The bounded region we're concerned with lies above the x-axis.
![y^2-x^2=1\implies y=\sqrt{1+x^2}](https://tex.z-dn.net/?f=y%5E2-x%5E2%3D1%5Cimplies%20y%3D%5Csqrt%7B1%2Bx%5E2%7D)
This hyperbola intersects with the line
for
![2=\sqrt{1+x^2}\implies4=1+x^2\implies x^2=3\implies x=\pm\sqrt3](https://tex.z-dn.net/?f=2%3D%5Csqrt%7B1%2Bx%5E2%7D%5Cimplies4%3D1%2Bx%5E2%5Cimplies%20x%5E2%3D3%5Cimplies%20x%3D%5Cpm%5Csqrt3)
Using the washer method, the volume of the resulting solid is
![\displaystyle\pi\int_{-\sqrt3}^3(2^2-(\sqrt{1+x^2})^2)\,\mathrm dx=2\pi\int_0^{\sqrt3}(3-x^2)\,\mathrm dx=\boxed{4\pi\sqrt3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cpi%5Cint_%7B-%5Csqrt3%7D%5E3%282%5E2-%28%5Csqrt%7B1%2Bx%5E2%7D%29%5E2%29%5C%2C%5Cmathrm%20dx%3D2%5Cpi%5Cint_0%5E%7B%5Csqrt3%7D%283-x%5E2%29%5C%2C%5Cmathrm%20dx%3D%5Cboxed%7B4%5Cpi%5Csqrt3%7D)
Answer:
240
Step-by-step explanation:
bruh all you have to do is (11+5)*15
Answer:
The length of HF is 73.9 feet.
Step-by-step explanation:
Let the length of HF be represented by x. So that applying the appropriate trigonometric function to the triangle FGH, we have;
Sin θ = ![\frac{opposite}{hypotenuse}](https://tex.z-dn.net/?f=%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D)
Where θ is the angle given in the triangle =
.
Then,
Sin 80 = ![\frac{x}{75}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B75%7D)
⇒ x = Sin 80 x 75
= 0.9848 x 75
= 73.86
x = 73.9
Thus, the length of HF is 73.9 feet.
-2x-3=-18, x = -3/2y + 9 and x-6y=-6, x = 6y-6