Calculus Answers

you have been given the mathematical model to calculate velocity of a car accelerating from rest in straight line: v(t) = A (1-e ^ - t/tmaxspeed) (anything after the symbol ^ is to the power of) v(t is instantaneous velocity of car (m/s), t is time in seconds, tmaxspeed is time to reach maximum speed in seconds and A is constant. you are given the information that t (0-28 m/s) is 2.6s, t (400m) is 10.46s & tmaxspeed is 7s. please derive an equation a(t) for the instantaneous position of the car as a function of time? Identify the acceleration of the car at t = 0s and asymptote of this function as t → ∞?

you have been given the mathematical model to calculate velocity of a car accelerating from rest in straight line: v(t) = A (1-e ^ - t/tmaxspeed) (anything after the symbol ^ is to the power of) v(t is instantaneous velocity of car (m/s), t is time in seconds, tmaxspeed is time to reach maximum speed in seconds and A is constant. you are given the information that t (0-28 m/s) is 2.6s, t (400m) is 10.46s & tmaxspeed is 7s. please explain and derive an equation x(t) for the instantaneous position of the car as a function of time.....identify the value of x when t=0s ? and asymptote of this function as t → ∞?

Convert the following vectors;
75 m/s on a bearing of 295° to Cartesian form
[-3, -8] to direction/magnitude form

Evaluate using root test.

Infinity

Summation sign (1- 1/k)^k

k = 1

Assume that a spherical raindrop evaporates at a rate proportional to its surface area. If its radius
originally is 3 mm, and one-half hour later has been reduced to 2mm, find an expression for the
radius of the raindrop at any time.

Obtain and classify the relative extrema values of the function F(x,y)=x³+y³-63(x+y)+12xy

Integrate tan³x dx using reduction method

Integrate sin³x dx using reduction method

Integrate dx/(4+x²)½ using trigonometric substitution

Integrate x²dx/(9-x²)½ using trigonometric substitution