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3 years ago

6

The length of a rectangular garden is 9 feet longer than its width. If the garden's perimeter is 194 feet, what is the area of t

he garden in square feet?

2 answers:

Anon25 [30]3 years ago

8 0

Answer:

2,332 square feet

Step-by-step explanation:

194-18(for the 2 sides that are 9 feet longer) = 176

176/4 = 44(the width)

44+9 = 53(the length)

44*53 = 2,332

W*L = A

Natasha_Volkova [10]3 years ago

6 0

194 feet

Answer: 195 feet

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3 years ago

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3 years ago

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3 years ago

The manager of a company uses the function shown to model the company’s daily profit based on the price of a product in dollars,

just olya [345]

Answer: 1) The minimum price, in dollars, to avoid a loss = 22,

2) the maximum price in dollars , to avoid a loss = 53,

3) The price that results the maximum profit = 37.5 dollars

Step-by-step explanation:

Since the given function that shows the total profit,

$f(x) = (x-22)(53-x)$

Where x is the price of the product.

Since for avoiding the loss,

$f(x) \geq 0$ ,

⇒ $(x-22)(53-x)\geq 0$

If $(x-22)\geq 0 \implies x\geq 22$

If $53 - x \geq 0 \implies 53 \geq x$

Thus, 53 ≥ x ≥ 22,

Therefore, the minimum price to avoid the loss = $ 22

And, the minimum price to avoid the loss = $ 53

$f'(x) =\frac{d}{dx}[(x-22)(53-x)] = (x-22)\frac{d}{dx} (53-x)+(53-x) \frac{d}{dx}(x-22)$

⇒ $f'(x) = - (x-22)+(53-x) = -x+22+53-x =-2x+75$

Now, For maximum or minimum,

$f'(x) = 0$ ,

⇒ $-2x+75 = 0$

⇒ $-2x = -75$

⇒ $x = 37.5$

$f''(x) = \frac{d}{dx}(-2x+75)=-1$

For x = 37.5, f''(x) is negative,

Thus, For the price of $ 37.5 dollars the company has the greatest profit.

4 0

3 years ago