The amount of energy needed to increase the radius of orbit of a 500-kg satellite from its original orbit r-10 000 of radius 10 000 km can be modelled by the function E = 2×10" where E is the energy, in Joules, and r is the new radius, in kilometers. a) How much energy must be given to the satellite ifr= 12 000 km? b) Calculate the new radius of the satellite if 10º Joules of energy are added to it. c) How much energy must be given to the satellite in order for it to escape Earth’s gravity completely (make its orbit's radius infinitely large)?

Q: A hot-air balloon rises straight up at a constant speed of 20 feet/sec. An observer stands 200 feet…

A: The speed of the balloon is dydt=20 ft/s2=VyThe distance between observer and launchingpoint, x=200…

Q: Linlo rode her scooter for 1/3 hour and traveled 2 1/6 kilometers. What is her average speed in…

A: To determine the average speed.

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A:

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A:

Q: iv) v) Calculate the voltage in the capacitor after 5 and 30 seconds. Determine the rate of change…

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Q: 2. Write the formula for area of a circle: (a) Which two variables are related by this formula? (b)…

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Q: Solve the formula for the variable t   h= 1/2gt^2 *Only the t here is squared

A: Given the data

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.