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3 years ago

What is a rational number

Mathematics

2 answers:

Olenka [21]3 years ago

8 0

A fraction, a squared number, a decimal, a repeating decimal

musickatia [10]3 years ago

6 0

A rational number is a number that can me a quotient or fraction

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Newton’s law of cooling states that dx/dt= −k(x − A) where x is the temperature, t is time, A is the ambient temperature, and k

Vadim26 [7]

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

x - A = Ce^(-kt) (Where C = ce^(-kt))

x = A + Ce^(-kx)

Now, we put A = A_0Coswt

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.

7 0

3 years ago

Wyatt is hiking a trail that is 11/12 miles long. After hiking 1/4 mile, he stops for water. How much farther must he hike to fi

ankoles [38]

Answer:

He had hiked 3/12 of a mile so the answer is 8/12 of a mile

Step-by-step explanation:

You need to make 1/4 into twelves by multiplying both sides by 3 to get 3/12.

You take that and subtract it from the total distance. 11/12 - 3/12 = 8/12

6 0

3 years ago

Describe how you would estimate the square root of a number that is not a perfect square without using a calculator

Keith_Richards [23]

Get as close to the perfect square, which you should have memorized. then divide the number by the perfect square. average the answers (perfect square and quotient) by adding them and diving by 2

5 0

3 years ago

Read 2 more answers

F:x = x²-4 and g:x = 2/x-2, x≠2, find g²(1)

ArbitrLikvidat [17]

Answer:

Sub to lazer beam

Step-by-step explanation:

6 0

3 years ago

From the sum of a2−2ab+b2 and 2a2+2ab+b2 subtract the sum of a2−b2 and a2+ab+3b2

Sedaia [141]

Answer:

$a^2-ab$

Step-by-step explanation:

We need to find the sum of $a^2-2ab+b^2$ and $2a^2+2ab+b^2$ first.

Adding $a^2-2ab+b^2$ + $2a^2+2ab+b^2$

Combining like terms, we get

$a^2+2a^2=3a^2$

-2ab+2ab = 0

$b^2+b^2=2b^2$

Therefore,

$a^2-2ab+b^2 +2a^2+2ab+b^2=3a^2+2b^2$ .

Now, we need to find the sum of $a^2-b^2 \ \ and \ \ a^2+ab+3b^2.$ .

Adding $a^2−b^2+a^2+ab+3b^2$ .

Combining like terms, we get

$a^2+a^2=2a^2$

$-b^2+3b^2=2b^2$ .

Therefore,

$a^2−b^2+a^2+ab+3b^2=2a^2+ab+2b^2.$

Now, subtracting

$3a^2+2b^2 -(2a^2+ab+2b^2)$ .

Distributing minus sign over second parenthesis, we get

$3a^2+2b^2-2a^2-ab-2b^2$ .

Combining like terms,

$3a^2-2a^2=a^2$

$2b^2-2b^2=0$

Therefore,

$3a^2+2b^2-2a^2-ab-2b^2=a^2-ab$ .

Therefore, the difference of the sum of $a^2-2ab+b^2$ + $2a^2+2ab+b^2$ and $a^2-b^2+a^2+ab+3b^2.$ is $a^2-ab.$

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3 years ago