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>
Let the two numbers be represented by x and y. The problem statement gives rise to two sets of equations.
x - y = 0.6
y/x = 0.6 . . . . . . . assuming x is the larger of the two numbers
or
x/y = 0.6 . . . . . . . assuming y has the larger magnitude
The solution of the first pair of equations is
(x, y) = (1.5, 0.9)
The solution of the first and last equations is
(x, y) = (-0.9, -1.5)
The pairs of numbers could be {0.9, 1.5} or {-1.5, -0.9}.
Answer:
1000÷50%=2000
Step-by-step explanation:
hope it helps
Answer:
Step-by-step explanation:
C and D answers look good
Answer:
in
Step-by-step explanation:
I don't know if you got this pic but this is the answer for this pic