8.) Find a line which is normal (perpendicular) to f(x,y) = x2 + 3y - 5...
21) 21. Given the line y = {x+4, find the slope of a line perpendicular to this line. A)-3/2 B) 3/2 C) 2/3 D) -2/3 E) None of the Above 22) 22. Which of the following represents x as a function of y? A) {(8,8), (8,7), (8, -3),(-8,1)} B) x2 = y C) {(1,5),(5,1),(6,6),(10,6)} D) (x + 3)2 + (y + 4)2 = 4 E) None of the Above 23. A polynomial function f(x) is known to have degree 3...
(5 points) 2. Find the line integral of f (x, y, z) = 2x – 3y + 5z along the straight line segment from (1,0, 2) to (3, 2, -1).
number 2 x + 3y - 9= 0 b) perpendicular on the line 3x + y + 9 = 0 2. Find the area of the triangle with vertices at the points (6, 7),(-4, 4) and (8, -7).
Find the slope of a line perpendicular to the line y=xUse the slope-intercept form of a linear equation to write the equation of each line with the given slope and y-intercept.slope -3; y-intercept (0, -1/5)write the equation of the line passing through the given points. write the equation in standard form Ax+By=C(8,-3) AND (4,-8)Write an equation of each line. Write the equation in the form x=a y=b or y =mx+bThrough (-2,-3): perpendicular to 3x+2y =5Find the equation of each line....
3. Consider the function f(x,y) = 4 + 2x - 3y - x2 + 2y2 - 3xy. a) (5 pts.) Calculate the partial derivative functions, and use them to calculate the gradient vector evaluated at c = b) (5 pts.) Write down the affine approximation to at the e given in a) /(x) = f(c)+ Vf(e)'(x - c) . Use it to calculate (1.1, 1.1). (Hint: it should be close to f(1.1, 1.1))
1) Let f(x) and g(x) be f(x)-x2-x (x)- x + 2 Find (f/gXx) 2 +a 2) Solve the 2-equation system for both the variables x and y 5x-4y1 2x + 3y-2 3) Find an equation for the line parallel to y x-8 with the y-intercept being(0,-5).
1. Find the equation of the tangent line to: a) y = x2 – 3 at the point (2,1) b) y = cos x at the point (1,1) c) y=e" at the point where r = 1 d) r3 + y3 = 19 at the point (3,-2) 2. Find the equation of the normal line to: a) y = r at the point (2,8) b) y=x+ at the point where x = 2 c) y = 2:03 - 5x +...
please answer both (12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0 (12(8 pts) Find parametric equations of the line through the point (2,...
7. The vector field F =< 3x2z In y + ze+2 +20, - 3y?, x° In y + ce2 +423 > is conservative. Find a potential function f(x, y, z) such that F=Vf. Y
For a vector field F(x)(2yarctanx)j find a function f such that F,y)-V/ h(2yarctanx)j find a function f such that F(x,y)-U For a vector field F(x,y)- 1+x2 and use this result to evaluate dr, where C: rit2, osis1 For a vector field F(x)(2yarctanx)j find a function f such that F,y)-V/ h(2yarctanx)j find a function f such that F(x,y)-U For a vector field F(x,y)- 1+x2 and use this result to evaluate dr, where C: rit2, osis1