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3 years ago

Find the sum of 2x^2 - 3x + 1 and x^2 + 8 - 9

Mathematics

1 answer:

Mnenie [13.5K]3 years ago

5 0

I think it's 3x^2 - 3x

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You have D dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom co

alex41 [277]

The perimeter of the rectangular plot of land is given by the expression below

$P=2x+2y$

On the other hand, since the available money to buy fence is D dollars,

$\begin{gathered} D=4(2x)+3(2y) \\ \Rightarrow D=8x+6y \\ D\rightarrow\text{ constant} \end{gathered}$

Furthermore, the area of the enclosed land is given by

$A=xy$

Solving the second equation for x,

$\begin{gathered} D=8x+6y \\ \Rightarrow x=\frac{D-6y}{8} \end{gathered}$

Substituting into the equation for the area,

$\begin{gathered} A=(\frac{D-6y}{8})y \\ \Rightarrow A=\frac{D}{8}y-\frac{3}{4}y^2 \end{gathered}$

To find the maximum possible area, solve A'(y)=0, as shown below

$\begin{gathered} A^{\prime}(y)=0 \\ \Rightarrow\frac{D}{8}-\frac{3}{2}y=0 \\ \Rightarrow\frac{3}{2}y=\frac{D}{8} \\ \Rightarrow y=\frac{D}{12} \end{gathered}$

Therefore, the corresponding value of x is

$\begin{gathered} y=\frac{D}{12} \\ \Rightarrow x=\frac{D-6(\frac{D}{12})}{8}=\frac{D-\frac{D}{2}}{8}=\frac{D}{16} \end{gathered}$ <h2>Thus, the dimensions of the fence that maximize the area are x=D/16 and y=D/12.</h2><h2>As for the used money,</h2> $\begin{gathered} top,bottom:\frac{8D}{16}=\frac{D}{2} \\ Sides:\frac{6D}{12}=\frac{D}{2} \end{gathered}$ <h2>Half the money was used for the top and the bottom, while the other half was used for the sides.</h2>

7 0

1 year ago

Solve the equation 1/x + 1/3x =4

vova2212 [387]

Answer:

4/3x

Step-by-step explanation:

4 0

3 years ago

−10x+5=−6x−35 ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

Zarrin [17]

Answer:

x=10

Step-by-step explanation:

Add 6x to both sides.

−4x+5=−35

Subtract 5 from both sides.

−4x=−40

Divide both sides by -4.

$\frac{-4x}{-4}=\frac{-40}{-4}$

x=10

hope this helps

8 0

3 years ago

Read 2 more answers

What is the answer??

masha68 [24]

The answer is 30, assuming it is a cube,

7 0

3 years ago

Please help me I don’t understand.

attashe74 [19]

Answer:

1 : 64

Step-by-step explanation:

Model:

1/2 in * 1/6 in = 1/12 in^2

Real:

1/3 ft * 1/9 ft = 1/3 * 12 in * 1/9 * 12 in = 16/3 in^2

model : real

1/12 / 16/3 = 1/12 * 3/16 = 3/192 = 1/64

model : real = 1 : 64

7 0

3 years ago