Kindly answer the following with solutions:

QUESTION 1 A particle is moving along a hyperbola xy = 8. As it reaches the point (4, 2) , the y-coordinate is decreasing at a rate of 3 cm/s. How fast is the x-coordinate of the point changing at that instant? O 6 cm/s O -6 cm/s O -5 cm/s 5 cm/s QUESTION 2 Where does the normal line to the ellipse x-xy + y'=3 at the point (- 1, 1) intersect the ellipse a second time? O (1,-1) O (2,1) O (-2, - 1) O (1,2)QUESTION 3- Two objects moving along x-axis are starting at the same time. Their positions are measured in centimeters at time f in seconds, If the equation of motion of objects and 2 are s, -212- 31 and s,= 3t-1 respectively, determine the distance between the objects at the instant when they have the same velocity. 4:cm O 3 cm 2 cm 1 cm QUESTION 4 Use differentials to approximate the value of 4.002 1999 8000 499 2000 999 4000 1997 $8000QUESTION 5 A projectile is shot vertically upward from a point 2 m above ground level with an initial velocity of 24.5 m/s. With what velocity does it hit the ground? O -26.7 m/s O -30.1 m/s O - 20.5 m/s O -25.3 m/s QUESTION 6 Given the function y = f(x) represented by the parametric equations x = 2 - 1 and y = 13 + 2, determine the equation of the tangent line at x = 3, t > 0. Oy+ 6=-3(x - 3) O y- 10=2(x - 3) O y+ 6 = 2(x -3) O y - 10 = 3(x - 3)QUESTION 7 One side of a right triangle is measured as 9:5 inches and opposite angle equal to 26 75" with 0.25" possible error. Using differentials, approximate the percent error in computing the length of the hypotenuse. O 50% O 0.87% O 0.45% O 33% QUESTION 8 A spherical balloon is being inflated. Find the rate of change of the surface area S with respect to the radius r when ? is 20 cm. 1600# cm-/cm 160x cm2/cm 20x cm /cm 80x cm-/cmQUESTION 9 The volume of a cylinder is fixed at a value of V. Find how fast the radius of the cylinder changes with respect to the height of the cylinder when the radiius and height are equal to each other. O -2 -1/3 0 -3 O-1/2 QUESTION 10 A cylindrical tank has radius 2'm and height 4 m. Water is being poured into the tank at the rate ir.my per minute. Find how fast the water rises when the tank is half-full, in-m/S. O 1/3 1/5 O 1/2 O 1/4