Write the verbal sentence as an equation. Then solve.
2 answers:
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Area = length x width
x² + 12x = l * x
A.
First, you factor x from x² + 12x
area = x (x+12)
area = (x+12) * x
Length = x + 12
B.
If x = 10,
l = x + 12 = 10 +12 = 22
length = 22
and
Area = x² + 12x = 10² + 12(10) = 100 + 120 = 220
area = 220
Hope this helps :)
x² + 12x = l * x
A.
First, you factor x from x² + 12x
area = x (x+12)
area = (x+12) * x
Length = x + 12
B.
If x = 10,
l = x + 12 = 10 +12 = 22
length = 22
and
Area = x² + 12x = 10² + 12(10) = 100 + 120 = 220
area = 220
Hope this helps :)
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>
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>