6. Find the area bounded by: a. The curve y3D4x-x and the lines y-0, x-1 and x=3. b. The curve x=1+y'and the line x-10. c. The curve y=9-x and the line y3x+3.

Q: x+2 What is the equation of the normal line of y = at the point x = 1? 2x+1

A: Let us consider function y=f(x) The normal line of function y=f(x) at point x0 is given by formulae:…

Q: 13) Find the points of intersecti on of the parabola and the line. y=2x^2-3x-1 and y=x+5

A: Equate the equations with each other and solve for x to find the point of intersection .

Q: Find the value of k so that the following curves y=(x^4)/k and y=-3x^3-2x^2 intersect at more than…

A: To find the value of k such that the curves y=kx4​ and y=−3x3−2x2 intersect at more than two points,…

Q: Calculate y" and y'. y = 0²(20 + 4) y" = y" : II

A: Given function is : y = Ѳ2( 2Ѳ + 4)

Q: 11) Find each of the two areas bounded by the curves y=x3-4x and y=x² + 2x Points of intersection:…

A:

Q: A city's commuter system has three zones covering the regions described. Zone 1 covers people living…

A: A. Given that zone 1 covers people living within three miles of the city center. So radius of zone…

Q: over the triangular region Cut from the * quadrant by the line x+y =1.

A:

Q: ****- # PANKK 245 w (0 6**) jead 243 www. (**) 4 Find the length of the curve

A:

Q: y=-2log_(2)(x+3)-1 Plot at least four points that fit on.

A:

Q: 9). Find the curve whose slope at any point is 3x – 5 that passes through point (5,3).

A:

Q: Consider point P(4, 2) and line l with equation −3x+4y=6 .

A: Substitute x=4 and y=2 into the given equation. -12+8=-4

Q: Find the three areas of the region bounded by y= 2x²+10 , y=4x+1 and the lines x=-2 and x=5.

A: We need to find the area between two curves. The area between two curves y=fx, y=gx for x∈a,b is…

Q: Sketch one loop of the curve 9y² = x(3x)² Find the area of the surface of revolution generated by…

A:

Q: Q2) Find the distance between the line y= - (x+2 ) & the center of the circle y + x – 4(x+ y )= 9

A: The center of the circle x2+y2-2ax-2by+c=0 is a, b Therefore, the center of the given circle…

Q: Find the set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?

A: Given: y=2x+kat 2 distinct points

Q: 7. Find the distance from the point A to the line through the points B and C where A, B, and C have…

A:

Q: ind point P and Q on the parabola y=(-x^2)+1 so that the triangle ABC formed by the x-axis and the…

A: Given that the curve is                         To find point P and Q on the given parabola, so that…

Q: Show that the distance between the line 3x 4y + 3 = 0 and the point (1, –1) is 2. |

A: In this question, we have to prove that the distance between line and point is 2.