How to get answer by Mimiwhatsup:
6(12m+12b−2b)
=(6)(12m+12b+−2b)
=(6)(12m)+(6)(12b)+(6)(−2b)
=72m+72b−12b
=60b+72m
(a)

or, via symmetry

____________
(b)
By the chain rule:

For polar coordinates, x = rcosθ and y = rsinθ. Since
<span>r = 3 + 2cosθ, it follows that

Differentiating with respect to theta

2/3 is the slope
____________
(c)
"</span><span>distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3
A</span>ngle θ and r are related via <span>r = 3 + 2cosθ, so implicitly differentiating with respect to time
</span><span />
We know that
cos²(theta)=0.21
sin²(theta)+cos²<span>(theta)=1
</span>sin²(theta)=1-cos²(theta)------> sin²(theta)=1-(0.21)-----> 0.79
sin(theta)=√0.79
sin(theta)=0.89
the answer is
the value of sin(theta) is 0.89
We know that
the number of coins that each roll contains is
<span>rolls of quarters-------> 40 coins
</span><span>rolls of Dimes---------> 50 coins
</span><span>rolls of nickels------> 40 coins
</span><span>four rolls of quarters------> 4*40*$0.25-----> $40
</span>t<span>hree rolls of Dimes-----> 3*50*$0.10------> $15
</span><span>six rolls of nickels-------> 6*40*$0.05-----> $12
total=[40+15+12]------> $67
the answer is
$67</span>