Answer:
The integral for the arc of length is:
By using Simpon’s rule we get: 1.5355453
And using technology we get: 2.3020
The approximation is about 33% smaller than the exact result.
Explanation:
The formula for the length of arc of the function f(x) in the interval [a,b] is:
We need the derivative of the function:
And we need it squared:
Then the integral is:
Now, the Simposn’s rule with n=4 is:
In this problem:
So, the Simposn’s rule formula becomes:
Then simplifying a bit:
Then we just do those computations and we finally get the approximation via Simposn's rule:
While when we do the integral by using technology we get: 2.3020.
The approximation with Simpon’s rule is close but about 33% smaller:
Answer:
sinθ = 
Step-by-step explanation:
sinθ =
=
= 
Answer:
a=19
Step-by-step explanation:
Since it is a parallelogram, adjacent angles are supplementary, or add to 180 degrees.
In this parallelogram, 5a+1 and 3a+27 are adjacent. Therefore, when added, they should equal 180.
5a+1+3a+27=180
Combine like terms
(5a+3a) + (1+27) = 180
8a +28 =180
Now, solve for a, by isolating it.
Subtract 28 from both sides
8a+28-28=180-28
8a=152
Divide both sides by 8
8a/8=152/8
a=19
Answer:
120
Step-by-step explanation:
The sum of the angles is 180 since it forms a straight line
2x+ x+90 = 180
Combine like terms
3x +90=180
Subtract 90 from each side
3x+90-90=180-90
3x= 90
Divide each side by 3
3x/3 = 90/3
x = 30
We want angle DBC = x+90
= 30+90
=120