What is the value of this equation
1 answer:
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Answer: 4,111.7 mm³
Step-by-step explanation:
You need to use this formula to calculate the volume of the square pyramid:
Where "s" is the lenght of any side of the square base and "h" is the height of the pyramid.
Find the height with the Pythagorean Theorem:
Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle. Let be "c" the height of the pyramid.
You can identify in the figure that:
Then, you can find the height:
Then, knowing that:
You can calculate the volume:
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.
