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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.a. -5sinx b. -5sin(0.05x) c. -5sin(5x) d. -5sin(50x)Write f(t) = 7e.8t in the form f(t) = Pob' and determine Po and b. (Give exact answers using symbolic notation and fractions if needed.) Po = b =
- 3- Solve for x+4|>2|x−1| 4- For the function y=sinx, shift the function by units to the left and stretch 4 units in the vertical direction. Graph the resulted function.Algebra with step by step working required2. 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) =
- Using a calculator, pencil and paper, apply the bisection method to find a root of y=f(x)=1-2x cosx by filling in a table of the form shown below. For the “sign" columns enter + or – sign f (a) sign f (x) b sign f (b) а 0.5 0.7 In each row x=(a+b)/2 . Once the table is complete, report your best estimate of the root in the form r±d.do only A). Find the composition of function and its domain.2. Determine whether these are well-defined functions. Explain. 3 (a) f:R → R, where f(x) = x² + 5° 7 (b) g: (5, 0) → R, where g(x) = 4 (c) h:R → R, where h(x) = –/7 – 4x + 4x². |
- A child builds two wooden train sets. The path of one of the trains can be represented by the function y = 2cos²x, where y represents the distance of the train from the child as a function of x minutes. The distance from the child to the second train can be represented by the function y = 3 + cos x. What is the number of minutes it will take until the two trains are first equidistant from the child? a b C d 6 minutes n minutes 1 minute 1.5 minutes(d) Determine of the behavior of tm and ym as B → 00. Enclose arguments of functions in parentheses. For example, sin (2x).