Leslie is a costume designer for the local children's theater company. Yesterday, she sewed 3 female costumes and 4 male costume
s, which used 73 meters of fabric. Today, she sewed 4 female costumes and 2 male costumes, which used a total of 74 meters. How many meters of fabric does each type of costume require?
Each female costume requires ________ meters of fabric, and every male costume requires _____ meters.
Each female costume requires ________ meters of fabric, and every male costume requires _____ meters.
1 answer:
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Answer:
x ≈ 63.27
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan49° = =
=
( multiply both sides by 55 )
55 × tan49° = x , then
x ≈ 63.27 ( to the nearest hundredth )
Let z = sin(x). This means z^2 = (sin(x))^2 = sin^2(x). This allows us to go from the equation you're given to this equation: 7z^2 - 14z + 2 = -5
That turns into 7z^2 - 14z + 7 = 0 after adding 5 to both sides. Use the quadratic formula to solve for z. The only solution is z = 1 (see attached image). Since we made z = sin(x), this means sin(x) = 1. All solutions to this equation will be in the form x = (pi/2) + 2pi*n, which is the radian form of the solution set. If you need the degree form, then it would be x = 90 + 360*n
The 2pi*n (or 360*n) part ensures we get every angle coterminal to pi/2 radians (90 degrees), which captures the entire solution set.
Note: The variable n can be any integer.
