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alexandr1967 [171]
2 years ago
6

PLEASE HHELP!!! Bring the fraction:

Mathematics
1 answer:
Anna35 [415]2 years ago
8 0

Answer:

\frac{b}{7a^2c} = \frac{5abc^2}{35a^3c^3}

\frac{a}{a - 4} = \frac{-a^2 - 4a}{16 -a^2}

Step-by-step explanation:

Given

\frac{b}{7a^2c}

Express the denominator as 35a^3c^3

To do this, we divide35a^3c^3 by the denominator

\frac{35a^3c^3}{7a^2c} = 5ac^2

So, the required fraction is:

\frac{b}{7a^2c} * \frac{5ac^2}{5ac^2}

\frac{5abc^2}{35a^3c^3}

Hence:

\frac{b}{7a^2c} = \frac{5abc^2}{35a^3c^3}

Given

\frac{a}{a - 4}

Express the denominator as 16 - a^2

Multiply the fraction a+4/a+4

So, we have:

\frac{a}{a - 4} * \frac{(a + 4)}{(a + 4)}

Apply difference of two squares to the denominator

\frac{a^2 + 4a}{a^2 - 16}

Take the additive inverse of the numerator and denominator

\frac{-(a^2 + 4a)}{-(a^2 - 16)}

\frac{-a^2 - 4a}{16 -a^2}

Hence:

\frac{a}{a - 4} = \frac{-a^2 - 4a}{16 -a^2}

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Answer:

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Step-by-step explanation:

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Use the Chain Rule (Calculus 2)
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1. By the chain rule,

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I'm going to switch up the notation to save space, so for example, z_x is shorthand for \frac{\partial z}{\partial x}.

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We have

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Similarly,

w_t=w_xx_t+w_yy_t+w_zz_t

where

x=\cosh^2t\implies x_t=2\cosh t\sinh t

y=\sinh^2t\implies y_t=2\cosh t\sinh t

z=t\implies z_t=1

To capture all the partial derivatives of w, compute its gradient:

\nabla w=\langle w_x,w_y,w_z\rangle=\dfrac{\langle1,-1,1\rangle}{\sqrt{1-(x-y+z)^2}}}=\dfrac{\langle1,-1,1\rangle}{\sqrt{-2t-t^2}}

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2. The problem is asking for \frac{\partial z}{\partial x} and \frac{\partial z}{\partial y}. But z is already a function of x,y, so the chain rule isn't needed here. I suspect it's supposed to say "find \frac{\partial z}{\partial s} and \frac{\partial z}{\partial t}" instead.

If that's the case, then

z_s=z_xx_s+z_yy_s

z_t=z_xx_t+z_yy_t

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x=s+t\implies x_s=x_t=1

y=s^2t\implies\begin{cases}y_s=2st\\y_t=s^2\end{cases}

Putting everything together, we get

z_s=\cos(s+t)\cos(s^2t)-2st\sin(s+t)\sin(s^2t)

z_t=\cos(s+t)\cos(s^2t)-s^2\sin(s+t)\sin(s^2t)

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Answer:

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Step-by-step explanation:

A local aquarium purchased a new turtle tank for their giant turtle exhibit  for their giant turtle exhibit.

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Answer:

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