Answer:
14 ft
Step-by-step explanation:
Focus on the triangle, and temporarily neglect the 2 ft measurement at the top of the triangle. Then the 2 legs of the triangle have lengths h - 2 ft and 5 ft, and the hypotenuse is 13.
Applying the Pythagorean Theorem, we get:
13^2 = (h - 2)^2 + 5^2, or
169 = h^2 - 4h + 4 + 25, or
144 = h^2 - 4h + 4, or
140 = h^2 - 4h, or, finally,
h^2 - 4h - 140 = 0. We must find the value of h.
I graphed this function on a calculator and found that -10 is a zero. Thus, the function factors into (h + 10)(h - 14) = 0, or h = 14.
The total height of the piece of plywood is 14 ft.
Check this: does a right triangle with legs (14 - 2) and 5 have a hypotenuse of 13? Yes.
Answer:
1) -10^3 (-10 to the power of 3)
2) r^5 (pie to the power of 5)
3) 1/2^2 + x^3 (1/2 to the power of 2 + x to the power of 3)
Answer:
Step-by-step explanation:
I think you have the question incomplete, and that this is the complete question
sin^4a + cos^4a = 1 - 2sin^2a.cos^2a
To do this, we can start my mirroring the equation.
x² + y² = (x + y)² - 2xy,
This helps us break down the power from 4 to 2, so that we have
(sin²a)² + (cos²a)² = (sin²a + cos²a) ² - 2(sin²a) (cos²a)
Recall from identity that
Sin²Φ + cos²Φ = 1, so therefore
(sin²a)² + (cos²a)² = 1² - 2(sin²a) (cos²a)
On expanding the power and the brackets, we find that we have the equation proved.
sin^4a + cos^4a = 1 - 2sin^2a.cos^2a
Log81 (9) = 1/2
The 81 is a subscript don’t know if I could type it like that so I just put it like that
