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2 years ago

The sum of two numbers is 8, and the sum of their squares is 34. what is the larger number

Mathematics

1 answer:

bija089 [108]2 years ago

6 0

Answer:

The larger number is 5.

Step-by-step explanation:

Let the numbers be represented by x and y. Then:

x + y = 8 is their sum, and

x² + y² = 34 is the sum of their squares.

Let's solve this system of equations using substitution. Since x + y = 8,

x = 8 - y. Subbing this 8 - y for x into the second equation, we get:

(8 - y)² + y² = 34, or

64 - 16 y + y² + y² = 34

Simplifying, we get first: 30 - 16y + 2y² = 0, and then:

2y² - 16y + 30 = 0, and after reducing, y² - 8y + 15 = 0.

This factors into (y - 3)(y - 5) = 0, and so y = 3 and y = 5.

The larger number is 5.

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Convert 1 cal/(m^2 * sec * °C) into BTU/(ft^2 * hr * °F)

Crazy boy [7]

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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Answer:

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