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2 years ago

Integrate with respect to x -2/3√((2-5x)^3)

Mathematics

1 answer:

salantis [7]2 years ago

5 0

Hello,

$\displaystyle \int {-\dfrac{2}{3} \sqrt{(2-5x)^3}} \, dx \\\\\displaystyle=-\dfrac{2}{3}*\dfrac{-1}{5} \int {-5*(2-5x)^{\frac{3}{2} }} \, dx \\\\\displaystyle=\dfrac{4}{3}*(2-5x)^{\frac{5}{2} }+C$

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The greatest common factor of two numbers is 4. The sum of the numbers is 76. What are the two numbers? A. 38 and 38 B. 12 and 6

Rashid [163]

Answer: B. 12 and 64

Step-by-step explanation:

Option A is incorrect because the highest common factor for both numbers would be 38 not 4.

Option B:

Factors of 12 are: 1, 2 , 3, 4, 6, 12

Factors of 64 are: 1, 2, 4, 8, 16, 32 and 64.

Highest factor of both is 4 and they both add up to 76 so option B must be correct. 

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Setler [38]

The mean of the data is given

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3 years ago

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Prove that:

devlian [24]

Answer:

Identities used:

1/cosθ = secθ
1/sinθ = cosecθ
sinθ/cosθ = tanθ
cosθ/sinθ = cotθ
sin²θ + cos²θ = 1

<h3>Question 1 </h3>

(1 - sinθ)/(1 + sinθ) =
(1 - sinθ)(1 - sinθ) / (1 - sinθ)(1 + sinθ) =
(1 - sinθ)² / (1 - sin²θ) =
(1 - sinθ)² / cos²θ

Square root of it is:

(1 - sinθ)/ cosθ =
1/cosθ - sinθ / cosθ =
secθ - tanθ

<h3>Question 2 </h3>

The first part without root:

(1 + cosθ) / (1 - cosθ) =
(1 + cosθ)(1 + cosθ) / (1 - cosθ)(1 + cosθ)
(1 + cosθ)² / (1 - cos²θ) =
(1 + cosθ)² / sin²θ

Its square root is:

(1 + cosθ) / sinθ =
1/sinθ + cosθ/sinθ =
cosecθ + cotθ

The second part without root:

(1 - cosθ) / (1 + cosθ) =
(1 - cosθ)²/ (1 + cosθ)(1 - cosθ) =
(1 - cosθ)²/ (1 - cos²θ) =
(1 - cosθ)²/sin²θ

Its square root is:

(1 - cosθ) / sinθ =
1/sinθ - cosθ / sinθ =
cosecθ - cotθ

Sum of the results:

cosecθ + cotθ + cosecθ - cotθ =
2cosecθ

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Step-by-step explanation:

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Answer:

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