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OLEGan [10]
3 years ago
6

If y varies directly as x^2 and y=12 when x=2, find y when x=5

Mathematics
1 answer:
Shkiper50 [21]3 years ago
7 0
y=ax^2\\\\y=12\ \ \ and\ \ \ x=2\ \ \ \Rightarrow\ \ \ 12=a\cdot 2^2\ \ \ \Rightarrow\ \ \ a= \frac{4}{12}= \frac{1}{3}  \\\\y=\frac{1}{3} x^2\\\\x=5\ \ \ \Rightarrow\ \ \ y=\frac{1}{3} \cdot5^2=\frac{25}{3} =8\frac{1}{3}
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Convert 1 cal/(m^2 * sec * °C) into BTU/(ft^2 * hr * °F)
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Answer:

1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=0.03926\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}

Step-by-step explanation:

To find : Convert 1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C} into \frac{\text{BTU}}{ft^2\times hr\times ^\circ F}

Solution :

We convert units one by one,

1\text{ m}^2=10.7639\text{ ft}^2

1\text{ sec}=\frac{1}{3600}\text{ hour}

1\text{ cal}=0.003968\text{ BTU}

Converting temperature unit,

^\circ C\times \frac{9}{5}+32=^\circ F

1^\circ C\times \frac{9}{5}+32=33.8^\circ F

So, 1^\circ C=33.8^\circ F

Substitute all the values in the unit conversion,

1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=\frac{0.003968}{10.7639\times \frac{1}{3600}\times 33.8}\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}

1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=\frac{0.003968}{0.101061}\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}

1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=0.03926\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}

Therefore, The conversion of unit is 1\ \frac{\text{cal}}{m^2\times sec\times ^\circ C}=0.03926\frac{\text{BTU}}{ft^2\times hr\times ^\circ F}

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