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3 years ago

The sum of three consecutive odd integers is at most 123. Find the pair with the greatest sum

Mathematics

1 answer:

galben [10]3 years ago

4 0

Answer:

a1 = 39, a2 = 41, a3 = 43

The pair with the greatest sum is a2 + a3 = 41 + 43 = 84

Step-by-step explanation:

Let the first integer be a1 = a.

Let the second odd integer be a2 = a + 2

Let the third odd integer be a3 = (a + 2) + 2 = a + 4

The sum of three consecutive odd integers is 123.

123 = a1 + a2 + a3

123 = a + (a + 2) + (a + 4)

123 = 3a + 6

117 = 3a

a = 39

a1 = a = 39

a2 = a + 2 = 39 + 2 = 41

a3 = a + 4 = 39 + 4 = 43

The pair with the greatest sum is a2 + a3 = 41 + 43 = 84

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3 years ago

According to Boyle's Law, if the temperature of a confined gas is held fixed, then the product of the pressure P and the volume

Bad White [126]

If PV = 800, then P can be written as a function of V,

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(P (250) - P (200)) / (250 in³ - 200 in³) = (3.2 lb/in² - 4lb/in²) / (50 in³)

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(Or -0.016 lb/in⁵, but I figure writing the rate as (units of pressure) per (unit volume) makes more sense.)

(b) We can also write V as a function of P :

V(P) = 800 / P

Take the derivative:

V'(P) = - 800 / P²

which immediately demonstrates that V'(P) ∝ 1 / P², as required. (The fish-looking symbol, ∝, means "is proportional to".)

If differentiating is supposed to be more involved, you can use the limit definition:

$V'(P)=\displaystyle\lim_{h\to0}\frac{V(P+h)-V(P)}h$

$V'(P)=\displaystyle\lim_{h\to0}\frac{\frac{800}{P+h}-\frac{800}P}h$

$V'(P)=\displaystyle\lim_{h\to0}\frac{\frac{800P-800(P+h)}{P(P+h)}}h$

$V'(P)=\displaystyle800\lim_{h\to0}\frac{-\frac h{P(P+h)}}h$

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7 0

3 years ago

I need help with this question

klemol [59]

Answer:

The answer is going to be option 1.

Step-by-step explanation:

The answer you get from multiply an number by itself is a perfect square.

4 0

4 years ago

Read 2 more answers

Suntract decimals 11.63_6.7

kozerog [31]

Answer:

11.63 - 6.7 = 4.93

Hope this helps!

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3 years ago

A number is multiplied by 12, and that product is added to 6. The sum is equal to the product of 6 and 15. Find the number.

satela [25.4K]

Answer:

The number is 7

Step-by-step explanation:

let number be x

12x+6=6x15

12x+6=90

12x=90-6

12x=84

x=7

Hope this was helpful

5 0

2 years ago