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3 years ago

I don’t understand this!!

Mathematics

1 answer:

Rufina [12.5K]3 years ago

6 0

Answer:

9, 11, 13

Step-by-step explanation:

We can rephrase an odd number into an algebraic equation of (2n+1)

Therefore, 3 consecutive odd numbers would be written as:

(2n+1), (2n+3), (2n+5)

We can then rewrite the question as:

3 x (2n+1) = 2 x (2n+5) + 1

Work out the equation to find n:

6n + 3 = 4n + 10 + 1

(minus 4n from both sides)

2n + 3 = 11

(minus 3 from both sides)

2n = 8

(divide both sides by 2 to get)

n = 4

To find the original 3 consecutive numbers, we just input (4) into (2n+1), (2n+3), (2n+5) to get:

(8+1), (8+3), (8+5)

= 9, 11 and 13

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Answer:

(a) The solution to the differential equation is x = A_0Coswt + Ce^(-kx)

(b) The initial condition t > 0 will not make much of a difference.

Step-by-step explanation:

Given the differential equation

dx/dt= −k(x − A); t > 0, A = A_0Coswt

(a) To solve the differential equation, first separate the variables.

dx/(x - A) = -kdt

Integrating both sides, we have

ln(x - A) = -kt + c

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x = A_0Coswt + Ce^(-kx) (Where C is constant.)

And we have the solution.

(b) Since temperature t ≠ 0, the initial condition t > 0 will not make much of a difference because, Cos(wt) = Cos(-wt).

It is not any different from when t < 0.

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3 years ago

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Answer: $\frac{20}{3}\ minutes$ or $6 \frac{2}{3}\ minutes$

Step-by-step explanation:

For this exercise you can convert the mixed number to an improper fraction:

1. Multiply the whole number part by the denominator of the fraction.

2. Add the product obtained and the numerator of the fraction (This will be the new numerator).

3. The denominator does not change.

Then:

$23\frac{1}{3}= \frac{(23*3)+1}{3}= \frac{70}{3}\ minutes$

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Then, in order to calculate the time Calvin spent making faces at his stuffed tiger, you need to subract 30 minutes and $\frac{70}{3}$ minutes:

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