Assume 0 < <em>x</em>/2 < <em>π</em>/2. Then
tan²(<em>x</em>/2) + 1 = sec²(<em>x</em>/2) ===> sec(<em>x</em>/2) = √(1 - tan²(<em>x</em>/2))
===> cos(<em>x</em>/2) = 1/√(1 - tan²(<em>x</em>/2))
===> cos(<em>x</em>/2) = 1/√(1 - <em>t</em> ²)
We also know that
sin²(<em>x</em>/2) + cos²(<em>x</em>/2) = 1 ===> sin(<em>x</em>/2) = √(1 - cos²(<em>x</em>/2))
Recall the double angle identities:
cos(<em>x</em>) = 2 cos²(<em>x</em>/2) - 1
sin(<em>x</em>) = 2 sin(<em>x</em>/2) cos(<em>x</em>/2)
Then
cos(<em>x</em>) = 2/(1 - <em>t</em> ²) - 1 = (1 + <em>t</em> ²)/(1 - <em>t</em> ²)
sin(<em>x</em>) = 2 √(1 - 1/(1 - <em>t</em> ²)) / √(1 - <em>t</em> ²) = 2<em>t</em>/(1 - <em>t</em> ²)
Answer:
63 units
Step-by-step explanation:
The profit function P(x) is given by the revenue function minus the cost function:
The number of units sold 'x' for which the derivate of the profit function is zero, is the number of units that maximizes profit:
The number of units that should be manufactured so that profit is maximum is 63 units.
D is 11
2d - 5 = 17 add 5 to both sides
2d = 22 divide by 2
d = 11 answer
This would be 3! ways
= 3*2*1 = 6 ways Answer
Answer:
21 are purple
63 are green
36 are yellow
Step-by-step explanation:
30% of 120 is 36
120 - 36 = 84
75% of 84 is 63
84 - 63 = 21
