Step-by-step explanation:
sin(2x) + cos(3x)
Use double angle formula sin(2x) = 2 sin x cos x.
Use triple angle formula cos(3x) = 4 cos³x − 3 cos x.
Substitute:
2 sin x cos x + 4 cos³x − 3 cos x
3+2 is 5.
1/7 +1/7 is 2/7.
Thus, the answer is 5 2/7.
Answer:
The rock remains in the air for t = 3.832 s
Step-by-step explanation:
To easily solve this equation, we can graph the equation with a calculator and see the interval for which the rock remains in the air.
(There is a minor problem with the equation, the last term should be 120 to model the 120 ft building)
h(t)= -16t^2 -30t + 120
Please see attached picture for the graph.
The time it takes for the ball to hit ground can be found by making
h(t) = -16t^2 -30t + 120 = 0
In the graph this point is equal to
t = 3.832 s
h(t) = 0
Simplifying
5x + 7 = 2x + 4
Reorder the terms:
7 + 5x = 2x + 4
Reorder the terms:
7 + 5x = 4 + 2x
Solving
7 + 5x = 4 + 2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2x' to each side of the equation.
7 + 5x + -2x = 4 + 2x + -2x
Combine like terms: 5x + -2x = 3x
7 + 3x = 4 + 2x + -2x
Combine like terms: 2x + -2x = 0
7 + 3x = 4 + 0
7 + 3x = 4
Add '-7' to each side of the equation.
7 + -7 + 3x = 4 + -7
Combine like terms: 7 + -7 = 0
0 + 3x = 4 + -7
3x = 4 + -7
Combine like terms: 4 + -7 = -3
3x = -3
Divide each side by '3'.
x = -1
Simplifying
x = -1
