The total cost of a new automobile, including a 5% sales tax on the price of the automobile, is $ 26,708. How much of the tot
1 answer:
Let's say the price without tax of the car is "x", then you add 5% of "x" and it becomes $26,708.
now, if we take "x" to be the 100% of the price, and then adding a 5% of "x" will simply give us a 100 + 5 = 105%, and that's what 26,708 is, thus, 26,708 is the 105%, and if "x" is the 100%, what is "x" anyway?
now, if we take "x" to be the 100% of the price, and then adding a 5% of "x" will simply give us a 100 + 5 = 105%, and that's what 26,708 is, thus, 26,708 is the 105%, and if "x" is the 100%, what is "x" anyway?
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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>