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>
5(4)+5x=60
x=8
x= number of pies the club made
Answer:
See explanation
Step-by-step explanation:
Among 806 people asked which is there favorite seat on a plane, 492 chose the window seat, 8 chose the middle seat, and 306 chose the aisle seat, then

a) One randomly selected person preferes aisle seat with probability

b) Two randomly selected people both prefer aisle seat (with replacement) is

c) Two randomly selected people both prefer aisle seat (without replacement) is

Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identity
• tan²x + 1 = sec²x
⇒ tan²x - sec²x = - 1
Thus the derivative reduces to
( - 1 ) = 0
Answer:
15
Step-by-step explanation: