The speed of sound in air changes with the temperature. When the temperature 7 is 32 degrees Fahrenheit, the speed S of sound is 1087.5 feet per second. For each degree increase in temperature, the speed of sound increases by 1.1 feet per second. (Round your answers to two decimal places.) (a) Explain why speed S is a linear function of temperature T. Because S always increases by 1.1 when 7 increases by ,Shas a constant rate of change and is a linear function of T. Identify the slope of the function. (b) Use a formula to express S as a linear function of T. (c) Solve for 7 in the equation from part (b) to obtain a formula for temperature T as a linear function of speed S.

Q: The function models variation in body temperature, y, in °F, x hours after midnight. a. What is body…

A: Consider the given equation: y=98.6+0.3sinπ12x-11π12 Where The function models variation in body…

Q: Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high…

A: The equation of a sinusoidal function of amplitude A, phase difference C, vertical shift D, time…

Q: Find an equation to model the vertical motion of the tip of a second hand on a clock, if the second…

A:

Q: The grade of one of America's steepest roads is 37%. When walking from point A to point B, a total…

A:

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.