Answer:
(b) I, III
Step-by-step explanation:
The correct answer can be chosen based on your knowledge of the shape of the graph of f(x).
<h3>General shape</h3>
The leading coefficient of this quadratic function being positive tells you the graph will be a parabola that opens upward. The left branch of the parabola will extend to positive infinity, as will the right branch.
If there are x-intercepts, the x-values between those will be where the graph has crossed the x-axis and function values are negative.
<h3>Specific shape</h3>
The answer choices suggest that x=2 and x=5 are x-intercepts of the function's graph. These can be checked, if you like, by evaluating f(2) and f(5).
f(2) = 2² -7·2 +10 = 4 -14 +10 = 0
f(5) = 5² -7·5 +10 = 25 -35 +10 = 0
This means the function will be positive for x < 2 and for x > 5. These intervals are described by I and III.
Kindly, check the attachment below to see the answer.
Multiply the first bracket by 6.
Multiply the second bracket by 8
6(x+1)-5x= 8+2(x-1)
6(x)+6(1)-5x= 8+2(x)+2(-1)
6x+6-5x= 8+2x-2
6x-5x+6= 8-2+2x
x+6= 6+2x
Move +2x to the other side. Sign changes from +2x to -2x.
x-2x+6= 6+2x-2x
-x+6= 6
Move +6 to the other side. Sign changes from +6 to -6.
-x+6-6= 6-6
-x=0
Multiply by -1 for -x and 0
-x(-1)= 0(-1)
x= 0
Answer: x= 0
First of all we need to find a representation of C, so this is shown in the figure below.
So the integral we need to compute is this:
So, as shown in the figure, C = C1 + C2, so:
Computing first integral:
Applying derivative:
Substituting this value into
Computing second integral:
Applying derivative:
Substituting this differential into
We need to know the limits of our integral, so given that the variable we are using in this integral is x, then the limits are the x coordinates of the extreme points of the straight line C2, so:
![I_{2}= -8\int_{4}^{8}}dx=-8[x]\right|_4 ^{8}=-8(8-4) \rightarrow \boxed{I_{2}=-32}](https://tex.z-dn.net/?f=I_%7B2%7D%3D%20-8%5Cint_%7B4%7D%5E%7B8%7D%7Ddx%3D-8%5Bx%5D%5Cright%7C_4%20%5E%7B8%7D%3D-8%288-4%29%20%5Crightarrow%20%5Cboxed%7BI_%7B2%7D%3D-32%7D)
Finally:
