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VladimirAG [237]
1 year ago
15

Yes or no easy math plus another math question

Mathematics
1 answer:
Fed [463]1 year ago
3 0

Answer:

10 yes 18 no 17 no

Step-by-step explanation:

Hope this helps

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Can you guys pls help me with this math question
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Answer:

Dimensions:  150 m x 150 m

Area:  22,500m²

Step-by-step explanation:

Given information:

  • Rectangular field
  • Total amount of fencing = 600m
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Let x = width of the field

Let y = length of the field

Create two equations from the given information:

  <u>Area of field</u>:   A= xy

  <u>Perimeter of fence</u>:   2(x + y) = 600

Rearrange the equation for the perimeter of the fence to make y the subject:

\begin{aligned} \implies 2(x + y) & = 600\\ x+y & = 300\\y & = 300-x\end{aligned}

Substitute this into the equation for Area:

\begin{aligned}\implies A & = xy\\& = x(300-x)\\& = 300x-x^2 \end{aligned}

To find the value of x that will make the area a <em>maximum</em>, <u>differentiate</u> A with respect to x:

\begin{aligned}A & =300x-x^2\\\implies \dfrac{dA}{dx}& =300-2x\end{aligned}

Set it to zero and solve for x:

\begin{aligned}\dfrac{dA}{dx} & =0\\ \implies 300-2x & =0 \\ x & = 150 \end{aligned}

Substitute the found value of x into the original equation for the perimeter and solve for y:

\begin{aligned}2(x + y) & = 600\\\implies 2(150)+2y & = 600\\2y & = 300\\y & = 150\end{aligned}

Therefore, the dimensions that will give Tanya the maximum area are:

150 m x 150 m

The maximum area is:

\begin{aligned}\implies \sf Area_{max} & = xy\\& = 150 \cdot 150\\& = 22500\: \sf m^2 \end{aligned}

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F(g(x))=2(x-4)+8

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