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The area of the surface generated by revolving the curve about the axis y = 9-x² is 12π
<h3>What is a revolution on a graph? or curve?</h3>
Surfaces of revolution are graphs of functions f(x,y) that rely exclusively on the distance from the origin of the point (x,y).
Polar coordinates (r,) are one approach to discuss such surfaces. A "surface of revolution" is formed by rotating a curve around an axis.
Consider a curve with coordinates x and z in the "x0" half of the Euclidean plane.
<h3>What is the calculation justifying the above answer?</h3>y = √(9-x²)
⇒ dy = (-2x)/2√9-x²)
= -x/√(9-x²)
Note that surface area (s) is given as:
√1 + (dy/dx)² dx
= 2
√9-x² * √[1 + (-x)/√9-x²)]dx
= 2π 3dx
= 6π [x]₋¹₁
= 6π (1-(-1)
= 6π (2)
= 12π
Learn more about revolving on a curve:
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The option (C) Mus. Apt. = -22.26 + 0.4925(IQ score) is correct because the value of slope is 0.4925 and y-intercept is -22.26.
<h3>What is the line of best fit?</h3>A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
We have data shown in the picture.
Let's suppose the regression line is:
y = mx + c
Where m is the slope of the regression line and c is the y-intercept of the line.
We can calculate the value of m and c by using the formula.
After calculating, we get:
m = 0.4925
c = -22.26
Mus. Apt. = 0.49253(IQ score) - 22.26
or
Mus. Apt. = -22.26 + 0.4925(IQ score)
Thus, the option (C) Mus. Apt. = -22.26 + 0.4925(IQ score) is correct because the value of slope is 0.4925 and y-intercept is -22.26.
Learn more about the line of best fit here:
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