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ivolga24 [154]
3 years ago
7

Working out 34 x 17 using an area model

Mathematics
1 answer:
Troyanec [42]3 years ago
4 0
Your answer is going to be 578 because you had to add 300+210+40+28 and it = to 578 your welcome
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If g(x)=4x^2-16 were shifted 5 units to the right and 2 down hat would the new equation be
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Answer:

\displaystyle x = \frac{1}{3}.

Step-by-step explanation:

Consider the double angle identity for tangents:

\displaystyle \tan(2\theta) = \frac{2\tan{\theta}}{1 - \tan^{2}{\theta}}.

Also, for two complementary angles,

\displaystyle \tan{\left(\frac{\pi}{2} - \theta \right)} = \frac{1}{\tan{\theta}}.

Subtract \tan^{-1}(x + 1) from both sides of this equation:

\displaystyle 2\tan^{-1}{x} = \frac{\pi}{2} + (-\tan^{-1}(x + 1)).

Take the tangent of both sides of this equation:

\displaystyle \tan(2\tan^{-1}{x}) = \tan\left(\frac{\pi}{2} -\tan^{-1}\left(x + 1\right)\right).

Apply the double-angle identity to the left-hand side of this equation:

\displaystyle \tan(2\tan^{-1}{x}) \implies \frac{2\tan(\tan^{-1}x)}{1 - \tan^{2}(\tan^{-1}x)}\implies \frac{2x}{1 - x^{2}}.

The two angles \displaystyle \left(\frac{\pi}{2} + (-\tan^{-1}\left(x + 1\right))\right) and (x - 1) are complementary. Therefore, for the right-hand side of this equation,

\displaystyle \tan\left(\frac{\pi}{2} -\tan^{-1}\left(x + 1\right)\right)\implies \frac{1}{\tan(\tan^{-1}(x + 1))} \implies \frac{1}{x + 1}.

Equate the two sides of this equation:

\begin{aligned} & \frac{2x}{1 - x^{2}} = \frac{1}{x + 1}\\ \implies & \frac{2x}{(1 - x)(1 + x)} = \frac{1}{1 + x}\\\implies & 2x = 1 - x,\; x \ne 1,\; x \ne -1\\\implies & x = \frac{1}{3}\end{aligned}.

5 0
3 years ago
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