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:
First, find two points on the graph:
- (x₁, y₁) = (0, 2)
- (x₂, y₂) = (2, 8)
Slope = 
16 + (-3) = 16 - 3 = 13
Answer:
what does this mean
Step-by-step explanation:
Since we don't want to use the Pythagorean Theorem on all of these, first we look for some Pythagorean Triples. Its very helpful to know some of the common ones, so here's a list:
3, 4, 5
5, 12, 13
7, 24, 25
8, 15, 17
So we either look for these or a multiple of these numbers.
The last one is the only one that fits because 15, 20, 25 is a multiple of the triple 3, 4, 5 by multiplying all of them by 5.
Thus, 15, 20, 25 forms a right triangle.
Need more detail to solve