y 0.8 0.6 0.4 0.2 -0.2 -0.4 -0.6 -0.8 -14 -0.8 -0.6 -0.4 -0.2 0 0.2 Figure 1.3E.1 A direction field for y' 0.4 = บ HP 0.6 0.8

a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t, where x is the horizontal direction and y is the upward direction. the projectile lands after  a. 16 seconds b. 8 seconds c. 4seconds

(e) The instructor adds 4 points to the average exam score ofeveryone in the class. Describe the changes in the positionsof the plotted points and the change in the equation of theline.

Find y in terms of x. dy 12x(3x 2 - 1)3, curve passes through (1, -3) dx y = (3x 2. 1)4 B y= (3x 2 - 1) 4 - 3 © y= (3x 2-1) 4 - 11 y = (3x 2 - 1) 4 - 19

10. The pendulum of a Grandfather clock completes 20 cycles/minute. It moves a horizontal distance of 30 cm. Write a sinusoidal function which expresses the movement of the pendulum assuming the pendulum starts at the farthest left position at the beginning. 30

According to the following data: (0,0), (0.2, 1), (0.4, 3), (0.6, 5), (0.8, 7), (1.0, 5), (1.2, 3) find the first derivative at point 0.6 by using the following stencil form. * i-2 i-1 i ÖÖÖÖÖ -10 3 -2 6hD= -9 The value is -18 The Value is -15 O the value is -16 the Value is -17 O No one i+1 i+2 4

Q2/ Defined x as 100 linearly spaced values between -2n to 2n. Defined y1 and y2 as sine and cosine values of x. create a line plot of both sets of data &add a title to the graph.

13. Find. themodimum.rabe.f.change.of.f.(xg}= Sin Xy at.P.C.l.p.o)...and. the directan..w.hich.it.o.cenr.s..

A tornado can be represented in polar cords by the velocity 7 =4 +ig. Show that streamline from logarithmic A = Ce. 020

SOLVE STEP BY STEP IN DIGITAL FORMAT Determine the equations of the lines tangent and normal to the curve defined by x² + 4xy + y² = 13 at the point (2,1). mmmmmm