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:
1,000,000= 10^6
10 times 10 is 100 (10^2)
10,000 times 10 is 100,000 (10^5)
8 pencils = 1 package
28 children need pencils
Each child gets 4 pencils
28x4 = 112 (pencils needed)
112/8 = 14 packages needed.
x=8+sqrt-8/12, x=8-sqrt-8/12
I think...