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3 years ago

14

Theo wants to use a cokkie recipe that makes 36 cookies but he wants to reduce the number of cookies to 24.if the recipe specife

s using 2 cups of sugar, how many sugar should he use ?

1 answer:

Ratling [72]3 years ago

8 0

Answer:

Theo Should use <u>1.3 cups</u> of Sugar to make 24 cookies.

Step-by-step explanation:

Given;

Number of cookies required by recipe = 36 cookies

Number of cookies Theo wants to use = 24 cookies

Number of cups sugar recipe requires = 2 cups

We need to find Number of cups sugar Theo should use to make cookie according to recipe.

Now,

For 36 cookies = 2 cups of sugar

So For 24 cookies = Number of cups of sugar required for 24 cookies.

By Using Cross Multiplication we get;

Number of cups of sugar required for 24 cookies = $\frac{24\times2}{36}= 1.33\ cups$

Hence Theo Should use <u>1.3 cups</u> of Sugar to make 24 cookies.

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The perimeter of a rectangle is given by the formula,

$P=2l+2w$

We substitute,

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and

$l=\frac{7}{2}x+7y$

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$15x+17y=2(\frac{7}{2}x+7y)+2w$

$15x+17y=7x+14y+2w$

We now group the x and y terms on the Left Hand Side of the equation to get.

$15x-7x+17y-14y=2w$

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If there is such a scalar function <em>f</em>, then

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$f(x,y,z)=4xy^2+g(y,z)$

Differentiate both sides with respect to <em>y</em> :

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$\implies\dfrac{\partial g}{\partial y}=4e^{4z}$

Integrate both sides with respect to <em>y</em> :

$g(y,z)=4ye^{4z}+h(z)$

Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :

$f(x,y,z)=4xy^2+4ye^{4z}+h(z)$

$\dfrac{\partial f}{\partial z}=16ye^{4z}=16ye^{4z}+\dfrac{\mathrm dh}{\mathrm dz}$

$\implies\dfrac{\mathrm dh}{\mathrm dz}=0$

Integrate both sides with respect to <em>z</em> :

$h(z)=C$

So we end up with

$\boxed{f(x,y,z)=4xy^2+4ye^{4z}+C}$

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