Answer:
a) integral = 24.72
b) |Error| ≤ 0.4267
Step-by-step explanation:
a)
The integral:

can be approximated with the midpoint rule, as follows:
6.7*(0.8 - 0.0) + 8.9*(1.6 - 0.8) + 6.9*(2.4-1.6) + 8.4*(3.2 - 2.4) = 24.72
(that is, all the intervals are 0.8 units length and f(x) is evaluated in the midpoint of the interval)
b)The error bound for the midpoint rule with <em>n</em> points is:
|Error| ≤ K*(b - a)^3/(24*n^2)
where <em>b</em> and are the limits of integration of the integral and K = max |f''(x)|
Given that -5 ≤ f''(x) ≤ 1, then K = 5. Replacing into the equation:
|Error| ≤ 5*(3.2 - 0)^3/(24*4^2) = 0.4267
Answer:
24 units ^2
Step-by-step explanation:
The base runs from 3 to 7 so the base is 7-3 = 4 units
The height runs from 2 to 8 so the height is 8-2 = 6 units
The area is
A = bh
= 6*4 = 24 units ^2
Answer:
1. x=-6
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3(2x+3)−4x=−3
(3)(2x)+(3)(3)+−4x=−3(Distribute)
6x+9+−4x=−3
(6x+−4x)+(9)=−3(Combine Like Terms)
2x+9=−3
2x+9=−3
Step 2: Subtract 9 from both sides.
2x+9−9=−3−9
2x=−12
Step 3: Divide both sides by 2.
x=-6
Answer:
I believe it's enlargement
Step-by-step explanation:
because you have a positive scale factor and it goes to the right 3 and up 4