12.7
Using the Pythagorean theorem, you can easily calculate the length of BC.
So:
BC = sqrt(12^2 - 6^2) = sqrt(144 - 36) = sqrt(108) = 10.39230485
Now consider triangle BCD. You know all three angles and one side. Using the law of sines you know that ratio of the sine of each angle over the opposite side is constant. So:
BC/sin(55) = CD/sin(90)
BC/sin(55) = CD/sin(90)
sin(90)BC/sin(55) = CD
1*BC/sin(55) = CD
BC/sin(55) = CD
10.39230485/0.819152044 = CD
12.68666167 = CD
12.7 = CD
Problem 7)
The answer is choice B. Only graph 2 contains an Euler circuit.
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To have a Euler circuit, each vertex must have an even number of paths connecting to it. This does not happen with graph 1 since vertex A and vertex D have an odd number of vertices (3 each). The odd vertex count makes it impossible to travel back to the starting point, while making sure to only use each edge one time only.
With graph 2, each vertex has exactly two edges attached to it. So an Euler circuit is possible here.
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Problem 8)
The answer is choice B) 5
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Work Shown:
abc base 2 = (a*2^2 + b*2^1 + c*2^0) base 10
101 base 2 = (1*2^2 + 0*2^1 + 1*2^0) base 10
101 base 2 = (1*4 + 0*2 + 1*1) base 10
101 base 2 = (4 + 0 + 1) base 10
101 base 2 = 5 base 10
The area of the region shown in the coordinate plane is 2.7823 units square.
<h3>What is integration?</h3>
It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
It is given that:
The graph of a function:
y = sinx
And a line segment passed through:
(0, 0) and (7π/6, -1/2)
First, find the equation of the line:
y = (-1/2)/(7π/6)[x]
y = (-3/7π)x
The area by definite integration:
![\rm Area = \int\limits^{7\pi/6}_0 {[sinx - (-3/7\pi)x]} \, dx](https://tex.z-dn.net/?f=%5Crm%20Area%20%3D%20%5Cint%5Climits%5E%7B7%5Cpi%2F6%7D_0%20%7B%5Bsinx%20-%20%28-3%2F7%5Cpi%29x%5D%7D%20%5C%2C%20dx)
![\rm Area = \int\limits^{7\pi/6}_0 {[sinx +3x/7\pi ]} \, dx](https://tex.z-dn.net/?f=%5Crm%20Area%20%3D%20%5Cint%5Climits%5E%7B7%5Cpi%2F6%7D_0%20%7B%5Bsinx%20%2B3x%2F7%5Cpi%20%5D%7D%20%5C%2C%20dx)
After solving the above definite integral:
Area = 2.7823 units square
Thus, the area of the region shown in the coordinate plane is 2.7823 units square.
Learn more about integration here:
brainly.com/question/18125359
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