What is the equation of a line perpendicular to y=-2/5X-1 that passes through (2,-8)
1 answer:
Answer:
Step-by-step explanation:
Given the equation
comparing the equation with the slope-intercept form
Here,
- m is the slope
- b is the intercept
so the slope of the line is m = -2/5
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line,
so the slope of the perpendicular line will be: 5/2
Therefore, the point-slope form of the equation of the perpendicular line that goes through (2,-8) is:
subtract 8 from both sides
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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:
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