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.
Answer:
x ≤ 207 crates
Step-by-step explanation:
Greatest weight of the container = 27,500 kilograms
Weight of other shipment = 6,800 kilograms
Weight of a crate = 100 kilograms
Number of 100-kilogram crates that can be loaded into the shipping container = x
The inequality is
27,500 ≤ 6800 + 100x
27,500 - 6800 ≤ 100x
20,700 ≤ 100x
x ≤ 20,700 / 100
x ≤ 207 crates
Answer: The quotient is (2x+1)
Step-by-step explanation:
Here, the dividend = 
Divisor = 
By the long division method for finding the quotient we will follow the following steps,
Steps 1 : Write dividend inside the division sign and divisor outside the division sign,
Step 2: Multiply the divisor by 2x and subtract the result by the dividend,
Step 3: Now, again multiply the divisor by 1,
Step 4: Subtract the result by the remaining dividend,
Since, further division is not possible,
Hence, the sum of all terms that are multiplied = 2x+1
Which is our quotient.
Answer:
The vertical distance is 1.
Explanation:
Coordinates are structured as ( x , y )
The "x" is horizontal and the "y" is vertical, when placed onto a graph.
In the question, 8 is "x" and 1 is "y". Meaning the vertical number is 1.
Answer:
£342,000
Step-by-step explanation:
190,000 x 1.8=342,000
for 1 year
