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3 years ago

A heat pump cycle whose coefficient of performance is 2.5 delivers energy by heat transfer to a dwelling at a rate of 20 kW.

Mathematics

1 answer:

jasenka [17]3 years ago

3 0

Answer:

Net power = 20kW

B.) $128

Step-by-step explanation:

Given that :

Coefficient of performance = 2.5

Rate = 20kW

The net power required to operate the heat pump :

Energy delivery rate / Coefficient of performance

= 20kW / 2.5

= 8kW

B.) Given that electricity cost equals $0.08 per kW

If pump operates for 200 hours

Total energy used in kWhr :

8kW * 200= 1600kW

Cost per kW = $0.08

1600 * 0.08 = $128

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a farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. no fencing is needed along the bar

xenn [34]

The constraint for the maximum enclosed area is the amount the farmer is

willing to spend on fencing.

The width of the plot that will give the most area, y = 83. $\underline{\overline 3}$ feet

The length of the plot that will give the most area, y = 125 feet

Reasons:

The given parameters are;

The cost of fencing per foot = $20

The maximum amount the farmer is willing to spend = $5000

Number of sides of fencing = 3 sides

Cost of the west side of the = Split with neighbor

Solution:

Let, y, represent the length of the fence, and let x represent the width of

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Length of fence required = y + 2·x

Cost of the fence = 20·y + 20·x + (20÷2)·x = 20·y + 30·x

Therefore;

Maximum amount to be spent on the fence, 5000 = 20·y + 30·x

$\therefore y = \dfrac{5000 - 30 \cdot x}{20} = 250 - \dfrac{3}{2} \cdot x$

$y = \mathbf{250 - \dfrac{3}{2} \cdot x}$

Area of a rectangle = Length × Width

The enclosed rectangular area of the fencing, A = y × x

$\therefore A = \left(250 - \dfrac{3}{2} \cdot x\right) \cdot x = 250 \cdot x - \dfrac{3}{2} \cdot x^2$

$\therefore A = -\mathbf{ \dfrac{3}{2} \cdot x^2 + 250 \cdot x}$

The leading coefficient of the quadratic function of the area is negative,

therefore, the function only has a maximum point.

At the point of the most area, the slope, $\dfrac{dA}{dx} = 0$

Finding the value of x at the maximum point, we get;

$\dfrac{dA}{dx} = \mathbf{ \dfrac{d}{dx} \left( 250 \cdot x - \dfrac{3}{2} \cdot x^2\right)} = 250- 3 \cdot x = 0$

Therefore;

$\mathrm{ The \ width \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ x = \dfrac{250}{3} \ feet = \underline{83.\overline 3 \ feet}$

$\mathrm{ The \ length \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ y = 250 - \dfrac{3}{2} \times \dfrac{250}{3} = 125$

The length of the plot that will give the most area, y = 125 feet

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Rudik [331]

Answer:

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3 years ago

At a football stadium, 25% of the fans in attendance were teenagers. If there were 130 teenagers at the football stadium, what w

Licemer1 [7]

Answer:

Total number of people in the stadium = 520

Step-by-step explanation:

Let the total number of people in the stadium = x

Since, 25% of the fans are teenagers, number of teenagers in the stadium

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= 0,25x

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0.25x = 130

x = $\frac{130}{0.25}$

x = 520

Therefore, total number of fans in the stadium = 520.

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4 years ago