Need help for4,5,6 dealing with isosceles triangles
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The volume of the region R bounded by the x-axis is:
The volume of a solid is the degree of space occupied by a solid object. If the axis of revolution is the planar region's border and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.
In the graph, the given straight line passes through two points (0,0) and (2,8).
Therefore, the equation of the straight line becomes:
where:
- (x₁, y₁) and (x₂, y₂) are two points on the straight line
Thus, from the graph let assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8), we have:
y = 4x
Now, our region bounded by the three lines are:
- y = 0
- x = 2
- y = 4x
Similarly, the change in polar coordinates is:
- x = rcosθ,
- y = rsinθ
where;
- x² + y² = r² and dA = rdrdθ
Now
- rsinθ = 0 i.e. r = 0 or θ = 0
- rcosθ = 2 i.e. r = 2/cosθ
- rsinθ = 4(rcosθ) ⇒ tan θ = 4; θ = tan⁻¹ (4)
- ⇒ r = 0 to r = 2/cosθ
- θ = 0 to θ = tan⁻¹ (4)
Then:
Learn more about the determining the volume of solids bounded by region R here:
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The prime factorization of 240 is . 3 . 5 ⇒ last answer
Step-by-step explanation:
Prime number is the number that has only 2 factors 1 and itself
{2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , ............}
In prime factorization we use only the prime numbers
Ex: The factors of 15 are 1 , 3 , 5 , 15,
Then the prime factors of 15 are 3 and 5 only because they are
prime numbers
So to find the prime factors of a number do that
1. Factorize the number by divide it using prime numbers only
2. Write the number as a product of its prime factors
∵ 240 divisible by first prime number 2
∴ 240 ÷ 2 = 120
∵ 120 ÷ 2 = 60
∵ 60 ÷ 2 = 30
∵ 30 ÷ 2 = 15
- We divided the number by 2 for 4 times
∴ is a prime factor of 240
∵ 15 is divisible by prime number 3
∴ 15 ÷ 3 = 5
∴ 3 is a prime factor of 240
∵ 5 is divisible by prime number 5
∴ 5 ÷ 5 = 1
∴ 5 is a prime factor of 240
∴ The prime factors of 240 are , 3 , 5
The prime factorization of 240 is . 3 . 5
Learn more:
You can learn more about factors in brainly.com/question/5194236
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