Assignment
1 answer:
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Answer:
9 bottles of soda and 7 bottles of juice
Step-by-step explanation:
Let x be the number of bottles of soda purchased and y be the number of bottles of juice purchased.
1. Gabriel purchased 2 more bottles of soda than bottles of juice, then
2. Each bottle of soda has 35 grams of sugar, then there are 35x g of sugar in x bottles of soda.
Each bottle of juice has 10 grams of sugar, then there are 10y g of sugar in y bottles of juice.
In total, there are 35x+10y g of sugar.
All bottles collectively contain 385 grams of sugar, thus
3. Solve the system of two equations:
Substitute the first equation into the second equation:
Answer:
-2, 8/3
Step-by-step explanation:
You can consider the area to be that of a trapezoid with parallel bases f(a) and f(4), and width (4-a). The area of that trapezoid is ...
A = (1/2)(f(a) +f(4))(4 -a)
= (1/2)((3a -1) +(3·4 -1))(4 -a)
= (1/2)(3a +10)(4 -a)
We want this area to be 12, so we can substitute that value for A and solve for "a".
12 = (1/2)(3a +10)(4 -a)
24 = (3a +10)(4 -a) = -3a² +2a +40
3a² -2a -16 = 0 . . . . . . subtract the right side
(3a -8)(a +2) = 0 . . . . . factor
Values of "a" that make these factors zero are ...
a = 8/3, a = -2
The values of "a" that make the area under the curve equal to 12 are -2 and 8/3.
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<em>Alternate solution</em>
The attachment shows a solution using the numerical integration function of a graphing calculator. The area under the curve of function f(x) on the interval [a, 4] is the integral of f(x) on that interval. Perhaps confusingly, we have called that area f(a). As we have seen above, the area is a quadratic function of "a". I find it convenient to use a calculator's functions to solve problems like this where possible.
