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3 years ago

A rectangular wall in Andrew's house has the dimensions shown. If

Mathematics

1 answer:

trasher [3.6K]3 years ago

3 0

Answer:

b. 189 square feet

18 X 12 = 216 square feet

4.5 X 3 = 13.5

13.5 X 2 = 27

216 - 27 = 189 square feet

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I NEED HELP FAST LIKE REAAAAAL FAST!

Georgia [21]

Answer: The third one is the correct answer.

Step-by-step explanation: If you do the count, you will see that the number of goats added five times is equal to the number of cows.

4 0

3 years ago

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

A truck enters a highway at 60 mph. A car enters the highway at the same place 11 minutes later and drives 74 mph in the same di

Crank

Answer:

Since speed is given in terms of "hours" we must convert 9 minutes to hours:

9 minutes = 9/60 hours = 3/20 hours

Let x = time (hours) it takes car to pass the truck

then

60(x + 3/20) = 69x

multiplying both sides by 20:

60(20x + 3) = 1380x

1200x + 180 = 1380x

180 = 180x

1 hour = x

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

What is the area of the square? Perimeter =108mi. 27 width

Leni [432]

Answer:

729 square units

Step-by-step explanation:

If the width of the square is 27, then the length is also 27. After all, this is a square with four equal sides.

The area of a square is A = s^2, where s is the length of one side.

Here, A = 27^2 = 729 square units.

4 0

4 years ago

-9n>-36? Solve and graph

wlad13 [49]

-9n>-36
divide both sides by -9
n<4

6 0

4 years ago