Find the indefinite integral using the substitution x = 10 sin(θ). (Use C for the constant of integration.) 1 (100 − x2)3/2 dx
Answers
Answer:
The indefinite integral
= ˣ
⁺ C
Step-by-step explanation:
x= 10sinθ
dx = 10cosθdθ
the step-to-step explanation is in the attachment
Final answer:
We solve the given integral using substitution and the trigonometric identity. The answer to the integral, after substitution and simplification, is x/10 + C, where C is the integration constant.
Explanation:
To solve the integral problem given, ´∫ 1/(100 − x²)^(3/2) dx´, we will apply the substitution method, which is a common technique in calculus. Here we are using the substitution x = 10 sin(θ) .
Firstly, substituting for x, we get dx/dθ = 10 cos(θ) or dx = 10 cos(θ) dθ. The integral becomes ∫ 10 cos(θ)/ (100 − 100sin²(θ))^(3/2) dθ = ∫ cos(θ) dθ. The indefinite integral of cos(θ) is sin(θ).
Re-substituting x = 10 sin(θ) back into the equation we get sin(θ) = x/10. Thus, the indefinite integral is x/10 + C. Here C is the constant of integration.
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The lines shown below are parallel. If the green line has a slope of -1/2, what is the slope of the red line? A.2B.-C.-2D.
• Water tank A has 220 gallons of water and is being drained at a constant rate of 5 gallons per minute.• Water tank B has 180 gallons of water and is being drained at a constant rate of 3 gallons per minute.Part How much time, in minutes, do water tank A and water tank B have to be drained in order for them to have the same amount of water?
A solid is composed of squares and equilateral triangles. Its net is shown below: The area of each triangle is 16 square units. The surface area of the triangular prism is _____ square units. (Input whole number only)
I need help plz and fast
Answers
Answer:
x^2+10x+21
Step-by-step explanation:
Blue box: x*x=x^2
Green box: x*3=3x
Purple box: 7*x=7x
Orange box: 7*3=21
x^2+(3x+7x)+21
Combine like term
A: x^2+10x+21
What is the value of x
Answers
Answer:
x = 15
--
Move 11 to the other side, with "16" after the equal sign.
We need to subtract: 16-11 = 5
x/3 = 5
x = 5 x 3
x = 15
--
To double check...
15/3 + 11 = 16
5 + 11 = 16
--
PS: In algebra we actually use "*" but for the sake of it I will use "x"
Have a nice day!
Answer:
15
Step-by-step explanation:
First you take all of the non-variables on to the other side of the equal sign. It then turns out to be SUPER easy. x/3 = 16 - 11
x/3 = 5
x = 5*3
x = 15
Answers
Answer:
If the integer is in the range 1–15, then the weather could be declared rainy
Step-by-step explanation:
Assuming the integers are uniformly distributed 15 of them will constitute 30% of the possible integer. If the integer is in the range 1–15, then the weather could be declared rainy. That would make the probability of rain 30%, as required.
What is the longest the bolt can be and still be acceptable?
What is the shortest the bolt can be and still be acceptable?
Answers
Answer:
- longest: 12.2 mm
- shortest: 11.8 mm
Step-by-step explanation:
The longest acceptable bolt is one that is longer than the mid-range value by an amount equal to the difference limit, 0.2 mm
12 mm + 0.2 mm = 12.2 mm . . . . longest acceptable bolt
The shortest acceptable bolt is one that is shorter than the mid-range value by an amount equal to the difference limit.
12 mm - 0.2 mm = 11.8 mm . . . . shortest acceptable bolt
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Answers
Answer:
Step-by-step explanation:
Given
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Recall that:
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Answers
Exact form :
C = -16/7 (16 over 7 in fraction form)
Mixed number :
C= -2 2/7 ( -2 and 2/7 is fraction)