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Question: Make the given changes in the indicated examples of this section and then solve the resulting problems.
In Example, change the coefficient of x on the left from 3 to 5 and then find the solution graphically.
Example: Solving quadratic equation graphically
Solve the equation 3x = x(2 - x) + 3 graphically. First, collect all terms on the left of the equal sign. This gives x2 + x - 3 = 0. We then let y = x2 + x - 3 and graph this function. The minimum point is (-1/2, 13/4) and the -intercept is (0,-3) Using the calculator, these points help us choose the window settings shown for
the graph of the function in Fig. Now, using the zero feature twice, we find the roots to be approximately
x = -2.3028 and x = 1.3028
Find the equation for the cubic function, f(x), with roots at 5, 4 and -4, and has a y-intercept at (0,3)
The two cars combined drive a total of 1775 miles, and the sum of their fuel efficiencies was 60 miles per gallon. What were the fuel efficiencies of each of the cars that week?
A 140 in. piece of wire is divided into two pieces and each piece is bent into a square. How should this be done in order to minimize the sum of the areas of the two squares?
scores on a statewide standardized test are normally distributed with a mean of 12.89 and a standard deviation of 1.95.
A number is divisible by 2 if the last digit is divisible by 2. A number is divisible by 4 if the last two digits form a number divisible by 4. A number is divisible by 8 if the last three digits for a number divisible by 8.
Calculate and interpret the coefficient of determination
In how many ways can all the trees be distributed and planted if the trees are distinct, any family can get any number, and a family must plant its trees in an evenly spaced row along the road?
Applying principles of probability, how can we improve random number generators and make them more unpredictable and thus more realistic? Share your thoughts and possible scenarios.
Suppose we are given the following programming segment:
Find the area of the region bounded by the graph of y = (x2 - 5x + 6)e2x and the x-axis. Find the volume of the solid obtained when the region under the graph of y = sin-1(x/ 2) for 0 ≤ x ≤ 2 revolved around the y-axis.
Of all numbers whose sum is 50, find the two that have the maximum product. That is, maximize Q=xy, where x+y=50
Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues.
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