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:
Diameter = 19.33
Step-by-step explanation:
Imaging a radius line from O to the endpoints of the 7. call this line R.
Label the part of the vertical line from O to the 90 degree intersection y.
Now you have a right triangle.
Using the Pythagorean theorem:
R² = 7² + y²
also
y = R - 3
substitute for y:
R² = 49 + (R-3)²
R² = 49 + R² - 6R + 9
simplify:
0 = 58 - 6R
6R = 58
R = 9.6667
Diameter = 2(9.6667) = 19.33
Answers:
11. 48%
12. 25%
13. 36%
15. 93%
16. 99%
17. 0.16%
18. 160%
19. 85%
Work for 19:
The chart is incorrect because it calculates 40% of 34 instead of 40 percent of x (we got 85% for our answer but I'm using x as the unknown number) results in the number of 34.
Percentage of 40% of what number = 34?
40% of what number = 34 is equivalent to: 40% × ? = 34
--------------------------
40% × ? = 34
? =
34 ÷ 40% =
34 ÷ (40 ÷ 100) =
(100 × 34) ÷ 40 =
3,400 ÷ 40 =
85
Proof:
If 40% × 85 = 34 =>
Divide 34 by 85...
... And see if we get as a result: 40%
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20. 21 students
Step-by-step explanation:
I hope I helped, and I always appreciate brainliest!!! ;)
Answer:
500 because when you dm yu multiply it
Step-by-step explanation:
Answer:
x= 85
Step-by-step explanation:
(7x+6)-(5x-4)=180
There is a negative 1 between the two parenthesis
-1(5x-4)
-5x+4
Now plug it back into the equation and take out the parenthesis
7x+6-5x+4= 180
2x+10=180 Now we can solve
-10 -10
2x= 170
2x/2 = 170/2
x= 85
I hope this helps! :)
