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...
Find the point P on the line y = 3x that is closest to the point (20,0). What is the least distance between P and (20,0)? The point P on the line y = 3x that is closest to the point (20,0) is (Type an ordered pair.) The least distance between P and (20,0) is approximately (Round to the nearest tenth as needed.)
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be the line in R3 that passes through the point P and is perpendicular to both of the vectors v and w. Find an equation for the line L in vector form. (iii) Find parametric equations for the line L.
(1 point) Find the point on the line y=6x that is closest to the point P=(1,2) Point = (_ , _)
(1 point) Line L in the figure below is parallel to the graph of y = 5x + 1. Find the coordinates of the point P. y=5x+1 (0,-5) (click on the graph to get a larger version) P= (-1,0) help (points)
y 1/(1-x) 5. The point P(2,-1) lies on the curve C If Q is the point (x,1/(1-x), use your calculator to find the slope of the secant line PQ a. (correct to six decimal places) for the following values of x: 1.5 (ii) 1.9 (i) 1.99 (iv) 1.999 (v) 2.5 (vi) 2.1 (vii) 2.01 (vii) 2.001 Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(2,-1) i. b. Using...
Q2)a) [5pt] Find the equation of the line in the plane (in y = mx +b form) that is perpendicular to the line y = 1/5x + 17 and goes through the point (9, 12). Equation of the line: _______ Q2)b) [5pt] Find the equation of the line in the plane that is perpendicular to the y axis and goes through the point (-2,4). Equation of the line:_______
Consider the line y=-5x+2. Find the equation of the line that is parallel to this line and passes through the point (6. 4). Find the equation of the line that is perpendicular to this line and passes through the point (6. -4). Note that the ALEKS graphing calculator may be helpful in checking your answer. E Equation of parallel line: DE X 5 ? Equation of perpendicular line:
Problem 4: (a) (5 points) Find the equation for the line that passes through the points (-4,-2) and (8, 1). Write your equation in se form, slope-intercept form, or point- slope form. (Extra Credit: Write the equation for the line in all three forms) (b) (5 points) Graph the line. Problem 5: (10 points) Find the equation for the line passing through the point (3.2) and perpendicular to the line y = ',x + 7. The the line Problem 6:...
please answer ASAP CHECK HERE AFTER MOBILE OR REMOTE DEPOSIT DO NOT WRITE STAMP OR SON BELOW THIS LINE SERVED TO PINANGON DATE ENDORSE HERE WRITING EQUATIONS OF LINES Show all work to receive full credit. 1. Find the equation of the line in slope-intercept form. Then graph the line. (a) Slope: 3; y-intercept -2 2 (b) Slope: 4 (c) Through (2,3); slope 5 (d) Through (2,1) and (1,6) (e) Through (-2,5) and (-1,-3) (f) Through (5,1); slope 0 (g)...