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- The radius r, in inches, of a spherical balloon isrelated to the volume, V, by r(V)=3V43 . Air is pumped into the balloon, so the volume after t seconds is given by V(t)=10+20t . a. Find the composite function r(V(t)) . b.Find the exact time when the radius reaches 10 inches.ver the following A) Show that: (r,y)-32y-y-7r is a harmonic function and find the harmonic conjugate function u(x,y).Q1: For v = 2x2y+x²y-y³, check the function for Harmonic and then find f(z).
- The height above the ground of a rider on a Ferris wheel can be modelled by the sinusoidal function h=4sin(3.44t+0.58)+13 where hℎ is the height of the rider above the ground, in metres, and t is the time, in minutes, after the ride starts Based on the sinusoidal function, the maximum height of the rider above the ground, to the nearest meter, isThe number of daylight hours, d, can be modeled as a function of the day of the year by the equation d (t) = 3.5 sin +12.2, where t represents the number of days since March 21st. Which of the following 365 represents the minimum number of daylight hours predicted by this model? (1) 7.2 (3) 8.7 (2) 8.1 (4) 9.22. In each case, write the function f(z) in the form f(z) = u(x, y) + iv(x, y): 7.² (a) f(z) = z³ +z+1; (b) f(z) = (z = 0). Z Suggestion: In part (b), start by multiplying the numerator and denominator by z. Ans. (a) f(z) = (x³ - 3xy² + x + 1) +i (3x²y - y³ + y); x³ - 3xy²y³ - 3x²y 3 +i x² + y² x² + y² (b) f(z) =
- 2) Differentiate and simplify: f(t) = 2et e 2t + 1Evaluate f(x) = x°+6x, (fof)(3) =? O 91,395 O 2025 O 45 O 90Zack's position on a Ferris wheel can be modelled by the function h(t) = 25.4sin(1.8t + 4.0) + 24.2 Where: • h(1) represents his height in metres • 1 represents the time in minutes. a) What is the maximum height of the Ferris wheel? b) What is the period of rotation of the Ferris wheel, to the nearest tenth of a minute?
- a.) Calculate L6 for f(x)= (squareroot (9x+1)) over [1,3] Give answer to three decimal places L6= b.) Calculate R5 for f(x)=3x^2+5x over [-1,1] (Give an exact answer. Use symbolic notation and fractions where needed.) R5= c.) Calculate M6 for f(x)=(squareroot(2x)) over [2,5] (Use decimal notation. Give your answer to two decimal places.) M6=1. a) Copy and complete the table below: Original Function First derivative Second Derivative f(t) = -5° Original Function First derivative Second Derivative fG)-100 b) After completing the table in part 1 a) above, copy and complete the table below by stating the name of EACH function used and their respective derivatives: h(p)--2³-p 2. a) Differentiate the function Q(p) = -2√/p³(e b) Hence or otherwise, determine Q'(1).Find the domain of the following function. 2 f(x,y)=√125-5x - 5y Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. 2 OA. {(x,y): x² + y² z 2 2 OB. {(x,y): x +y # OC. {(x,y): x* OD. {(x,y): x² + y² s 2 2 O E. R² and y # (Use a comma to separate answers as needed.)
