A <span>45 45 90 triangle
so a = b
a^2 + b^2 = </span>c^2<span>
a^2 + a^2 </span>= c^2<span>
2a^2 </span>= c^2<span>
2a^2 </span>= 24^2
<span> 2a^2 = 576
a^2 = 288
a = 12</span>√2
b = a = 12√2
<span>
Area of triangle:
= 1/2 (</span>12√2)(12√2)
<span>= 1/2(288)
= 144
answer
Area = 144 ft^2
</span>
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Midpoint = (8-5),(-3-9) / 2
= (3,-12)/2
= (3/2,-6)
With ϕ ≈ 1.61803 the golden ratio, we have 1/ϕ = ϕ - 1, so that
![I = \displaystyle \int_0^\infty \frac{\sqrt[\phi]{x} \tan^{-1}(x)}{(1+x^\phi)^2} \, dx = \int_0^\infty \frac{x^{\phi-1} \tan^{-1}(x)}{x (1+x^\phi)^2} \, dx](https://tex.z-dn.net/?f=I%20%3D%20%5Cdisplaystyle%20%5Cint_0%5E%5Cinfty%20%5Cfrac%7B%5Csqrt%5B%5Cphi%5D%7Bx%7D%20%5Ctan%5E%7B-1%7D%28x%29%7D%7B%281%2Bx%5E%5Cphi%29%5E2%7D%20%5C%2C%20dx%20%3D%20%5Cint_0%5E%5Cinfty%20%5Cfrac%7Bx%5E%7B%5Cphi-1%7D%20%5Ctan%5E%7B-1%7D%28x%29%7D%7Bx%20%281%2Bx%5E%5Cphi%29%5E2%7D%20%5C%2C%20dx)
Replace
:

Split the integral at x = 1. For the integral over [1, ∞), substitute
:

The integrals involving tan⁻¹ disappear, and we're left with

Answer:
i think the answer is -7/17
Step-by-step explanation:
hope it help :) i dont really good with fraction