What equation relates the radius of the balloon to the quantity of air in the balloon?

What equation relates the radius of the balloon to the quantity of air in the balloon?

1: As the balloon is being filled with air, both the radius and the volume are increasing with respect to time. V=43πr3cm3. V(t)=43π[r(t)]3cm3.

How do you create a related rate problem?

1. Draw a picture of the physical situation. Don’t stare at a blank piece of paper; instead, sketch the situation for yourself.
2. Write an equation that relates the quantities of interest.
3. Take the derivative with respect to time of both sides of your equation.
4. Solve for the quantity you’re after.

What is happening if the airplane is flying at constant altitude?

There are four major forces acting on an aircraft; lift, weight, thrust, and drag. If we consider the motion of an aircraft at a constant altitude, we can neglect the lift and weight. A cruising aircraft will fly at a constant airspeed and the thrust will exactly balance the drag of the aircraft.

How do related rates work?

In differential calculus, related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known. The rate of change is usually with respect to time.

Is the radius changing more rapidly when $$D 12 or when$$ D 16?

$$\frac{dr}{dt}=\frac{5}{64\pi}$$ inches per second when the diameter is 16 inches. Thus, the radius is changing more rapidly when the diameter is 12 inches.

How do you find the radius of a balloon?

If you assume that the balloon is spherical you can fill a bucket completely with water, gather the volume it displaced and measure it. Then you use the formula V=43πr3 to get the radius.

How fast is area of triangle changing?

The altitude of a triangle is increasing at a rate of 1.500 centimeters/minute while the area of the triangle is increasing at a rate of 3.000 square centimeters/minute.

What are related rate problems?

Related rates problems are word problems where we reason about the rate of change of a quantity by using information we have about the rate of change of another quantity that’s related to it. Let’s get acquainted with this sort of problem.

Can related rates be negative?

A negative answer tells us that that the quantity is decreasing and positive tells us it’s increasing. In some books all rates are positive in the final answers, even if the quantity is decreasing (the negative is inferred from inclusion of the word “decreasing” in the problem).

How is an airplane flying at a constant elevation?

An airplane is flying overhead at a constant elevation of ft. A man is viewing the plane from a position ft from the base of a radio tower. The airplane is flying horizontally away from the man.

How to calculate the height of an airplane?

Figure 4.1.2: An airplane is flying at a constant height of 4000 ft. The distance between the person and the airplane and the person and the place on the ground directly below the airplane are changing. We denote those quantities with the variables s and x, respectively.

How to calculate the distance between a person and an airplane?

The distance between the person and the airplane and the person and the place on the ground directly below the airplane are changing. We denote those quantities with the variables s and x, respectively. As shown, x denotes the distance between the man and the position on the ground directly below the airplane.

How is the speed of a plane related to distance?

The relationship we are studying is between the speed of the plane and the rate at which the distance between the plane and a person on the ground is changing. ft. A man is viewing the plane from a position 3000 ft from the base of a radio tower. The airplane is flying horizontally away from the man. If the plane is flying at the rate of 600