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Arisa [49]
3 years ago
7

Wiley wants to make as many snack

Mathematics
1 answer:
Ghella [55]3 years ago
6 0

Answer:

Wiley can make 10 snack packs.

Step-by-step explanation:

Assuming that you can't put a fraction of one item in a snack pack and yoou must use all the items, Each pack must contain a integer number of items. The smallest possible way is for each snack pack to contain 3 slices of cheese and 4 crackers. This results in a total of 10 snack packs.

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Differentiate with respect to X <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7Bcos2x%7D%7B1%20%2Bsin2x%20%7D%20
Mice21 [21]

Power and chain rule (where the power rule kicks in because \sqrt x=x^{1/2}):

\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'

Simplify the leading term as

\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}

Quotient rule:

\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}

Chain rule:

(\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)

(1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)

Put everything together and simplify:

\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{(1+\sin(2x))(-2\sin(2x))-\cos(2x)(2\cos(2x))}{(1+\sin(2x))^2}

=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2\sin^2(2x)-2\cos^2(2x)}{(1+\sin(2x))^2}

=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}

=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac{\sin(2x)+1}{(1+\sin(2x))^2}

=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}

=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}

=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}

5 0
3 years ago
Algebra 1 pls help :)
MaRussiya [10]

Answer:

c

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What’s the answer???
LuckyWell [14K]

Answer:

D

Step-by-step explanation:

8 0
3 years ago
Aimee must add together the following numbers:
Feliz [49]
The correct answer is C. Aimee used the Associative and Commutative properties to put numbers that are easy to add next to each other.
4 0
3 years ago
If 11! = 39,916,800, then 12!/4! =
Scrat [10]
12! / 4!
= 1×2×3×4×5×6×7×8×9×10×11×12 / 1×2×3×4
= 5×6×7×8×9×10×11×12 = 19958400
8 0
3 years ago
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