2cos(x) - 4sin(x) = 3
use identity [cos(x)]^2 +[ sin(x)]^2 = 1 => cos(x) = √[1 - (sin(x))^2]
2√[1 - (sin(x))^2] - 4 sin(x) = 3
2√[1 - (sin(x))^2] = 3 + 4 sin(x)
square both sides
4[1 - (sin(x))^2] = 9 + 24 sin(x) + 16 (sin(x))^2
expand, reagrup and add like terms
4 - 4[sin(x)]^2 = 9 + 24sin(x) + 16sin^2(x)
20[sin(x)]^2 + 24sin(x) +5 = 0
use quadratic formula and you get sin(x) = -0.93166 and sin(x) = -0.26834
Now use the inverse functions to find x:
arcsin(-0.93166) = 76.33 degrees
arcsin(-0.26834) = 17.30 degrees
Answer: 29.28 years
Explanation:
From Kepler's third law the square of orbital period of revolving celestial body is proportional to the cube of semi -major axis from the body it is revolving about.
P² =A³
Where, P is the orbital period in years and A is the semi-major axis in AU (Astronomical units)
It is given that, For Saturn, A = 9.5 AU. We need to find P
⇒P² = (9.5 AU)³
⇒P² = 857.38
⇒P = 29.28 years
Thus, the orbital period of Jupiter is 29.28 years around the Sun.
Answer:
He will earn $139,000 after 4 years
Step-by-step explanation:
32,500+34,000+35,500+37000= $139,000
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