1-3 are about trigonometric ratios (SOH CAH TOA). 4, 5 are about the Law of Cosines, and 6 uses the Law of Sines.
1. Sin = Opposite/Hypotenuse
x = 10*sin(40°) ≈ 6.428
2. Sin = Opposite/Hypotenuse
x = arcsin(7/12) ≈ 35.69°
3. Tan = Opposite/Adjacent
x = 18/tan(52°) ≈ 14.063
4. b^2 = a^2 +c^2 -2ac*cos(B)
B = arccos((a^2 +c^2 -b^2)/(2ac)) = arccos((7^2 +13^2 -8^2)/(2*7*13))
B = arccos(11/13) ≈32.20°
5. Same formula.
x = √(a^2 +c^2 -2ab*cos(B)) = √(157-132cos(42°)) ≈ 7.675
6. The ratio of side lengths is the same as the ratio of the sines of the opposite angles.
6/10 = sin(x)/sin(100°)
x = arcsin((6/10)*sin(100°)) ≈ 36.22°
Answer:
1. LCM of 18 & 12 = 36 minutes
2. 0.00095897
explanation.
2 18 2 12
____I______ ___l_________
3 9 2 6
____l_______. ___I_________
3 3 3 3
_____l________. ___l_________
l 1
18= 2×3×3 12=2×2×3
1 2 2 1
=1 × 3 =2 × 3
L.C.M= product of greatest power of each prime factor.
2 2
= 2 × 3
=4×9 = 36
hence, time taken by both to meet again
LCM of 18 & 12 =36 minutes
Get out your graphing paper. Since the slope formula is y=mx+b, we can say that +4 is b, which also stands for the y-intercept. Because +4 is the y intercept, place a point on (0,4). Then, using the slope (m or 3), we can figure out where the second point will go.
Slope is another word for rise over run. In this case it is 3/1 because that is what 3 is when converted to a fraction. So, from (0,4), we go up 3 and over to the right by 1 to plot the second point, (1,7). Connect the plotted points with the ruler.
Tldr; Plot a point at (0,4) because the y intercept is +4, plot a point at (1,7) because the slope is 3/1, and use a ruler to connect the two points in a line.
Answer:
5y
Step-by-step explanation:
Think of the distributive property here.
5y (y+3)