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Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting.
1. Imagine you are in the market for a new home and are interested in a new housing community under construction in a different city.a. The sales representative informs you that there are 48 houses for sale with two floor plans still available. Use x to represent floor plan one and y to represent floor plan two. Write an equation that illustrates the situation.
b. The sales representative later indicates that there are three times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in Part a.
c. Use the equations from Parts a. and b. of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem.
d. What are the intercepts of the equation from Part a. of this problem? What are the intercepts from Part b. of this problem? Where would the lines intersect if you solved the system by graphing?
Calculate the given quantities if a = , b= , and c= . Determine whether a and b are parallel, perpendicular or neither.
What is the maximum that Ernesto should be willing to pay to play this game if he wants to be sure that on average, if he plays very many times, he shouldn't lose money?
A rectangular parcel of land has an area of 5000 ft^2. A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. What are the dimensions of the land, rounded to the nearest foot?
For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v^3. It is believed that migrating fish try to minimize the total energy required to swim a fixed distance.
Solve this linear problem graphically and determine optimal quanitities of A, B, and value of Z.
Determine if the given set constitutes a real vector space. The operations of "multiplication by a number" and "addition" are understood to be the usual operations associated with the elements of the set:
How much would a brand manager in Los Angeles have to make in order to have a higher salary than 99% of the brand managers in Houston?
The trigonometric expression to estimate the value
Let f:R->R be a function that satisfies f(x+y) = f(x)+f(y) for all x,y in R. Suppose that f is continuous on R and that f(1)=k. Prove that f(x)=kx for all x in R.
Verify stokes theorem
Four positive numbers, each less than 80, are rounded to the first decimal place and then multiplied together. Use differentials to estimate the maximum possible error in the computed product that might result from the rounding.
The minute hand on a watch is 5 mm long and the hour hand is 4 mm long. How fast is the distance between the tips of the hands changing at one o'clock? (Round your answer to one decimal place.)
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