Amy finished her history assignment in 144 hours. Then she completed her math assignment in 1/3 hours. What was the total amount
1 answer:
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Answer:
X Y
-2 8
-1 7
0 6
1 5
2 4
3 3
Step-by-step explanation:
We have the equation: x+y=6
We want to get this in the form: y=mx+b (or in this case y=x+b)
To do this we need y to be positive and by itself
So we subtract y from both sides and divide by -1 (we divide by -1 because otherwise y would be negative and that does not fit our template of y=x+b)
Doing this we have
-x+6=y
From here we just plug in numbers -2 to 3 which I will assume you know how to do
X Y
-2 8
-1 7
0 6
1 5
2 4
3 3
9514 1404 393
Answer:
6. (A, B, C) ≈ (112.4°, 29.5°, 38.0°)
7. (a, b, C) ≈ (180.5, 238.5, 145°)
Step-by-step explanation:
My "work" is to make use of a triangle solver calculator. The results are attached. Triangle solvers are available for phone or tablet and on web sites. Many graphing calculators have triangle solvers built in.
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We suppose you're to make use of the Law of Sines and the Law of Cosines, as applicable.
6. When 3 sides are given, the Law of Cosines can be used to find the angles. For example, angle A can be found from ...
A = arccos((b² +c² -a²)/(2bc))
A = arccos((8² +10² -15²)/(2·8·10)) = arccos(-61/160) = 112.4°
The other angles can be found by permuting the variables appropriately.
B = arccos((225 +100 -64)/(2·15·10) = arccos(261/300) ≈ 29.5°
The third angle can be found as the supplement to the other two.
C = 180° -112.411° -29.541° = 38.048° ≈ 38.0°
The angles (A, B, C) are about (112.4°, 29.5°, 38.0°).
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7. When insufficient information is given for the Law of Cosines, the Law of Sines can be useful. It tells us side lengths are proportional to the sine of the opposite angle. With two angles, we can find the third, and with any side length, we can then find the other side lengths.
C = 180° -A -B = 145°
a = c(sin(A)/sin(C)) = 400·sin(15°)/sin(145°) ≈ 180.49
b = c(sin(B)/sin(C)) = 400·sin(20°)/sin(145°) ≈ 238.52
The measures (a, b, C) are about (180.5, 238.5, 145°).
