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 surface area of the box in square inches will be 39.0625 inches².
<h3>How to calculate the area?</h3>
From the information, the gift box has a surface area of 6.25 square feet.
Therefore, the surface area of the box in square inches will be:
= Side × Side
= 6.25 × 6.25
= 39.0625 inches²
Therefore, the surface area of the box will be 39.0625 inches².
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Answer:
The new account balance is <u>$812</u>.
Step-by-step explanation:
Given:
Larry Thomas's charge account statement shows an unpaid balance of $800.
The monthly finance charge is 1.5% of the unpaid balance.
Now, to find the new account balance.
Unpaid balance = $800.
Monthly finance charge of the unpaid balance = 1.5%.
Now, to get the new account balance:
$800 + 1.5% of $800.




Therefore, the new account balance is $812.
Answer:

Step-by-step explanation:
Let p be the number of identical packages.
We have been given that each package has a mass of 37.4 kg, so weight of p packages will be 37.4p.
The total mass of Renna and her load of identical packages is 620 kg.
We have been given that the mass limit for the elevator is 450 kg. This means that Renna can remove p packages from 620 kg such that 620 minus weight of p packages will be less than or equal to 450 kg.
We can represent this information in an inequality as:

Therefore, the inequality
can be used to determine the number of packages, p, Renna could remove from the elevator to meet the mass requirement.
Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of days that fluffy eats wet food in a week and y represents the number of days that fluffy eats dry food in a week.
Hence:
x + y = 7 (1)
Also, John wants to spend at most $9.00 on cat food each week. Hence:
1.5x + 0.75y ≤ 9 (2)
The list of possible points after solving graphically are:
(0,7), (6,0), (0,12) and (5, 2). If x,y > 0, then the point that satisfies the inequality is:
(5, 2) i.e. 5 wet food and 2 dry food