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.
Answer:
The table shows values for Variable A and Variable B.
Variable A 1 5 2 7 8 1 3 7 6 6 2 9 7 5 2
Variable B 18 22 19 7 24 16 17 20 20 23 17 25 21 18 15
Use the data from the table to create a scatter plot.
Step-by-step explanation:
PEMDAS.....parenthesis, exponents, multiplication/division, addition/subtraction
so step 2 is solving the exponents <==
Answer:
A) -9/2
B) 9/4
C) -9/2, same as A)
Step-by-step explanation:
We are given that 
. We use the properties of integrals to write the new integrals in terms of I.
A) 
. We have used that ∫cf dx=c∫f dx.
B) 
. Here we used that reversing the limits of integration changes the sign of the integral.
C) It's the same integral in A)
Write both sides as powers of 8, then simplify:
However, on the left hand side, this would mean we'd have, 
, which is undefined (assuming the real-valued logarithm), so this equation has no real solution.
