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posledela
3 years ago
14

A circular hot tub is surrounded by a cement path as shown in the diagram.

Mathematics
1 answer:
Natali [406]3 years ago
7 0

Answer:

Step-by-step explanation:

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Find the area enclosed by x2=2y and y2=16x​
jekas [21]

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.

4 0
3 years ago
Which order pairs is a solution of the equation y=10x
oksano4ka [1.4K]

Answer:

y=Mx+c

Step-by-step explanation:

i think this is the answer u are looking for

3 0
3 years ago
How might we know whether X is a positive number negative number or 0 without solving the equation 5x=-16.5
Taya2010 [7]

Answer:

Since 16.5 is negative, the only way to get that answer is to multiply 5 by something to negative(x)

Step-by-step explanation:

8 0
3 years ago
If the area of the right triangle is 72 what is the value of x
wel

36 i guess ha please that not right

8 0
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Jeffrey purchase and download 12 songs on Monday he purchase an additional 3 songs on Tuesday the cost to download each song is
bonufazy [111]
(12x3)+(3x2) Because on Monday he bought 12 songs for $3 each and on Tuesday he bought 2 songs for $3 each.
4 0
3 years ago
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