suppose that f(x)=-6x^2-7x. Find the slope of the line tangent to f(x) at x=5. Find the instantaneous rate of change of f(x) at x=5. Find the equation of the line tangent to f(x) at x=5. y= Solution Tangent Slope = dy/dx = -12x - 7 = -67 Instantaneous Rate of Change also = dy/dx = -67 Equation of line Tangent = y = mx + c Here m = -67 Thus y = -67x + c Putting x = 5 ; f(x)=-6x^2-7x. we get f(x) = -185 Thus -185 = -67*5 + C Thus C = 150 Equation = Y = -67x + 150.

1. Suppose that F2=510 N. Determine the magnitude of the resultant force, and find the direction
angles of alpha, beta, and gamma
Solution
Force F1: F1x = (400 N)(sen(60)º)(cos(20)º) = 325.519 N
F1y = -(400 N)(sen(60)º)(sen(20)º) = -118.479 N
F1z = (400 N)(cos(60)º) = 200 N
F1 = + (325.519 N) i - (118.479 N) j + (200 N) k
By cosine directors:
Force F2: F2x = (510 N)(cos(60)º) = 255 N
F2y = (510 N)(cos(60)º) = 255 N
F3z = (510 N)(cos(135)º) = -360.624 N
F2 = + (255 N) i + (255 N) j - (360.624 N) k
R = F1 + F2 = (580.519 N) i + (136.32 N) j - (160.624 N) k
FR = ((580.519)2 + (136.32 N)2 + (-160.624)2)1/2
FR = 617.56 N
cos(thetax) = Rx/FR = (580.519)/(617.56) = 0.94
thetax = Alpha = 19.95 º
cos(thetay) = Ry/FR = (136.32)/(617.56) = 0.2207
thetay = Betha = 77.25 º
cos(thetaz) = Rz/FR = (-160.624)/(617.56) = -0.2601
thetaz = Gamma = 105.08 º