Calculate the area of the segment cut from the curve y=x(3−x) by the line y=x. Also, sketch the graph.

Q: Determine the slope of the curve y = x² + 2x at the point (-1, -3) on the curve.

A: We have to determine the slope of the given curve at the point .

Q: Find the slope of the secant line to the function f(x)=4x²- 3x, through point P, where x= - 1, and…

A: To find the slope of secant line PQ to  the function f(x)

Q: Find the slope of the curve y = x3 + 8x +14, where the curve crosses the x-axis

A:

Q: Find the slope of line y =   2.7x

A: Given  The line equation is  y =   2.7x .

Q: Find slope of the line x = 5

A: Given,         Slope of the line x = 5.

Q: The line y = 2x + b is tangent to the graph of y = 1x at the point P = (a, 1a). Find P and determine…

A: Given: The line y=2x+b is tangent to the graph of y=x at the point Pa,a. To find P and determine b.…

Q: Find the distance between two points (1, 2) and (3, −1).

A: We want to find the distance between the given two points. We use formula for finding the distance…

Q: Find the length of the curve y=7x-13 between y=-6 and y=15.

A:

Q: Find the distance between the point (2, 9) and the line y = 3x + 4

A: Find the distance between the point (2, 9) and the line y = 3x + 4 To find the distance between a…