Halp please and show you work cuz I'm nervous TwT
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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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Answer:
Step-by-step explanation:
In the decimal of −12,405, leave the −12 and divide 405 by 1000 for now:
Greatest Common Divisor [GCD]: 5
Finally, you attach this back to the −12, giving you .
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