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:
<u>At a constant speed of 0.5 miles per minute, the ostrich can run 20 miles in 40 minutes. The unit rate is 0.5 miles per minute.</u>
Step-by-step explanation:
Distance run by the ostrich = 6 miles
Time the ostrich takes to run this distance = 12 minutes
Speed of the ostrich = Distance / Time
Speed of the ostrich = 6 miles / 12 minutes = 0.5 miles per minute
How far the ostrich could run in 40 minutes?
If the ostrich run 0.5 miles per minute, this is the formula:
Speed of the ostrich * 40 minutes = Distance
0.5 miles/minute * 40 minutes = 20 miles (Minutes is simplified in the numerator and the denominator on the left side)
<u>At a constant speed of 0.5 miles per minute, the ostrich can run 20 miles in 40 minutes. The unit rate is 0.5 miles per minute.</u>
Answer: option a
Step-by-step explanation: plz mark brainiest
