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3 years ago

PLZ HELP NOW (3^4)/(3^x)=27 what is x

Mathematics

2 answers:

Illusion [34]3 years ago

4 0

Answer:

x = 1

Step-by-step explanation:

Create equivalent expressions in the equation that all have equal bases, then solve for x.

x = 1

Hope this helped

cricket20 [7]3 years ago

3 0

The answer to your question is x=1

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How to prove tan z is analytic using cauchy-riemann conditions

Basile [38]

A function $f(z)=f(x+iy)=u(x,y)+i v(x,y)$ is analytic if the C-R conditions are satisfied:

$\begin{cases}u_x=v_y\\u_y=-v_x\end{cases}$

We have

$f(z)=\tan z=\tan(x+iy)$

Recall the angle sum formula for tangent:

$\tan(x+iy)=\dfrac{\tan x+\tan iy}{1-\tan x\tan iy}$

Now recall that

$\tan iy=\dfrac{\sin iy}{\cos iy}=\dfrac{-\frac{e^y-e^{-y}}{2i}}{\frac{e^y+e^{-y}}2}=\dfrac{i\sinh y}{\cosh y}=i\tanh y$

So we have

$\dfrac{\tan x+\tan iy}{1-\tan x\tan iy}=\dfrac{\tan x+i\tanh y}{1-i\tan x\tanh y}$
$=\dfrac{(\tan x+i\tanh y)(1+i\tan x\tanh y)}{(1-i\tan x\tanh y)(1+i\tan x\tanh y)}$
$=\dfrac{\tan x+i\tanh y+i\tan^2x-\tan x\tanh^2y}{1+\tan^2x\tanh^2y}$
$=\dfrac{\tan x(1-\tanh^2y)}{1+\tan^2x\tanh^2y}+i\dfrac{\tanh y(1+\tan^2x)}{1+\tan^2x\tanh^2y}$
$=\underbrace{\dfrac{\tan x\sech^2y}{1+\tan^2x\tanh^2y}}_{u(x,y)}+i\underbrace{\dfrac{\tanh y\sec^2x}{1+\tan^2x\tanh^2y}}_{v(x,y)}$

We could stop here, but taking derivatives may be messy and would be easier to do if we can write this in terms of sines and cosines.

$u(x,y)=\dfrac{\tan x\sech^2y}{1+\tan^2x\tanh^2y}=\dfrac{\frac{\sin x}{\cos x\cosh^2x}}{1+\frac{\sin^2x\sinh^2y}{\cos^2x\cosh^2y}}=\dfrac{\sin x\cos x}{\cos^2x\cosh^2y+\sin^2x\sinh^2y}$
$u(x,y)=\dfrac{\sin2x}{2\cos^2x\cosh^2y+2(1-\cos^2x)(\cosh^2y-1)}=\dfrac{\sin2x}{2\cosh^2y-1+2\cos^2x-1}$
$u(x,y)=\dfrac{\sin2x}{\cos2x+\cosh2y}$

With similar usage of identities, we can find that

$v(x,y)=\dfrac{\sinh2y}{\cos2x+\cosh2y}$

Now we check the C-R conditions.

$u_x=\dfrac{2\cos2x(\cos2x+\cosh2y)-(-2\sin2x)\sin2x}{(\cos2x+\cosh2y)^2}=\dfrac{2+2\cos2x\cosh2y}{(\cos2x+\cosh2y)^2}$
$v_y=\dfrac{2\cosh2y(\cos2x+\cosh2y)-(2\sinh2y)\sinh2y}{(\cos2x+\cosh2y)^2}=\dfrac{2+2\cosh2y\cos2x}{(\cos2x+\cosh2y)^2}$
$\implies u_x=v_y$

Similarly, you can check that $u_y=-v_x$ , hence the C-R conditions are satisfied, and so $\tan z$ is analytic.

6 0

3 years ago

7g:1kg to its simplest form

hammer [34]

Answer:

7kg:1kg=7:1 itself

Because 7 and 1 has one '1' as a common factor, so they can't be simplified

5 0

4 years ago

What is the area of this polygon?

Oksi-84 [34.3K]

all you have to do is add up all the sides and your answer will be 21 cm

7 0

4 years ago

If you cannot see the photo the question is A rental car charges 160.00 per week plus 0.25 per mile to rent a car. How many mile

Rzqust [24]

Answer:

You can travel 630 miles.

Step-by-step explanation:

317.5 - 160 = 157.5

157.5 / .25 = 630

8 0

3 years ago

Suzanne bought 50 apples at the apple orchard. She bought 4 times as many red apples as green apples. How many more red apples t

Natali [406]

Let x = the number of green apples, let 4x = the number of red apples
4x + x = 50 Set up the quation
5x = 50 Combine like terms
---- ---- Divide by 5 on both sides to get x alone
5 5
x = 10 green apples
4x = 4(10) = 40 red apples

40 - 10 = 30. Suzanne bought 30 more red apples than green apples.

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3 years ago