Two needed formulas,:
To find the area of a parallelogram, use
A = bh.
To find the area of a semicircle, use
Area = (πr^2)/2.
The area of the parallelogram is 11 x 32 or 352.
The two semicircle have the same measure.
The radius of the semicircle is (1/2)(16) or 8.
Area = (π8^2)/2
Area = 64π ÷ 2
A = 32π
There are two semicircle.
So, the area of both semicircle combined is
2(32π) or 64π.
Area of figure = 64π + 352.
Area of figure = 553.0619298304
We now round to the nearest tenths to get
Area of the figure = 553.06.
Answer:
119.05°
Step-by-step explanation:
In general, the angle is given by ...
θ = arctan(y/x)
Here, that becomes ...
θ = arctan(9/-5) ≈ 119.05°
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<em>Comment on using a calculator</em>
If you use the ATAN2( ) function of a graphing calculator or spreadsheet, it will give you the angle in the proper quadrant. If you use the arctangent function (tan⁻¹) of a typical scientific calculator, it will give you a 4th-quadrant angle when the ratio is negative. You must recognize that the desired 2nd-quadrant angle is 180° more than that.
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It may help you to consider looking at the "reference angle." In this geometry, it is the angle between the vector v and the -x axis. The coordinates tell you the lengths of the sides of the triangle vector v forms with the -x axis and a vertical line from that axis to the tip of the vector. Then the trig ratio you're interested in is ...
Tan = Opposite/Adjacent = |y|/|x|
This is the tangent of the reference angle, which will be ...
θ = arctan(|y| / |x|) = arctan(9/5) ≈ 60.95°
You can see from your diagram that the angle CCW from the +x axis will be the supplement of this value, 180° -60.95° = 119.05°.
Answer:
x=70°
Step-by-step explanation:
Three triangles can be made out of that shape so total int. angles = 3 x 180°=540°.
so 40 + 110 + 4x + 40 + x = 540°
190+5x=540°
5x=350°
x=350/5=70°
Step-by-step explanation:
-9x + 1 = -x + 17
collect like terms
-9x + x = 17-1
-8x = 16
divide both sides by -8
-8x/-8 = 16/8
x = 2
