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vlabodo [156]
3 years ago
7

Prove that for any natural n the value of the expression (n+7)^2–n^2 is divisible by 7.

Mathematics
1 answer:
Afina-wow [57]3 years ago
3 0

Step-by-step explanation:

(n + 7)² – n²

n² + 14n + 49 – n²

14n + 49

7 (2n + 7)

7 is a factor, so for any natural n, (n + 7)² – n² is a multiple of 7.

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6⋅7-3^2⋅9+4^3 what is the value?
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\textsf{Hey there!}

\mathsf{Equation: 6 \times 7- 3^2 \times9+4^3}

\mathsf{3^2 = 3\times3=9}

\mathsf{4^3= 4\times4\times4=16\times4 = 64}

\mathsf{6\times7 = 42}

\mathsf{9\times9= 81}

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Answer:

54 minutes

Step-by-step explanation:

From the question, we are given;

  • A room with dimensions 5.2 m by 4.3 m by 2.9 m
  • The exchange air rate is 1200 L/min

We are required to determine the time taken to exchange the air in the room;

First we are going to determine the volume of the room;

Volume of the room = length × width × height

                                  = 5.2 m × 4.3 m × 2.9 m

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Then we should know, that 1 m³ = 1000 L

Therefore, we can convert the volume of the room into L

= 64.844 m³ × 1000 L

= 64,844 L

But, the rate is 1200 L/min

Thus, time = Volume ÷ rate

                  = 64,844 L ÷ 1200 L/min

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Therefore, it would take approximately 54 minutes

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