Slope of line = tan(120) = -tan(60) = - √3
Distance from origin = 8
Let equation be Ax+By+C=0
then -A/B=-√3, or
B=A/√3.
Equation becomes
Ax+(A/√3)y+C=0
Knowing that line is 8 units from origin, apply distance formula
8=abs((Ax+(A/√3)y+C)/sqrt(A^2+(A/√3)^2))
Substitute coordinates of origin (x,y)=(0,0) =>
8=abs(C/sqrt(A^2+A^2/3))
Let A=1 (or any other arbitrary finite value)
solve for positive solution of C
8=C/√(4/3) => C=8*2/√3 = (16/3)√3
Therefore one solution is
x+(1/√3)+(16/3)√3=0
or equivalently
√3 x + y + 16 = 0
Check:
slope = -1/√3 .....ok
distance from origin
= (√3 * 0 + 0 + 16)/(sqrt(√3)^2+1^2)
=16/2
=8 ok.
Similarly C=-16 will satisfy the given conditions.
Answer The required equations are
√3 x + y = ± 16
in standard form.
You can conveniently convert to point-slope form if you wish.
A 30 60 90 triangle has its shorter side equal to one half the hypotenuse.
So, if hypotenuse = 11 cm then shorter side = 5.5.
Source:
http://www.1728.org/trig2.htm
Answer:
(1, 0.25)
Step-by-step explanation:
To find when f(x)=g(x), then look for a value that is the same for both functions in the table. 0.25 occurs twice for the same x value. This is when they are equal. The solution is (1, 0.25).
For The first question, the answer is 6.
For the 2nd question, the answer is 127
The solution is on the picture
Answer:
9 Elmo
Step-by-step explanation:
