<span>Let P be the cost per pound of peanuts.
Let M be the cost per pound of M&M's.
We can set up two equations to solve this question.
(1) 8P + 5M = 55.27
(2) 6P + 4M = 42.70
Let's multiply equation (1) by 3.
Let's multiply equation (2) by 4.
(1) 24P + 15M = 165.81
(2) 24P + 16M = 170.80
Let's subtract equation (1) from equation (2).
M = 4.99
Let's put M = 4.99 in equation (2) to find P.
6P + 4(4.99) = 42.70
6P = 42.70 - 19.96
6P = 22.74
P = 22.74 / 6
P = 3.79
The cost per pound of peanuts is $3.79
The cost per pound of M&M's is $4.99</span>
The first one (negative 5) (negative 9) is your answer
Answer:So the final sale would be $24
Step-by-step explanation:
By converting into parametric equations,
<span>{<span><span>x<span>(θ)</span>=r<span>(θ)</span><span>cosθ</span>=<span>cos2</span>θ<span>cosθ</span></span><span>y<span>(θ)</span>=r<span>(θ)</span><span>sinθ</span>=<span>cos2</span>θ<span>sinθ</span></span></span></span>
By Product Rule,
<span>x'<span>(θ)</span>=−<span>sin2</span>θ<span>cosθ</span>−<span>cos2</span>θ<span>sinθ</span></span>
<span>x'<span>(<span>π2</span>)</span>=−<span>sin<span>(π)</span></span><span>cos<span>(<span>π2</span>)</span></span>−<span>cos<span>(π)</span></span><span>sin<span>(<span>π2</span>)</span></span>=1</span>
<span>y'<span>(θ)</span>=−<span>sin2</span>θ<span>sinθ</span>+<span>cos2</span>θ<span>cosθ</span></span>
<span>y'<span>(<span>π2</span>)</span>=−<span>sin<span>(π)</span></span><span>sin<span>(<span>π2</span>)</span></span>+<span>cos<span>(π)</span></span><span>cos<span>(<span>π2</span>)</span></span>=0</span>
So, the slope m of the curve can be found by
<span>m=<span><span>dy</span><span>dx</span></span><span>∣<span>θ=<span>π2</span></span></span>=<span><span>y'<span>(<span>π2</span>)</span></span><span>x'<span>(<span>π2</span>)</span></span></span>=<span>01</span>=0</span>
I hope that this was helpful.
Explained the mistake and correct answer in photo.