Answer:
The slope is zero.
Step-by-step explanation:
Given that

, then

The slope of a tangent line in the polar coordinate is given by:

Thus, we have:

Part A:
For horizontal tangent lines, m = 0.
Thus, we have:

Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:
</span><span>θ = 0
</span>θ = <span>2.02875783811043
</span>
θ = <span>4.91318043943488
Part B:
For vertical tangent lines,

Thus, we have:

</span>Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:
</span>θ = <span>4.91718592528713</span>
Answer:
20 feet
Step-by-step explanation:
1st piece = x
2nd piece = 2x
3rd piece = 6x
x+2x+6x=180
9x=180
x=20
so the first piece is 20 feet, the second is 40, and the third is 120.
Answer:
5 and a half
Step-by-step explanation:
Because you can fit 2 liters in each can, to find how many you would need, divide 11 by 2, this would give you 5 and a half, 5.5.
It could be that they want you to round up to six or round down to five, so do consider that.
Speed
Riding speed = 9 mph
Driving speed = 27 mph
Time
If x hours is the time taken when riding, (x - 1/3) hours is the time taken when driving.
Distance in both instances is the same, D= Speed * time
Therefore,
9*x = 27(x-1/3)
9x = 27x - 27/2
9x = 27x - 9
(9-27)x = -9
-18x = -9
x = 9/18 = 1/2 hours
Distance, D = 1/2 *9 = 4.5 miles