Calculus Answers

Hi, my daughter is trying to solve a grade 12 calculus (I think) problem. Can you help us with how to think through this?
As as side business, Santa creates and sells red wagons. Santa can sell 30 red wagons at $20 each per week. If the price is increased, for each dollar increase there will be a loss of one sale per week. The cost to create a wagon is $10 each. What price will give Santa maximum profit?

Thanks!

Velocity car accelerating from rest in straight line. Equation is v(t) = A (1-e ^ -t/t max speed) the ^ means to power of. v(t) is instantaneous velocity of car (m/s), t is time in seconds, tmaxspeed is time to reach the max speed in seconds and A is a constant. given the information that car has a t(0-28m/s) of 2.6s, a t(400m) of 10.46s, and a tmaxspeed of 7s (s stands for seconds. coefficient A are said to be a unit same as velocity, that is, m/s. physical meaning of A is Terminal Velocity(as t tends to infinity, velocity tends to A). velocity of the car at t=0 and 4 is v(t) = A (1-e ^ -t/t max speed), A(1-e ^ -(2.6/7) ) = -28, A(0.31) = -28, A= -28/0.31 = -90.322m/s, v (0) = A(1-1) = 0 m/s. The asymptote of this function as t ⮕ ∞ is y = -90.322. 1. Sketch a graph of acceleration vs time? 2. Apply mathematical model. Use the given data for the 0-28 m/s and 400m times to calculate the: value of the coefficient A, maximum velocity and maximum acceleration?

Velocity of car accelerating from rest in straight line. Equation, v(t) = A (1-e ^ -t/t max speed) the ^ means to power of. v(t) is instantaneous velocity of the car (m/s), t is time in seconds, tmaxspeed is time to reach maximum speed in seconds, A is a constant. We are given the information that car has a t(0-28m/s) of 2.6s, a t(400m) of 10.46s, and a tmaxspeed of 7s (S stands for seconds in this instance). The coefficient A are said to be a unit same as the velocity, that is, m/s. The physical meaning of A is Terminal Velocity(as t tends to infinity, velocity tends to A). The velocity of the car at t=0 and 4 is v(t) = A (1-e ^ -t/t max speed), A(1-e ^ -(2.6/7) ) = -28, A(0.31) = -28, A= -28/0.31 = -90.322m/s, v (0) = A(1-1) = 0 m/s. The asymptote of this function as t ⮕ ∞ is y = -90.322. 1. Sketch a graph of position vs time? 2. Derive an equation a(t) for the instantaneous acceleration of the car as a function of time? Identify the acceleration of the car at t= 0s and asymptote this function as t ⮕ ∞?

Velocity of car accelerating from rest in straight line. Equation v(t) = A (1-e ^ -t/t max speed) ^ means to the power of. v(t) is the instantaneous velocity of the car (m/s), t is time in seconds, tmaxspeed is time to reach the maximum speed in seconds and A is a constant. We are given the information that the car has a t(0-28m/s) of 2.6s, a t(400m) of 10.46s, and a tmaxspeed of 7s (S stands for seconds in this instance). The coefficient A are said to be a unit same as the velocity, that is, m/s. The physical meaning of A is Terminal Velocity(as t tends to infinity, velocity tends to A). The velocity of the car at t=0 and 4 is v(t) = A (1-e ^ -t/t max speed), A(1-e ^ -(2.6/7) ) = -28, A(0.31) = -28, A= -28/0.31 = -90.322m/s, v (0) = A(1-1) = 0 m/s. The asymptote of this function as t ⮕ ∞ is y = -90.322. 1. Sketch a graph of velocity vs time? 2. 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 this function as t ⮕ ∞?

Using the mathematical model: to calculate velocity of a car accelerating from rest in straight line. Equation is v(t) = A (1-e ^ -t/t max speed) the ^ means to the power of. v(t) is the instantaneous velocity of the car (m/s), t is the time in seconds, tmaxspeed is the time to reach the maximum speed in seconds and A is a constant. We are given the information that the car has a t(0-28m/s) of 2.6s, a t(400m) of 10.46s, and a tmaxspeed of 7s (S stands for seconds in this instance) 1. Identify the units of the coefficient A, 2. physical meaning of A, 3. velocity of the car at t=0 and 4. asymptote of this function as t ⮕ ∞?

1.Use a triple integral to find the volume of the region bounded by z= 7x+8y, z=9, and the planes x=0 and y=0. Give the exact answer in the form of a fraction.

1. Use a double integral to find the volume V of the solid that is common to cylinders x^2 + y^2 = 81 and x^2 + z^2 = 81. Find the exact number and no tolerance

2. Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate planes and the plane 9x+18y+8z = 144.

3. Use a triple integral to find the volume of the solid bounded by the surface y=x^2 and the planes x+z=8 and z=0.Give the exact answer in the form of a fraction.

1. Use a double integral to find the volume under the plane z=2x+y and over the rectangle R={(x,y) : 8 ≤ x ≤ , 3 ≤ y ≤ 4}.

2. Use a double integral to find the volume of the solid enclosed by the surface z= x^2 and the planes x=0, x=6, y=6, y=0, and z=0.

3. Use double integration to find the volume of the solid bounded by the cylinder x^2 + y^2 = 9 and the planes z=0 and z= 3-x.

Trace the curce
Y=(x-2)(x+1)^2

suppose that a company manufactures flash drives has a revenue of given by: R(x)10x-.001x^2
where the production output in 1 week is x flash drives. If production is increasing at a rate of 650 flash drives per week when production is 6000 flash drives find the rate of increase in revenue.