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3 years ago

A recipe requires 4 cups of flour to make 3 dozen cookies. How many cups of flour are needed to make 10 dozen cookies?

Mathematics

2 answers:

Leona [35]3 years ago

7 0

Answer:

13 1/2 cups of flour.

Step-by-step explanation:

VikaD [51]3 years ago

6 0

9514 1404 393

Answer:

13 1/3 cups

Step-by-step explanation:

We assume flour is proportional to cookies, so we have ...

cups/dozens = x/10 = 4/3

Multiplying by 10 gives ...

x = 40/3 = 13 1/3

13 1/3 cups of flour are needed for 10 dozen cookies.

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2 years ago

Evaluate the definite integral. 1 x4(1 + 2x5)5 dx.

Nata [24]

Answer:

Step-by-step explanation:

Given the definite integral $\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx$ , we to evaluate it. Using integration by substitution method.

Let u = 1-2x⁵ ...1

du/dx = -10x⁴

dx = du/-10x⁴.... 2

Substitute equation 1 and 2 into the integral function and evaluate the resulting integral as shown;

$= \int\limits {\dfrac{x^4}{u^5} } \, \dfrac{du}{-10x^4}$

$= \dfrac{-1}{10} \int\limits {\dfrac{du}{u^5} } \\\\= \dfrac{-1}{10} \int\limits {{u^{-5}du } \\= \dfrac{-1}{10} [{\frac{u^{-5+1}}{-5+1}] \\\\= \dfrac{-1}{10} ({\frac{u^{-4}}{-4})\\\\$

$= \dfrac{u^{-4}}{40} \\\\\\= \dfrac{1}{40u^4} +C$

substitute u = 1-2x⁵ into the result

$= \dfrac{1}{40(1-2x^5)^4} +C$

Hence $\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx$ $= \dfrac{1}{40(1-2x^5)^4} +C$

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2 years ago

Peter is reading a 193-page book. He has read three pages more than one fourth of the number of pages he hasnt yet read. How man

Anit [1.1K]

Let n = the number of pages not read
Then the number of pages read = n/4 + 3
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n + n/4 + 3 = 193
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2 years ago

Solve the equation for y 1/3x+y=4

densk [106]

Answer:

y=-1/3x+4

Step-by-step explanation:

1/3x+y=4

y=4-1/3x

y=-1/3x+4

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3 years ago