Step-by-step explanation:

3/4 + 2 1/6

Add the fractions.

35/12

= 2 11/12

8 0

3 years ago

Read 2 more answers

Carly will be going to college in 3 years. she anticipates that she will need $12,000 to pay for the first year. she currently h

fgiga [73]

12000 - 2900 = 9100

9100 / 36 = 252.77.....about 253 per month

8 0

3 years ago

Read 2 more answers

a circular oil slick is expanding at a rate of 2m^2/h. Find the rate at which it's diameter is expanding when it's radius is 1.5

aleksandrvk [35]

Answer: $\frac{4\pi}{3} \text{ meter per hour}$

Step-by-step explanation:

The circular oil slick is expanding at a rate of $2 m^2/h$

Let A be the area of the circular oil slick,

So, the changes in A with respect to time (t),

$\frac{dA}{dt} = 2$

$\frac{d(\pi r^2)}{dt} = 2$

$2\pi r\frac{dr}{dt} = 2$

$\frac{dr}{dt} = \frac{1}{\pi r}$

Also, the change in diameter with respect to time(t),

$\frac{d}{dt} (2 r) = 2 \frac{dr}{dt}$

$\frac{d}{dt} (2 r) = 2 \times \frac{1}{\pi r}$

$\frac{d}{dt} (2 r) = \frac{2}{\pi r}$

For r = 1.5 m,

$\frac{d}{dt} ( 2 r)]_{r=1.5} = \frac{2}{\pi \times 1.5}=\frac{20}{\pi \times 15}=\frac{4\pi }{3}\text{ meter per hour}$

7 0

2 years ago

In a programming team of 20 persons, 1/4 are women and 3/4 are men. to obtain a team with 40% women, how many women should be hi

Savatey [412]

This is the concept of algebra, to solve the question we proceed as follows;
the current number of women is:
1/4*20=5 women
the percentage of women is:
1/4*100=25%
therefore for the team to have 40% women, the number of women should be:
40/25*5
=8 women
The answer is 8 women

3 0

3 years ago