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3 years ago

can anyone please help me, find the length of side x in simplest radical form with a rational denominator.

Mathematics

1 answer:

ANEK [815]3 years ago

6 0

X is 2.3094
Or 16/3
***/=root***

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3 years ago

Solve the differential equation y prime equals the product of 2 times x and the square root of the quantity 1 minus y squared .

MatroZZZ [7]

Answer:

1. y = sin(x²+C)

2. see below

Step-by-step explanation:

1. $\frac{dy}{dx} = 2x\sqrt{1-y^2}$

separation of variables

$\frac{dy}{\sqrt{1-y^2} } = 2xdx$

integration both sides $\int\frac{dy}{\sqrt{1-y^2} } = \int2xdx$

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4 0

3 years ago

Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$

horrorfan [7]

Answer:

$A +B+C+D = 3$ is the correct answer.

Step-by-step explanation:

Given:

$\frac{5}{2+\sqrt{6}}$

To find:

$A+B+C+D = ?$ if given term is written as following:

$\frac{A\sqrt{B}+C}{D}$

<u>Solution:</u>

We can see that the resulting expression does not contain anything under $\sqrt$ (square root) so we need to rationalize the denominator to remove the square root from denominator.

The rule to rationalize is:

Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.

Applying this rule to rationalize the given expression:

$\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \ (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}$