The traffic flow rate (cars per hour) across an intersection is r(t) = 400 + 800t – 120t, where t is in hours, and t=0 is 6am. How many cars pass through the intersection between 6 am and 7 am? cars

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A: The growth of the population of 500 bacteria is given by the equation

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A: To find the required t, we need to simplify the given integral

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A: Given, v(t)=t3-2t2   Interval [a,b]=[-2,3]

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Q: constant

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Q: y= lux of yoe Find DfR.

A: Explanation of the solution is given below...

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Q: SOLVE THE FIRST ORDER DE. (x³ + y*)dx + 8y³xdy = 0 when x = 4, y = 2

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Q: The traffic flow rate past a certain point on a highway is q(t) = 1300 + 2300t – 270r where t is in…

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Q: Identify f(x) to be used in variation of parameters to solve for y, e" y" + y' – 3y = x

A: To find f(x) write equation in form of y" + P y' +Q y = f(x).

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A: Find the rate at which this average cost is changing when 10 shirts are being produced.

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A: Explanation and solutions is given below....

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Q: r. Using differentials, approximate the percent error in computing the length of the hypotenuse.

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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.