All categories

3 years ago

Theperimeter ofrectangle is 36 cmIf its width is 7cm Exaluate to its length

Mathematics

1 answer:

maxonik [38]3 years ago

8 0

Answer:

Step-by-step explanation:

You might be interested in

A truck driver traveled forty-two thousand, three hundred fifty-two miles last year. Write this number in standard form

pentagon [3]

The number is 42,352 in standard form.

7 0

3 years ago

Read 2 more answers

5 + 9y - 2=?<br> I WILL GIVE BRAINLIEST TO THE FIRST TO GET IT RIGHT!!!!

Phoenix [80]

The answer is 9y+3

simplify:
5+9y-2
=5+9y+-2

combine like terms:
= (9y)+(5+-2)
= 9y+3

7 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

Dr. Kora borrowed $8000 to purchase new medical equipment for her new office . If she paid 7.5% simple interest for 10 years. Ho

faltersainse [42]

Answer:

Dr. Kora will pay an interest of $6,000

Step-by-step explanation:

Simple interest = P × R × T

Where:

P = Principal = $8000

R = Rate = 7.5% = 0.075

T = Time = 10 years

∴ Simple interest = 8000 × 0.075 × 10 = $6,000

Therefore Dr. Kora will pay an interest of $6,000

8 0

3 years ago

Rewrite the following equation in logarithmic form and exponential form

Slav-nsk [51]

Answer:The answer for the first one is log2(.25)=-2

The answer for the second one is 8^3=512

Step-by-step explanation:

7 0

3 years ago

Theperimeter ofrectangle is 36 cmIf its width is 7cm Exaluate to its length​

Theperimeter ofrectangle is 36 cmIf its width is 7cm Exaluate to its length