<h3>Exact area = 12pi - 9*sqrt(3) square inches</h3><h3>Approximate area = 22.1106545749577 square inches</h3>
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Work Shown:
Assuming the chord is horizontal along with the diameter, then this means the two smallest minor arcs are both 30 degrees each. This leaves the northern most arc to be 180-30-30 = 120 degrees in measure
A = area of northern sector (you can think of it as a pizza slize)
A = (angle/360)*pi*r^2
A = (120/360)*pi*6^2
A = 12pi
B = area of triangle
B = (1/2)*side1*side2*sin(included angle)
B = (1/2)*6*6*sin(120)
B = 18*sqrt(3)/2
B = 9*sqrt(3)
C = area of shaded region
C = A - B
C = 12pi - 9*sqrt(3) .... exact area
C = 22.1106545749577 ... use a calculator to get the approximate area
What kind of triangle is it?
Answer:
165
Step-by-step explanation:
base x base x height
Answer:
- 6 + 3
Step-by-step explanation:
hope this helps
Answers:
So the solution is (x,y) = (4, -1)
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Work Shown:
6x + 7y = 17
6x + 7( y ) = 17
6x + 7( -3x+11 ) = 17 ... replace every copy of y with -3x+11
6x - 21x + 77 = 17
-15x = 17-77
-15x = -60
x = -60/(-15)
x = 4
We'll use this x value to find y
y = -3x+11
y = -3(4)+11 ... replace x with 4
y = -12+11
y = -1
We have x = 4 and y = -1 pair up together to give us the solution (x,y) = (4, -1)
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To check the solution, we plug x = 4 and y = -1 into each equation
Plugging the values into the first equation leads to...
y = -3x+11
-1 = -3(4)+11
-1 = -1
This is effectively already done in the last part of the previous section. But it doesn't hurt to verify like this regardless.
We'll need to verify the second equation as well.
6x + 7y = 17
6(4) + 7(-1) = 17
24 - 7 = 17
17 = 17
We get a true equation, so the solution is confirmed with both equations. Overall, the solution to the system of equations is confirmed. This system is independent and consistent.
