If e =mc square what does mc square =

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft and on the other three s

makvit [3.9K]

Answer:

The dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)

Step-by-step explanation:

Let the length of garden be x

Let the breadth of garden be y

Area of Rectangular garden = $Length \times Breadth = xy$

We are given that the area of the garden is 122 square feet

So, $xy=122$ ---A

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft

So, cost of brick along length x = 20 x

On the other three sides by a metal fence costing $10/ft.

So, Other three side s = x+2y

So, cost of brick along the other three sides= 10(x+2y)

So, Total cost = 20x+10(x+2y)=20x+10x+20y=30x+20y

Total cost = 30x+20y

Substitute the value of y from A

Total cost = $30x+20(\frac{122}{x})$

Total cost = $\frac{2440}{x}+30x$

Now take the derivative to minimize the cost

$f(x)=\frac{2440}{x}+30x$

$f'(x)=-\frac{2440}{x^2}+30$

Equate it equal to 0

$0=-\frac{2440}{x^2}+30$

$\frac{2440}{x^2}=30$

$\sqrt{\frac{2440}{30}}=x$

$9.018 =x$

Now check whether it is minimum or not

take second derivative

$f'(x)=-\frac{2440}{x^2}+30$

$f''(x)=-(-2)\frac{2440}{x^3}$

Substitute the value of x

$f''(x)=-(-2)\frac{2440}{(9.018)^3}$

$f''(x)=6.6540$

Since it is positive ,So the x is minimum

Now find y

Substitute the value of x in A

$(9.018)y=122$

$y=\frac{122}{9.018}$

$y=13.528$

Hence the dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)

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3 years ago

Molly uses 192 beads to make a bracelet and a necklace. It takes 5 times as many beads to make a necklace than t does to make a

neonofarm [45]

Solve for the bracelet first. x represents number of beads for bracelet So it would be number of beads for the bracelet + number of beads for necklace (5x) and they both equal 192 x + 5x = 192 Then you would add the x and 5x.<br />6x = 192 Now all you have to do is divide by 6 on both sides. 6× ÷ 6 = 192 ÷ 6 You know have the number of beads it takes for a bracelet. x = 32 to get the necklace all you need to do is multiply it by 5 because you need 5 times more for the necklace. 32 × 5 total beads needed is 160. 160 x+5x=192 6×=192 6x÷6=192÷6 x=32 necklace needs 32x5 beads per necklace is 160

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3 years ago

Select all the true statements.

dangina [55]

Answer:

Dont get it either im stuck on it

Step-by-step explanation:

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3 years ago

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which answer choice explains the pattern for how to find the slope using an equation in standard form?

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