The sum of two numbers is 43. The larger number is 21 more than the smaller number. What are the numbers?
1 answer:
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Multiply all terms by x
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.
For this case we have the following equation:
Where,
w: The weight of a spring in pounds
E: the energy stored by the spring in joules.
Substituting values we have:
Making the corresponding calculation:
Answer:
the approximate weight of the spring in pounds is:
Where,
w: The weight of a spring in pounds
E: the energy stored by the spring in joules.
Substituting values we have:
Making the corresponding calculation:
Answer:
the approximate weight of the spring in pounds is: