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Natali5045456 [20]
2 years ago
9

Find the area enclosed by x2=2y and y2=16x​

Mathematics
1 answer:
jekas [21]2 years ago
4 0

Answer: \dfrac{32}{3}

Step-by-step explanation:

Given

The parabolas are x^2=2y and y^2=16x

Find the point of intersection of two parabolas

\Rightarrow \left(\dfrac{x^2}{2}\right)^2=16x\\\\\Rightarrow x^4=64x\\\Rightarrow x(x^3-64)=0\\\Rightarrow x=0,4

Obtain y using x

(x,y)\rightarrow (0,0)\ \text{and }(4,8)

Area enclosed between the two is

\Rightarrow I=\int\limits^4_0 ({4\sqrt{x}-\dfrac{x^2}{2}}) \, dx\\\\\Rightarrow I=\left ( 4\times \dfrac{2}{3}x^{\frac{3}{2}}-\dfrac{x^3}{2\times 3} \right) _0^4\\\\\Rightarrow I=\left ( \dfrac{8}{3}\times 8-\dfrac{4^3}{6} \right )-0\\\\\Rightarrow I=\dfrac{128-64}{6}\\\\\Rightarrow I=\dfrac{64}{6}\\\\\Rightarrow I=\dfrac{32}{3}

Thus, the area bounded by the two parabolas is  \dfrac{32}{3} sq. units.

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Answer:

12 rolls

Step-by-step explanation:

Jason wants to cut roll into pieces that are each 1/2 inches thick. 1/2 is equal to 0.5, so thickness of each roll is 0.5 inches

Total length of the roll is 6 inches. We have to find how many small 0.5 inch rolls can he cut.

In simple words we can say that we have to find: how many 0.5 inches can be out from 6 inches. This type of problem is solved by division. Dividing 6 inches by 0.5 inches will give us: How many 0.5 inches can be cut out from 6 inches i.e. how many 0.5 inches roll can be made from 6 inches roll

6 divided by 0.5 is 12.

This means Jason can cut 12 rolls of sausages each with thickness of 0.5 inches from a roll of 6 inches.

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In a certain region, there is a 0.1 probability that any checked passerine bird's nest will
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Probability of at least two cuckoo eggs is 0.738.

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