Answer:
x = 4 or x = 12
Step-by-step explanation:
Given:
y = -10x² + 160x - 430
When y = $50
50 = -10x² + 160x - 430
50 + 430 = -10x² + 160x
480 = -10x² + 160x
-10x² + 160x - 480 = 0
Divide through by -10
x² - 16x + 48 = 0
Solve the quadratic equation using factorization method
+48 = -12 × -4
-16 = -12 -4
Therefore,
-12 and -4 are both factors
x² - 16x + 48 = 0
(x - 4 )(x - 12 ) = 0
x - 4 = 0
x = 4
OR
x - 12 = 0
x = 12
6 sin 2x = 6 cos x Using the identity sin 2x = 2 sin x cos x:-
12 sin x cos x = 6 cos x
6 cos x ( 2 sin x - 1) = 0
either 6 cos x = 0 or 2 sin x - 1 = 0 so sin x = 1/2
x = pi/2, 3pi/2 , pi/6, 5pi / 6
answer is ( pi/6, pi/2, 5pi/6, 2pi/2)
Combine numbers with the same variable so 10a + 7a = 17a and 3b + 6b = 9b. So the full answer is 17a + 9b.
