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irinina [24]
3 years ago
14

A rectangle whose area is 180 square feet has a width that is 3 feet less than the length. Find the dimensions of the rectangle.

Mathematics
1 answer:
Yuliya22 [10]3 years ago
4 0

Answer:

The length is 15\ ft

The width is 12\ ft

Step-by-step explanation:

we know that

The area of rectangle is equal to

A=LW

we have

A=180\ ft^{2}

so

180=LW -----> equation A

W=L-3 ------> equation B

substitute equation B in equation A and solve for L

180=L(L-3)

180=L^{2}-3L

L^{2}-3L-180=0

using a graphing tool------> solve the quadratic equation

The solution is L=15\ ft

see the attached figure

<em>Find the value of W</em>

W=15-3=12\ ft

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at 10a.m. you consume an energy drink containing 800mg of caffeine. if the half-life of caffeine is 5.7 hours, how much caffeine
icang [17]

Answer:

268 mg

Step-by-step explanation:

Let A₀ = the original amount of caffeine

The amount remaining after one half-life is ½A₀.

After two half-lives, the amount remaining is ½ ×½A₀ = (½)²A₀.

After three half-lives, the amount remaining is ½ ×(½)²A₀ = (½)³A₀.

We can write a general formula for the amount remaining:

A =A₀(½)ⁿ

where n is the number of half-lives .

n = t/t_½

Data:

  A₀ = 800 mg

    t₁ = 10 a.m.

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t_½ = 5.7 h

Calculations:

(a) Calculate t

t = t₂ - t₁ = 7 p.m. - 10 a.m. = 19:00 - 10:00 = 9:00 = 9.00 h

(b) Calculate n

n = 9.00/5.7 = 1.58

(b) Calculate A

A = 800 × (½)^1.58 = 800 × 0.334 = 268 mg

You will still have 268 mg of caffeine in your body at 10 p.m.

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6 0
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Step-by-step explanation:

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Which equation represents this statement? One-third of a number is 21.
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Duffs Co. is growing quickly. Dividends are expected to grow at a 24% rate for the next three years, with the growth rate fallin
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Based on the fact that Duffs Co. dividends grow at 24% for three years and then 6%, the current share price of the company is $63.29.

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First, find the price of the stock in year 3 when the stock grows at 6%:

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This amount is the terminal value. You are to take the present value of this amount along with the present value of the dividends up to year 3:

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