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san4es73 [151]
3 years ago
12

Karen buys a fish tank that holds 12 gallons of water. What is the capacity, in quarts, of the fish tank?

Mathematics
1 answer:
Mars2501 [29]3 years ago
6 0
4 quarts in a gallon so the 12 gallon fish tank holds 48 quarts
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A rectangular parcel of land has an area of 3,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than o
Kazeer [188]

Answer:

40 ft × 75 ft

Step-by-step explanation:

Let x be the one side ( in feet ) of the rectangular parcel,

So, the diagonal between opposite corners = ( x + 10 ) feet,

Let y be the other side of the rectangle ( adjacent to side x ),

The area of the rectangle,

A = x × y,

According to the question,

A = 3000 square ft,

\implies xy = 3000\implies y=\frac{3000}{x}

∵ In a rectangle,

D^2=a^2+b^2

Where, a and b are the adjacent side of the rectangle and D is the diagonal,

(x+10)^2 = x^2 + y^2

(x+10)^2 = x^2 + \frac{9000000}{x^2}

x^2(x+10)^2 = x^4 + 9000000

x^2(x^2+100+20x) = x^4 + 9000000

x^4+100x^2 + 20x^3 = x^4 + 9000000

20x^3 + 100x^2 - 9000000=0

x^3 + 5x^2 - 450000 = 0

By graphing the equation,

We found that,

The only real zeros of the equation is at x = 75,

Hence, the one side of the rectangle = 75 ft,

And, second side = \frac{3000}{75} = 40 ft

Hence, the dimension of the land is 40 ft × 75 ft

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