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
The answers are..
6. 55
7. 6
8. 39
9. 17
Ariana cannot ship all the bags in one box.
Ariana will be sending 8 bags which will weigh a total of:
= 22 ounces x 8
= 176 ounces
You need to convert this to pounds to see if it will fit in the box:
<em>1 pound = 16 ounces </em>
176 ounces in pounds is therefore:
= 176 / 16
= 11 pounds
The box can only take 10 pounds and 5 ounces which is less than the 11 pounds the bags weigh.
Ariana cannot ship all the bags in one box.
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