# 7.4 Step by step solutions: 1 2 4 5 6 8 9 10 11

1. Using the arc length formula to find the length of the curve y = 2x-3, -2<= x<= 1. Check your answer by noting that the curve is a line segment and calculating its length by the distance formula.
2. Find the exact length of the curve.
x = 1/3sqrt(y)(y-3), 4<=y<=9
3.Find the exact length of the curve. y = ln(sec x), 0<=x<=pi/4
5.A steady wind blows a kite due west. The kite’s height above ground from horizontal position x = 0 to x = 100 ft is given by y = 150-1/40(x-50)^2. Find the distance traveled by the kite.(Round your answer to one decimal place.)
6. A hawk flying 17 m/s at an attitude of 204m accidently drops its prey. The parabolic trajectory of failing prey is described by the equation.
y = 204-x^2/51
until it hits the ground, where y is its height above the ground and x is its horizontal distance traveled in meters. Calculate the distance traveled by the prey from the time it is dropped until the time it hits the round. Express your answer correct to the nearest tenth meter.
7. Find the length of the arc of the curve from point P to point Q.
x^2 = (y-4)^3, P(1,5), Q(27,13)

10. Set up, but do not evaluate, an integral for the length of the curve.
y = 7cosx, 0<=x<=2pi
11. Y =xe^x^8 0<=x<=9