If f(x,y) = 160(y + 2) represents the "population density" of a planar region on Earth, where x and y are measured in miles, find the number of people in the region bounded by the curves x=y² and x = 2y-y².

Q: Find the length of the curve defined by Y = 3x³/2 + 3 from x :3 to x = 9.

A: Question: Find the length of the curve defined by y= 3x^3/2 + 3 From x=3 to x= 9

Q: On the curve y = x², find a point at which the tangent is parallel to the chord joining (0, 0) and…

A: To find the point

Q: Find the minimum distance from the origin (0,0,0) the line L: 1 +t -3 distance =

A:

Q: The parabola y = x2 + C is to be tangent to the line y = x. Find C.

A: To find the value of C.

Q: Find the equation of the tangent line to the curve of intersection of the surface z = x² - y² with…

A:

Q: A person's body mass index (BMI) is calculated with B (m, h) = m/ h2, where m is the mass of the…

A:

Q: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: 5. Consider the two curves y = x° - 3x + 20x + 88x² + 71x – 74 and y = 2a+ 50x – 22x + 42.x + 31. |…

A:

Q: Find the length of the curve y = In(1-2) over the interval

A:

Q: The average rate of change of the constant on the line at the points P(-1, 2) and Q(9, -13)…

A: Average rate of change can be calculated as follows:

Q: What is the area of the largest triangle in the first quadrant with two sides on the axes and the…

A:

Q: An object weighting w pounds on the surface of the earth, will weight wR² W(x)=² x2 R. at distance z…

A:

Q: Find the lengths of the curves x = (y3/12) + (1/y), 1 ≤ y ≤ 2

A: