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2 years ago

Please help ASAP! thank you ( geometry)

Mathematics

2 answers:

Svetlanka [38]2 years ago

8 0

Plus in the numbers my advice

Lostsunrise [7]2 years ago

7 0

Answer:

Step-by-step explanation:

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Using elimination method, what will be the value of y after solving -x - y = 5 and -x + 4y = 15?

natka813 [3]

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Answer:

y = 2

Step-by-step explanation:

The variable x can be eliminated by subtracting the first equation from the second.

(-x +4y) -(-x -y) = (15) -(5)

5y = 10 . . . . . . . simplify

y = 2 . . . . . . . . . divide by 5

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2 years ago

Separate the number 18 into two parts where the product of those parts is 77

mart [117]

Answer: 11, 7

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alina1380 [7]

Answer:

1/2

Step-by-step explanation:

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2 years ago

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If x = a cosθ and y = b sinθ , find second derivative

Olin [163]

I'm guessing the second derivative is for y with respect to x, i.e.

$\dfrac{\mathrm d^2y}{\mathrm dx^2}$

Compute the first derivative. By the chain rule,

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

We have

$y=b\sin\theta\implies\dfrac{\mathrm dy}{\mathrm d\theta}=b\cos\theta$

$x=a\cos\theta\implies\dfrac{\mathrm dx}{\mathrm d\theta}=-a\sin\theta$

and so

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{b\cos\theta}{-a\sin\theta}=-\dfrac ba\cot\theta$

Now compute the second derivative. Notice that $\frac{\mathrm dy}{\mathrm dx}$ is a function of $\theta$ ; so denote it by $f(\theta)$ . Then

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm dx}$

By the chain rule,

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm df}{\mathrm d\theta}\dfrac{\mathrm d\theta}{\mathrm dx}=\dfrac{\frac{\mathrm df}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$