OC userin Mathematics·23 Dec 20173 Problem 9. Find all solutions to the following system of equations: 2 - + + 2y 2y 6y = + + Coco 4z = A) X= -4, y = -3.5, 2 = 0; B) <=3+2y, y arbitrary, z arbitrary; x=3+2y, y arbitrary, z=0; D) x = 3 – 7, y=-zz, z arbitrary; E) NO solution; F) none of these.
OC userin Mathematics·23 Dec 20177. Consider the region bounded by y = r, y = 1 and 2 = 4. Set-up, but do not evaluate, integrals to find the following: (a) Area of region (b) Volume of solid obtained by rotating the region around the x-axis. (c) Volume of solid obtained by rotating the region around the y-axis. (d) Volume of solid obtained by rotating the region around the line y = 1. (e) Volume of solid obtained by rotating the region around the line <= 5.
OC userin Mathematics·22 Dec 2017[5] 8. Let V = {x,y} be a set with exactly two vectors, r and y. Define vector addition and scalar multiplication in V by the following rules: Vector addition: 2+r= x, y + y = 1, + y = y, and y + x = y. Scalar multiplication: cx = I, and cy = y for all c ER Prove that V is not a vector space by finding one axiom in the definition of a vector space that fails to hold. You must state the axiom clearly and show it does not hold.
OC userin Mathematics·21 Dec 2017On Main Street, there are three traffic lights which operate independently. Each light is red for 1 minute and not red for 4 minutes. If a car travels down Main Street, what is the probability the car will meet exactly two red lights? a) 0.032 b) 0432 c) 0.096 d) 13 e) 0.144 0.288 B) none of the others
OC userin Mathematics·21 Dec 20177. Let p(x) = 3x4 – 2r3 + x – 5. (d) Find the coordinates of the points of intersection of the graphs of p(x) and q(X) = 34 – 4x2 + 3x – 5.
OC userin Mathematics·22 Dec 2017PROBLEM 15: For three consecutive weeks, the Big Ten Player of the Week is either Eric Gordon or DJ White. If the selection each week is made by randomly choosing between the two players, and it is known that Eric Gordon is chosen at least once, what is the probability that he is chosen at most two times? A) 1/2 B) 6/7 C) 2/3 D) 3/4 E) none of the above
OC userin Mathematics·21 Dec 2017(c) You invest $P at the beginning of the year 2000 at an interest rate of 5%. What must P be in order to be able to withdraw $10000 at the beginning of 2010, then $20000 at the beginning of 2020?
OC userin Mathematics·21 Dec 2017(m) Letſ be a differentiable function such that f(3) = 2 and f'(3) = 5. If the tangent line to the graph off at a = 3 is used to approximate f(x), then an approximate solution for x to the equation f(x) = 0 is (A) x = 0.4 (B) x = 0.5 (C) x = 2.6 (D) x= Answer:
OC userin Mathematics·19 Dec 2017[3] 3. (a) Find the indefinite integral re dr. [4] (b) Evaluate the integral (* In 1 dr. J (c) Evaluate the integral sin rd.r.
OC userin Mathematics·19 Dec 20177. Let p(x) = 3x4 – 2r3 + x – 5. (C) Find the quotient ? 2 + . State the quotient and residue. 1
OC userin Mathematics·19 Dec 20177. Suppose a function f has a local maximum at r=0 with f(0) = 4, f"(x) > 0 for 2 € (-1,0) and f"(x) > 0 for x = (0,2). What can you say about f'(0)? Hint: It might help to try to sketch the graph of f(x) near x = 0.
OC userin Mathematics·18 Dec 2017(4) A spherical balloon is inflated at a rate of 5cm3/s. At what rate is its radius increasing, when the balloon is 30 cm in diameter? Hint: The volume of a sphere is given by V =
OC userin Mathematics·20 Dec 20174. A computer randomly prints a three-digit string of numbers. The string consists only of the digits 0, 1, 2, or 3 and satisfies the extra condition that the sum of its digits is 3. As an example, 021 is one such string. e. Use your answers from part d. to find the probability P(G) of selecting a 0 digit from any randomly printed string.
OC userin Mathematics·17 Dec 20175. Evaluate the following expressions. (e) p(-3), where p(x) = 24 – 3x2 + 8x – 2, using the remainder theorem.