Answer:
35/12
Step-by-step explanation:
The tangent in a triangle is always the opposite side divided by the adjacent side. In this triangle, BC is the side opposite to angle a, and AC is the side adjacent to angle A.
However, we do not know what AC is, but we can use the pythagorean theorem to solve. 
, which is 12 squared. Therefore, AC is 12 units in length.
Now we have all the sides of the triangle and we can divide the opposite side by the adjacent side. We get 35/12.
Hope this helps!
Answer:D
Step-by-step explanation:
factorise 2x²-16x+32
x²-8x+16
(x-4)²
factorise 4x²-2x-20
2x²-x-10
2x²+4x-5x-10
2x(x+2)-5(x+2)
(2x-5)(x+2)
solving for (f/g)(x)
(x-4)²/(x+2)÷(2x-5)(x+2)/(x-4)²
(x-4)²/(x+2)*(x-4)²/(2x-5)(x+2)
(x-4)⁴/(2x-5)(x+2)²
Given f(x) = [(x^2 -2x -15)/x-5], notice it is a rational
function
But the numerator x^2 -2x -15 could be factored, which
yields
(x – 5)(x + 3)
Therefore f(x) = (x – 5)(x + 3)/ (x-5)
Cancelling x-5, f(x)
= x + 3
In this way, the f(x) is continuous at any point, and is
basically a line.
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Answer:
Solution : Option B, or 9π
Step-by-step explanation:
We are given that y = x, x = 3, and y = 0.
Now assume we have a circle that models the given information. The radius will be x, so to determine the area of that circle we have πx². And knowing that x = 3 and y = 0, we have the following integral:
So our set up for solving this problem, would be such:
By solving this integral we receive our solution:
![\int _0^3x^2\pi dx,\\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=> \pi \cdot \int _0^3x^2dx\\\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1}\\=> \pi \left[\frac{x^{2+1}}{2+1}\right]^3_0\\=> \pi \left[\frac{x^3}{3}\right]^3_0\\\mathrm{Compute\:the\:boundaries}: \left[\frac{x^3}{3}\right]^3_0=9\\\mathrm{Substitute:9\pi }](https://tex.z-dn.net/?f=%5Cint%20_0%5E3x%5E2%5Cpi%20dx%2C%5C%5C%5Cmathrm%7BTake%5C%3Athe%5C%3Aconstant%5C%3Aout%7D%3A%5Cquad%20%5Cint%20a%5Ccdot%20f%5Cleft%28x%5Cright%29dx%3Da%5Ccdot%20%5Cint%20f%5Cleft%28x%5Cright%29dx%5C%5C%3D%3E%20%5Cpi%20%5Ccdot%20%5Cint%20_0%5E3x%5E2dx%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3APower%5C%3ARule%7D%3A%5Cquad%20%5Cint%20x%5Eadx%3D%5Cfrac%7Bx%5E%7Ba%2B1%7D%7D%7Ba%2B1%7D%5C%5C%3D%3E%20%5Cpi%20%5Cleft%5B%5Cfrac%7Bx%5E%7B2%2B1%7D%7D%7B2%2B1%7D%5Cright%5D%5E3_0%5C%5C%3D%3E%20%5Cpi%20%5Cleft%5B%5Cfrac%7Bx%5E3%7D%7B3%7D%5Cright%5D%5E3_0%5C%5C%5Cmathrm%7BCompute%5C%3Athe%5C%3Aboundaries%7D%3A%20%5Cleft%5B%5Cfrac%7Bx%5E3%7D%7B3%7D%5Cright%5D%5E3_0%3D9%5C%5C%5Cmathrm%7BSubstitute%3A9%5Cpi%20%7D)
As you can tell our solution is option b, 9π. Hope that helps!
