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ruslelena [56]
3 years ago
7

Please help me thanks :))

Mathematics
1 answer:
Andrei [34K]3 years ago
5 0
Hello!

You use the Pythagorean Theorem to solve this

a^{2} + b^{2} = c^{2}

Put in the values it tells you

a^{2} + 1^{2} =   \frac{5}{4} ^{2}

Square the numbers

a^{2} + 1 =  \frac{25}{16}

Subtract 1 from both sides

a^{2} =  \frac{9}{16}

Take the square root of both sides

a =  \frac{3}{4}

The answer 3/4 or 0.75

Hope this helps!
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Answer:

\displaystyle  \frac{dy}{dx} =    \frac{2x + 2}{x^3}

Step-by-step explanation:

we would like to figure out the derivative of the following:

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to do so, let,

\displaystyle y =  \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }

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take derivative in both sides:

\displaystyle  \frac{dy}{dx} =  \frac{d}{dx}  (3 -  2 {x}^{ - 1}  -   { {x}^{  - 2} } )

use sum derivation rule which yields:

\rm\displaystyle  \frac{dy}{dx} =  \frac{d}{dx}  3 -   \frac{d}{dx} 2 {x}^{ - 1}  -     \frac{d}{dx} {x}^{  - 2}

By constant derivation we acquire:

\rm\displaystyle  \frac{dy}{dx} =  0 -   \frac{d}{dx} 2 {x}^{ - 1}  -     \frac{d}{dx} {x}^{  - 2}

use exponent rule of derivation which yields:

\rm\displaystyle  \frac{dy}{dx} =  0 -   ( - 2 {x}^{ - 1 -1} ) -     ( - 2 {x}^{  - 2 - 1} )

simplify exponent:

\rm\displaystyle  \frac{dy}{dx} =  0 -   ( - 2 {x}^{ -2} ) -     ( - 2 {x}^{  - 3} )

two negatives make positive so,

\displaystyle  \frac{dy}{dx} =   2 {x}^{ -2} +      2 {x}^{  - 3}

<h3>further simplification if needed:</h3>

by law of exponent we acquire:

\displaystyle  \frac{dy}{dx} =   \frac{2 }{x^2}+       \frac{2}{x^3}

simplify addition:

\displaystyle  \frac{dy}{dx} =    \frac{2x + 2}{x^3}

and we are done!

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