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Flura [38]
3 years ago
9

Given radical a and radical b are in simplest radical form and radical a timed radical b equals c radical d and c radical d is i

n simplest form. Explain in words how c and d are related to a and b. Then give an example to support your solution.

Mathematics
1 answer:
lawyer [7]3 years ago
6 0

Answer:

See below.

Step-by-step explanation:

Since sqrt(a) and sqrt(b) are in simplest radical form, that means a and b have no perfect square factors. When sqrt(a) and sqrt(b) are multiplied giving c * sqrt(d), the fact that c came out of the root means that there was c^2 inside the product sqrt(ab). This means that a and b have at least one common factor.

ab = c^2d

Example:

Let a = 6 and let b = 10.

sqrt(6) and sqrt(10) are in simplest radical form.

Now we multiply the radicals.

sqrt(a) * sqrt(b) = sqrt(6) * sqrt(10) = sqrt(60) = sqrt(4 * 15) = 2sqrt(15)

We have c = 2 and d = 15.

ab = c^2d

6 * 10 = 2^2 * 15

60 = 60

Our relationship between a, b and c, d works.

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Ivanshal [37]

Answer:

yes

Step-by-step explanation:

We are given that a Cauchy Euler's equation

t^2y''-ty'+y=0 where t is not equal to zero

We are given that two solutions of given Cauchy Euler's equation are t,t ln t

We have to find  the solutions are independent or dependent.

To find  the solutions are independent or dependent we use wronskain

w(x)=\begin{vmatrix}y_1&y_2\\y'_1&y'_2\end{vmatrix}

If wrosnkian is not equal to zero then solutions are dependent and if wronskian is zero then the set of solution is independent.

Let y_1=t,y_2=t ln t

y'_1=1,y'_2=lnt+1

w(x)=\begin{vmatrix}t&t lnt\\1&lnt+1\end{vmatrix}

w(x)=t(lnt+1)-tlnt=tlnt+t-tlnt=t where t is not equal to zero.

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3 years ago
Akiko, manager of Little Ginza, is concerned about ordering the right amount of salmon. Daily consumption of salmon has a mean o
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Cindy dissolves 19 1 /4 grams of drink mix in 1 3 /4 ounces of water. What is the unit rate in grams of drink mix per ounce of w
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Answer:

Unit rate in grams of drink mix per ounce of water = 11 gram / ounces

Step-by-step explanation:

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⇒  Unit rate in grams of drink mix per ounce of water = Amount of drink mix / Amount of water

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Answer:

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