I'll abbreviate the definite integral with the notation,
We're given
Recall that the definite integral is additive on the interval ![[a,b]](https://tex.z-dn.net/?f=%5Ba%2Cb%5D)
, meaning for some ![c\in[a,b]](https://tex.z-dn.net/?f=c%5Cin%5Ba%2Cb%5D)
we have
The definite integral is also linear in the sense that
for some constant scalars 
.
Also, if 
, then
a. 
b. 
c. 
d. 
e. 
f. 
Answer:
Here's what we know:
A = Lw (Area is length times width)
L = 2w + 6 (length is twice the width plus 6)
A = 140 (Area is 140 m2)
Plug in the variable values:
140 = w(2w + 6)
Distribute:
140 = 2w2 + 6w
Subtract 140:
2w2 + 6w - 140 = 0
Factor out a 2:
2(w2 + 3w - 70) = 0
Divide both sides by 2:
w2 + 3w - 70 = 0
(w + m)(w - n)
When we factor out the quadratic, we know it's going to be a +/- situation because the c value in the quadratic is negative, and the two numbers are going to be three away, the plus next to the 3 meaning that the larger number is going to be positive:
(w + 10)(w - 7) = 0
w = -10, 7
We can't have a negative length, so we can toss out the -10, leaving us with w = 7 meters.
L = 2 * 7 + 6
L = 14 + 6
L = 20
Check:
140 = 20 * 7
140 = 140
Answer: 4 Ounces.
Step-by-step Explanation: I don't know the full context of the problem, but if Seth used 4 ounces, that means that he used 4 ounces all together.
The answer should be A. If you need work I can show you.
