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MaRussiya [10]
3 years ago
5

Can someone explain (with steps) how to rationalize the following expression?

Mathematics
1 answer:
insens350 [35]3 years ago
6 0
F(x)=(-2/((x+y-2)^(1/2))-(x+y+2)^(1/2)
the only irrational part of this expression is the (x+y-2)^(1/2) in the denominator, so, to rationalize this, you multiply the numerator and denominator by the denominator, as well as the other parts of the expression
also, you must multiply the -sqrt(x+y+2) by sqrt(x+y-2)/sqrt(x+y-2) to form a common denominator
(-2)/(x+y-2)^(1/2)-(x+y+2)^(1/2)(x+y-2)^(1/2)/(x+y-2)^(1/2)
(common denominator)
(-2-(x^2+xy+2x+xy+y^2+2y-2x-2y-4))/(x+y-2)^(1/2)
(FOIL)
(-2-x^2-y^2-2xy+4)/(x+y-2)^(1/2)
(Distribute negative)
(-x^2-y^2-2xy+2)/(x+y-2)^(1/2)
(Simplify numerator)
(-x^2-y^2-2xy+2)(x+y-2)^(1/2)/(x+y-2)^(1/2)(x+y-2)^(1/2)
(Rationalize denominator by multiplying both top and bottom by sqrt)
(-x^2-y^2-2xy+2)((x+y-2)^(1/2))/(x+y-2)
(The function is now rational)
=(-x^2-y^2-2xy+2)(sqrt(x+y-2))/(x+y-2)
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Answer:

The bells ring again together at 6:30

Step-by-step explanation:

10 minute bell

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15 minute bell

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C: (500 divided by 4)+(30 divided by 4)+2

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8 0
3 years ago
Read 2 more answers
Find the volume of the cone. Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and round yo
NeTakaya

Answer:

Volume of the cone = 130.83 cubic units

Step-by-step explanation:

The question us incomplete without the diagram of the cone and it's dimensions as this would enable us get the exact answer.

Find attached the diagram used in solving the solution.

Volume of cone = ⅓ πr²h

Radius = r = 5 unit

Height = h = 5 unit

π = 3.14

By inserting the values of each variables, we have:

Volume of cone = ⅓ × 3.14× (5)² × 5

= ⅓ × 3.14× 25×5 = ⅓ × 3.14×125

Volume of cone = (392.5)/3

Volume of cone = 130.8333

Volume of cone = 130.83 cubic units (to the nearest hundredth)

Volume of cone = 130.83 unit³

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3 years ago
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