Exercise 02 - CE18

EXERCISE 02 – CE 18 – CORRELATION COURE1 DIRECTIONS: SOLVE THE FOLLOWING PROBLEMS. SHOW YOUR SOLUTION AND BOX YOUR FINAL ANSWER. SUBMIT YOUR SOLUTION AND ANSWER IN PDF OR JPEG FORMAT. Problems: 1. Determine the radius of curvature of the curve x=y3 at point (1, 1). 2. Calculate the area enclosed by the curve x2+y2−10x+4y−196=0. 3. The first three terms of a geometric progression are 2x, 4x + 14 and 20x - 14. Find the sum of the first ten terms. 4. A 50-m steel tape that is is 0.02 m too long was used to measure the distance between two points A and B. If the measured distance was 160.42 m, calculate the correct distance between A and B. 5. A circle has an equation of x2+y2+2cy=0. Find the value of c when the length of the tangent from (5, 4) to the circle is equal to one. 6. Calculate the acute angle between two intersecting surfaces whose equations are as follows: 2x−4y−z=−5 3x+4y+5z=−6 7. The digits of a three-digit number are in arithmetic progression. If you divide the number by the sum of its digits, the quotient is 26. If the digits are reversed, the resulting number is 198 more than the original number. Find the sum of all the digits. 8. There are 7 arithmetic means between 3 and 35. What is the sum of all the terms? 9. A boat going upstream takes 1.5 times longer than going the same distance downstream. If the water current in the river is 8 kph, calculate the speed of the boat in still water. 10. What is the equation of the normal to the curve x 2+y2=25 at (4, 3)? 11. What is the radius of the circle x2+y2−6x=0? 12. When the polynomial x4+bx3+5x2+dx+6 is divided by x−2 the remainder is 16. When it is divided by x+1 the remainder is 10. Find the value of constant d. 13. Gas is escaping from a spherical balloon at a constant rate of 2 ft 3/min. How fast, in ft2/min, is the outer surface area of the balloon shrinking when the radius is 12 ft? 14. Determine the percentage uncertainty in the area of a square that is 6.08 ± 0.01 m on a side. 15. In still water, your small boat averages 8 miles per hour. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. What is the rate of water's current?

PREPARED BY: ENGR. RUEL CATAPANG