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artcher [175]
3 years ago
14

A gardener will use up to 250 square feet for planting flowers and vegetables. He wants the area used for flowers to be at least

three times the area used for vegetables. Let x denote the area (in square feet) used for flowers. Let y denote the area (in square feet) used for vegetables. Shade the region corresponding to all values of x and that y satisfy these requirements.
Mathematics
1 answer:
anyanavicka [17]3 years ago
8 0
The answer 
<span>Let x denote the area (in square feet) used for flowers.
</span><span>Let y denote the area (in square feet) used for vegetables.

we have    x + y =250
                 x<= 3y

</span>x + y =250
x - 3y <= 0

graph this system and <span>shade the region corresponding to all values of x and that y satisfy these requirements.</span>
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Answer:

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Step-by-step explanation:

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Alona [7]

Answer:

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Step-by-step explanation:

Let \rho(x,y) be a continuous density function of a lamina in the plane region D,then the mass of the lamina is given by:

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The mass of the lamina can be found by evaluating the double integral:

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Since D is a rectangular region, we can apply Fubini's Theorem to get:

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Let the inner integral be: I_0=\int\limits^1_0xye^{x+y}dy, then

I=\int\limits^1_0(I_0)dx.

The inner integral is evaluated using integration by parts.

Let u=xy, the partial derivative of u wrt y is

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and

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v=\int\limits e^{x+y}

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This implies that:

\int\limits xye^{x+y}dy=xye^{x+y}-\int\limits e^{x+y}\cdot xdy

\int\limits xye^{x+y}dy=xye^{x+y}-xe^{x+y}

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We substitute the limits of integration and evaluate to get:

I_0=xe^x

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I=\int\limits^1_0(xe^x)dx.

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I=\int\limits^1_0xe^xdx.

We again apply integration by parts formula to get:

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I=\int\limits^1_0xe^xdx=e^1(1-1)-e^0(0-1).

I=\int\limits^1_0xe^xdx=0-1(0-1).

I=\int\limits^1_0xe^xdx=0-1(-1)=1.

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