How do you write a ratio as a percent

Mathematics

1 answer:

Vikentia [17]4 years ago

3 0

Take the ratio
4:8
Convert it to a fraction
4/8
Divide
.5
Multiply by 100 and add a % sign
50%

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Hi, help with question 18 please. thanks

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Answer:

See Below.

Step-by-step explanation:

We are given the equation:

$\displaystyle y^2 = 1 + \sin x$

And we want to prove that:

$\displaystyle 2y\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right) ^2 + y^2 = 1$

Find the first derivative by taking the derivative of both sides with respect to x:

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Divide both sides by 2y:

<h3> $\displaystyle \frac{dy}{dx} = \frac{\cos x}{2y}$ </h3>

Find the second derivative using the quotient rule:

$\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{(\cos x)'(2y) - (\cos x)(2y)'}{(2y)^2}\\ \\ &= \frac{-2y\sin x-2\cos x \dfrac{dy}{dx}}{4y^2} \\ \\ &= -\frac{y\sin x + \cos x\left(\dfrac{\cos x}{2y}\right)}{2y^2} \\ \\ &= -\frac{2y^2\sin x+\cos ^2 x}{4y^3}\end{aligned}$