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Chapter 11: Q. 77 (page 774)
The ratio of a to b is. The sum of a and b is . What is the ratio of to ?
The ratio is .
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Descartes鈥檚 Method of Equal Roots: Descartes鈥檚 method for finding tangents depends on the idea that, for many graphs, the tangent line at a given point is the unique line that intersects the graph at that point only. We apply his method to find an equation of the tangent line to the parabola at the point (2,4). See the figure.
First, we know that the equation of the tangent line must be in the form . Using the fact that the point is on the line, we can solve for b in terms of m and get the equation . Now we want to be the unique solution to the system
From this system, we get . By using the quadratic formula, we get
To obtain a unique solution for x, the two roots must be equal; in other words, the discriminant must be 0.
Complete the work to get m, and write an equation of the tangent line.
A movie theater charges \(9.00 for adults and \)7.00 for senior citizens. On a day when 325 people paid an admission, the total receipts were $2495. How many who paid were adults? How many were seniors?
Ice Cream The Mom and Pop Ice Cream Company makes two kinds of chocolate ice cream: regular and premium. The properties of 1 gallon (gal) of each type are shown in the table:
In addition, current commitments require the company to make at least 1 gal of premium for every 4 gal of regular. Each day, the company has available 725 pounds (lb) of flavoring and of milk-fat products. If the company can ship no more than 3000 lb of product per day, how many gallons of each type should be produced daily to maximize profit?
A cookie company makes three kinds of cookies, oatmeal raisin, chocolate chip, and shortbread, packaged in small, medium, and large boxes. The small box contains dozen oatmeal raisin and dozen chocolate chip; the medium box has dozen oatmeal raisin, dozen chocolate chip, and dozen shortbread; the large box contains dozen oatmeal raisin, dozen chocolate chip, and dozen shortbread. If you require exactly dozen oatmeal raisin, dozen chocolate chip, and dozen shortbread, how many of each size box should you buy?
True or False If any row (or any column) of a determinant is multiplied by a nonzero number k, the value of the determinant remains unchanged.
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