& Let P=(x,y) be a point on graph y=x²-8 Express the distance d from p to...
Let P = (x,y) be a point on the graph of y=x- 2. (a) Express the distance d from P to the origin as a function of x. d(x)= (b) What is d if x = 0? d(0)= (Round to two decimal places.) (C) What is d if x= 1? d(1) = (Round to two decimal places.) Use a graphing utility to graph d=d(x) in order to answer the following question. (d) For what positive value of x is d...
. ? Express the distance, d, from Co to a point (x,y) ony = V/ as a function of x. (10)
Find a formula for the distance from the point P{x,y,z) to each of the following planes. a. Find the distance from P(x,y,z) to the xy-plane. b. Find the distance from P(x,y,z) to the yz-plane. c. Find the distance from P(x,y,z) to the xz-plane. a. Choose the correct formula for the distance from the point P(x,y,z) to the xy-plane. O A. Iz OB. Mx2 + y2 OC. Vz OD. x² + y² + 2? b. Choose the correct formula for the...
For the function f(x,y,z)==xyz and the point P=(-1, 8, 2): a) Calculate the gradient at P. Vf(-1, 8, 2) = b) Find the rate of change in the direction v=(2, 2, - 1) at P. D.f(-1, 8, 2)= c) Find the maximum rate of change of f at P. MAX RATE OF CHANGE =
(1 point) Let x and y have joint density function p(2, y) = {(+ 2y) for 0 < x < 1,0<y<1, otherwise. Find the probability that (a) < > 1/4 probability = (b) x < +y probability =
in urgent need with help on these three What point on the line y-7x + 8 is closest to the origin? Let D be the distance between the two points. What is the objective function in terms of the x-coordinate? (Type an expression.) a. Find the radius and height of a cylindrical soda can with a volume of 398 cm3 that minimize the surface area. b. Compare your answer in part (a) to a real soda can, which has a...
8) (S3.7) Finding Minimum Distance. Find the point on the graph of the function that is closest to the given point. a) fx) -(x-2)2, (-5, 3) b) f(x)x 6, (10, 0)
Only need help with (d) = 0 ( [this point is away from 0] A conducting sphere of radius a is hollow and grounded (V = 0). A particle of charge q is a placed inside at a distance b from the center. We wish to find the potential anywhere inside the sphere. This problem can be solved with the image charge method. The image charge d' should be placed a distance b = from the center, so that the...
For the first order linear ODE: y'(x)+p(x)y(x)=r(x) and let D(y(x))=y'(x)+p(x)y(x), Find the solution of the following ODE: y'+y(x^5)=cos(wx), y(0)=0
9 Geometry via calculus In this exercise you will see one way to use calculus to do grometry a) Here is one way to find the perpendicsler distance from a point to a line L (no caleulus yet) Let's say L has equation y-3r+2 and the point is (2.1) First, make a graph (picture) of the situation 2Now find an equation for the line AM through (2, 1) perpendicular to L (draw it first, of course). 3. Find the (coordinates...