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mestny [16]
3 years ago
12

A solid lies between planes perpendicular to the​ x-axis at x = -2 and x = 2. The​ cross-sections perpendicular to the​ x-axis b

etween these planes are squares whose bases run from the semicircle y = -√(4 - x²) to the semicircle y = √(4 - x²).
Find the volume of the solid.

Mathematics
1 answer:
icang [17]3 years ago
8 0

Answer:

V = 128π/3 vu

Step-by-step explanation:

we have that: f(x)₁ = √(4 - x²);  f(x)₂ = -√(4 - x²)

knowing that the volume of a solid is  V=πR²h, where R² (f(x)₁-f(x)₂) and h=dx, then

dV=π(√(4 - x²)+√(4 - x²))²dx;  =π(2√(4 - x²))²dx ⇒

dV= 4π(4-x²)dx , Integrating in both sides

∫dv=4π∫(4-x²)dx , we take ∫(4-x²)dx and we solve

4∫dx-∫x²dx = 4x-(x³/3) evaluated -2≤x≤2 or too 2 (0≤x≤2) , also

∫dv=8π∫(4-x²)dx evaluated 0≤x≤2

V=8π(4x-(x³/3)) = 8π(4.2-(2³/3)) = 8π(8-(8/3)) =(8π/3)(24-8) ⇒

V = 128π/3 vu

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{-210, -156, -366,-471, -108,-627, -579}
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Option D I and IV only is correct option

Step-by-step explanation:

We need to identify that the numbers {-210, -156, -366,-471, -108,-627, -579} belong to which of the following set of numbers.

I. Rational Numbers

II. Natural Numbers

III. Whole Numbers

IV. Integers

We will consider each option

Rational numbers: numbers that can be written by dividing two integers. They can be positive or negative.

all the numbers given can be divided by 1 to make them fractions. So all numbers are rational numbers.

Natural numbers: numbers that are positive integers excluding 0 i.e 1,2,3...

So, the given numbers are not natural numbers

Whole numbers: all natural numbers including 0. These are positive numbers. So, the given numbers are not whole numbers

Integers: it is a whole number (not fraction) that can be positive,negative or zero. So, the numbers given are integers.

So, Option D I and IV only is correct option

Keywords: Set of numbers

Learn more about set of numbers at:

  • brainly.com/question/537998
  • brainly.com/question/5030671
  • brainly.com/question/10894205

#learnwithBrainly

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