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3 years ago

Find dy/dx by implicit differentiation. 4x2 + 5xy - y2 = 6

1 answer:

5 0

4x^2 + 5xy - y^2 = 6
Implicitly differentiating both sides,
4(2x) + 5(x y' + y) - 2yy' = 0

where y' = dy/dx

8x + 5xy' +5y -2yy' = 0

combining y' terms
y' (5x-2y) +8x +5y = 0

y'(5x-2y) = -(8x+5y)

dy/dx = -(8x+5y)/(5x-2y)
or
dy/dx = (8x+5y)/(2y-5x)

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lidiya [134]

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2r - 11 = 17

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2 years ago

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2 years ago

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mamaluj [8]

Answer:

$P(blue)=37.5\%$

Step-by-step explanation:

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2 years ago

Read 2 more answers

I’m Really lost if I could get a answer it would be greatly appreciated

Nataly [62]

<h3>Answers:</h3>

$f(g(x)) = \sqrt{x^2+5}+5\\\\g(f(x)) = x+30+10\sqrt{x-1}$

================================================

Work Shown:

Part 1

$f(x) = \sqrt{x-1}+5\\\\f(g(x)) = \sqrt{g(x)-1}+5\\\\f(g(x)) = \sqrt{x^2+6-1}+5\\\\f(g(x)) = \sqrt{x^2+5}+5\\\\$

Notice how I replaced every x with g(x) in step 2. Then I plugged in g(x) = x^2+6 and simplified.

------------------

Part 2

$g(x) = x^2+6\\\\g(f(x)) = \left(f(x)\right)^2+6\\\\g(f(x)) = \left(\sqrt{x-1}+5\right)^2+6\\\\g(f(x)) = \left(\sqrt{x-1}\right)^2+2*5*\sqrt{x-1}+\left(5\right)^2+6\\\\g(f(x)) = x-1+10\sqrt{x-1}+25+6\\\\g(f(x)) = x+30+10\sqrt{x-1}\\\\$

In step 4, I used the rule (a+b)^2 = a^2+2ab+b^2

In this case, a = sqrt(x-1) and b = 5.

You could also use the box method as a visual way to expand out $\left(\sqrt{x-1}+5\right)^2$

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RoseWind [281]

$0.15 per ounce * 26 Oz = $3.90

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2 years ago

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