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slamgirl [31]
3 years ago
13

mrs. Williams uses the following recipe for crispy rice treats. She decided to make 2/3 of the recipe. 2 cups of melted butter,

24 oz marshmallow, 13 cups rice crispy treats.

Mathematics
2 answers:
lianna [129]3 years ago
4 0
Multiply the Ingredients by 2/3, 
2 cups of butter times 2/3 is 1.333... or (4/3)
24 oz of Marshmallows would be 16
and 13 cups of rice crispy cereal is 8.6666... or (26/3)

Ilya [14]3 years ago
3 0
To find how much she needs of every ingredient, multiply every ingredient by 2/3.

Butter: 2•2/3=4/3=1&1/3 cups
Marshmallows: 24•2/3=16 oz
Cereal: 13•2/3= 26/3=8&2/3 cups
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It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for \sqrt x.

In that case, you want to find the antiderivative,

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}

Complete the square in the denominator:

9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2

Now substitute x+4=5\sin y, so that \mathrm dx=5\cos y\,\mathrm dy. Then

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy

which simplifies to

\displaystyle\int\frac{5\cos 
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Now, recall that \sqrt{x^2}=|x|. But we want the substitution we made to be reversible, so that

x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)

which implies that -\dfrac\pi2\le y\le\dfrac\pi2. (This is the range of the inverse sine function.)

Under these conditions, we have \cos y\ge0, which lets us reduce \sqrt{\cos^2y}=|\cos y|=\cos y. Finally,

\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C

and back-substituting to get this in terms of x yields

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C
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<em>Greetings from Brasil...</em>

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