Answer:
17, 19, 21
Step-by-step explanation:
x = first number
x+2 = second number
x+4 = third number
4x + 3(x+2) + 2(x+4) = 167
simplify:
4x + 3x + 6 + 2x + 8 = 167
combine like terms:
9x + 14 = 167
subtract 14 from each side of the equation:
9x = 153
divide both sides by 9:
x = 17
Answer: at the values where cos(x) = 0Justification:1) tan(x) = sin(x) / cos(x).
2) functions have vertical asymptotes at x = a if Limit of the function x approaches a is + or - infinity.
3) the limit of tan(x) approaches +/- infinity where cos(x) approaches 0.
Therefore, the grpah of y = tan(x) has asymptotes where cos(x) = 0.
You can see the asympotes at x = +/- π/2 on the attached graph. Remember that cos(x) approaches 0 when x approaches +/- (n+1) π/2, for any n ∈ N, so there are infinite asymptotes.
N(3)-8=16
add 8 to both sides
3n=24
Divide each side by three
n=8
Check the picture below.
![\bf 0=AB^2+6AB-121\implies \stackrel{\textit{using the quadratic formula}}{AB=\cfrac{-6 \pm \sqrt{6^2-4(1)(-121)}}{2(1)}} \\\\\\ AB=\cfrac{-6 \pm \sqrt{520}}{2}\implies AB=\cfrac{-6 \pm \sqrt{4\cdot 130}}{2} \\\\\\ AB=\cfrac{-6 \pm \sqrt{2^2\cdot 130}}{2}\implies AB=\cfrac{-6 \pm 2\sqrt{130}}{2} \\\\\\ AB=-3\pm\sqrt{130}\implies AB= \begin{cases} \boxed{-3+\sqrt{130}}\\\\ -3-\sqrt{130} \end{cases}](https://tex.z-dn.net/?f=%5Cbf%200%3DAB%5E2%2B6AB-121%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Busing%20the%20quadratic%20formula%7D%7D%7BAB%3D%5Ccfrac%7B-6%20%5Cpm%20%5Csqrt%7B6%5E2-4%281%29%28-121%29%7D%7D%7B2%281%29%7D%7D%0A%5C%5C%5C%5C%5C%5C%0AAB%3D%5Ccfrac%7B-6%20%5Cpm%20%5Csqrt%7B520%7D%7D%7B2%7D%5Cimplies%20AB%3D%5Ccfrac%7B-6%20%5Cpm%20%5Csqrt%7B4%5Ccdot%20130%7D%7D%7B2%7D%0A%5C%5C%5C%5C%5C%5C%0AAB%3D%5Ccfrac%7B-6%20%5Cpm%20%5Csqrt%7B2%5E2%5Ccdot%20130%7D%7D%7B2%7D%5Cimplies%20AB%3D%5Ccfrac%7B-6%20%5Cpm%202%5Csqrt%7B130%7D%7D%7B2%7D%0A%5C%5C%5C%5C%5C%5C%0AAB%3D-3%5Cpm%5Csqrt%7B130%7D%5Cimplies%20AB%3D%0A%5Cbegin%7Bcases%7D%0A%5Cboxed%7B-3%2B%5Csqrt%7B130%7D%7D%5C%5C%5C%5C%0A-3-%5Csqrt%7B130%7D%0A%5Cend%7Bcases%7D)
since the distance AB cannot be a negative value, thus is not -3-√(130).
Use the definition of tangent
or inv tangent (arctan or atan)
tan(theta) = opposite side/ adjacent side
the vertical rise would be the opposite side, the horozontal distance would be the adjacent side
let rise = y
let distance= x
x=2y
so tan(theta) = y/2y
tan(theta) = 1/2
theta = atan(1/2)
grab a handy dandy calculator, unless you know this conversion off the top of your head