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3 years ago

-9 ÷ 7.2 as a decimal

Mathematics

1 answer:

Marat540 [252]3 years ago

3 0

Your answer as a decimal is -1.25

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(a) Find all points where the function f(z) = (x^2+y^2-2y)+i(2x-2xy) is differentiable, and compute the derivative at those poin

Olenka [21]

Answer:

The given function is differentiable at y = 1.

At y = 1, f'(z) = 0

Step-by-step explanation:

As per the given question,

$f(z)\ = (x^{2}+y^{2}-2y)+i(2x - 2xy)$

Let z = x + i y

Suppose,

$u(x,y) = x^{2}+y^{2}-2y$

$v(x,y) = 2x - 2xy$

On computing the partial derivatives of u and v as:

$u'_{x} =2x$

$u'_{y}=2y -2$

And

$v'_{x} =2-2y$

$v'_{y}=-2x$

According to the Cauchy-Riemann equations

$u'_{x} =v'_{y} \ \ \ \ \ \ \ and\ \ \ \ \ \ u'_{y} = -v'_{x}$

Now,

$(u'_{x} =2x) \neq (v'_{y}=-2x)$

$(u'_{y}=2y -2) \ = \ (- v'_{x} =-(2-2y) =2y-2)$

Therefore,

$u'_{y}=- v'_{x}$ holds only.

This means,

2y - 2 = 0

⇒ y = 1

Therefore f(z) has a chance of being differentiable only at y =1.

Now we can compute the derivative

$f'(z)=\frac{1}{2}[(u'_{x}+iv'_{x})-i(u'_{y}+iv'_{y})]$

$f'(z) =\frac{1}{2}[(2x+i(2-2y))-i(2y-2+i(-2x))]$

$f'(z) = i(2-2y)$

At y = 1

f'(z) = 0

Hence, the required derivative at y = 1 , f'(z) = 0

7 0

3 years ago

Which of the following se solutions to the inequality -7x+14>3x-6? Select all that apply. A. -10 B. 10 C. -5 D. 5 E. -3 F. 3

sweet-ann [11.9K]

A, C, E, and G i thinkk

8 0

4 years ago

Rina draws a plan of her school on a coordinate grid. She plots the school gate at point p(-8,-1) and the library at point Q(2,5

natka813 [3]

Answer:

The coordinates of the science lab is:

x = -14/3 , y = 1

Step-by-step explanation:

∵ P is (-8 , -1) and Q is (2 , 5)

∵ The point of the science lab is (x , y)

∵ The science lab point divided PQ at ratio 2 : 1 from Q (two thirds PQ)

∴ $x=\frac{m_{1}x_{p}+m_{2}x_{q}}{m_{1}+m_{2}}$

∴ $y=\frac{m_{1}y_{p}+m_{2}y_{q}}{m_{1}+m_{2}}$

∴ $x=\frac{2(-8)+1(2)}{1+2}=\frac{-14}{3}$

∴ $y=\frac{2(-1)+1(5)}{2+1}=\frac{3}{3}=1$

∴ The point of science lab = (-14/3 , 1)

5 0

3 years ago

In order to verify the equation sin (θ +π/4) =-cosθ. What value would you need to know besides sin (π/4)?

ziro4ka [17]

Answer: A cos (π/4)

I just took a test with this question and got it right

6 0

2 years ago

What is f(5)<br> 0-8<br> -1<br> 1<br> 8

Irina-Kira [14]

F is 5 because -1 and 1 are not web that makes 8 odd so f is 5

7 0

3 years ago