Symbolic answers must be entered using notation similar to the examples given below. If you enter decimal numbers for questions that indicate that a symbolic answer is required, it will be marked as zero, regardless of whether the decimal number is correct or not. Integer numbers (positive, negative, and O) are allowed. Below are some examples. Example Math Expression How to Enter the Answer 2 -3/5 infinity 2\"8+l 2+exp(5) 5*pi/9 4/7-3*ln (2) sqrt(2) 5"(l/3) sqrt(5exp(3)+2*ln(7*pi)) fac(5) PrOblem # 1: A gate in an irrigation canal is constructed in the form of a trapezoid 7 In wide at the bottom, 25 In wide at the top, and 2 In high. It is placed vertically in the canal so that the water just covers the gate. Find the hydrostatic force on one side of the gate. Note that your answer should be in Newtons, and use g = 9.8 m/sz. I Just Save I I Submit Problem #1 for Grading Problem #1 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: PI'Oblem # 2: Check which one of the following functions is a solution to the differential equation y" - y = sin x. (A) %(sinx x cos x) (B) %(sinx + x cos x) (C) % (ex - cos x) (D) %(ex sinx) (E) %(ex + cos x) l cosx+xsinx 2 Problem #2: I Just Save I I Submit Problem #2 for Grading Problem #2 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: PI'Oblem # 3: For what two values of r does the lnction y = e 'x satisfy the differential equation y\"-y'-6y=0? Problem #3_ l:! If there is only one value of r then enter it ' twice, separated with a comma (e.g., 12,12). I Just Save I I Submit Problem #3 for Grading Problem #4: By inspecting the following differential equation and its properties, determine which of the given graphs could be the graph of a solution to the equation. y' =e y+ sinx (A) 2- (B) y 0.5 0 2 N (C) (D) Z 3 y V - 6 -4 -2 - 1 5 5 10 -2 (E) 1 (F) A y 0.5 N 2 3 X Problem #4: Select vProblem #5: Let y(x) be the solution to the following initial value problem. dy (In .x)S dx *1/ 2 y(1) = 1 Find y(e). Enter your answer symbolically, Problem #5: as in these examples Just Save Submit Problem #5 for Grading Problem #5 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #6: Find the orthogonal trajectories of the family of curves y' = kx3. ( A ) 213 + 2 x2 = C ( B) 213 + 2 x2 = C ( C) 12 + 2 x2 = C (D) 312 + 2x2 = C (E) 2,3 + 3x3 = C 212+383 - C (G) 312 + 2x2 - C (H) 3y3 + 3x3 = C Problem #6: Select v Just Save Submit Problem #6 for Grading Problem #6 |Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #7: A sample of tritium-3 decayed to 75% of its original amount after 2 years. How long would it take the sample (in years) to decay to 22% of its original amount? Enter your answer symbolically, Problem #7: as in these examples