Work out the following without a calculator (show working out) please help 144x6^-2
1 answer:
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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.
The linear equation for the given situation is represented as:
20x + 12y = 1,300
correct answer option: b
<h3>What is a linear equation with two variables?</h3>A general linear equation in two variables is defined as an equation of the form ax + by + c = 0, where x and y are the two variables and a, b, and c are real numbers and a and b are non-zero (x and y).
Given:
We use variables to represent the cost of the big and the smaller boxes.
According to the question, let x be the selling price of the big boxes.
The selling price of the bigger boxes is y.
The total selling price of the smaller boxes is 20x.
The total selling price of the bigger ones is 12y.
Now we know he is making a profit of $1,300 on the total transaction.
Hence the linear equation in two variables for the given situation is represented as:
20x + 12y = 1,300
To learn more about linear equations in two variables visit:
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I understand that the question you are looking for is:
Jackson sells two types of toolboxes. he plans on selling them during a farming fair this weekend. He estimates he will sell 20 of the smaller boxes (X) and 12 of the larger boxes (Y). if he'd like the profit to be $1300, which of the following best displays the equation that represents this information?
A- y+12=20(x-1300)
B- y=- x+
C- 20x+12y=1300
D- 12y=20x-1300