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4 years ago

100 POINTS QUESTION ON ATTACHMENT

Mathematics

2 answers:

Nadya [2.5K]4 years ago

7 0

Answer:

Step-by-step explanation:

Vlada [557]4 years ago

3 0

Answer:

the answer is d because you have to follow the order of operations.

Step-by-step explanation:

You might be interested in

A complex number, represented by z = x + iy, may also be visualized as a 2 by 2 matrix

Marat540 [252]

Answer:

Step-by-step explanation:

A) Suppose that we have the complex numbers

$z= x + iy \quad \text{and} \quad \\\\ \tilde{z}=\tilde{x} + i \tilde{y}$

Remember that to sum complex numbers, we sum the real parts of the two numbers to get the real part and the imaginary parts of the two numbers to get the imaginary part. Hence,

$z+\tilde{z} = (x + i y) + (\tilde{x} + i \tilde{y}) = (x + \tilde{x})+i (y+\tilde{y})$

On the other hand, if we sum the matrix visualizations of $z \quad \text{and} \quad \tilde{z}$ we get

$\left[\begin{array}{cc}x &y\\-y&x\end{array}\right] + \left[\begin{array}{cc}\tilde{x}&\tilde{y}\\ -\tilde{y}&\tilde{x}\end{array}\right] = \left[\begin{array}{cc}x + \tilde{x}& y + \tilde{y}\\-(y+\tilde{y})&x+\tilde{x}\end{array}\right]$

which is the matrix visualization of $z + \tilde{z}$ .

To multiply two complex numbers, we use the distributive law to multiplly and then separete the real part from the imaginary part

$z \cdot \tilde{z}= (x + iy) \cdot (\tilde{x} + i \tilde{y})=(x \tilde{x} + i x \tilde{y} + i \tilde{x} y - y\tilde{y} ) = (x\tilde{x}-y\yilde{y})+i(x\tilde{y}+\tilde{x}y)$

Again, if we multiply the matrix visualizations of $z \quad \text{and} \quad \tilde{z}$ we get

$\left[\begin{array}{cc}x&y\\-y&x\end{array}\right]\left[\begin{array}{cc}\tilde{x}&\tilde{y}\\-\tilde{y}&\tilde{x}\end{array}\right] = \left[\begin{array}{cc}x\tilde{x}-y\tilde{y}&x\tilde{y}+y\tilde{x}\\-y\tilde{x}-x\tilde{y}&x\tilde{x}-y\tilde{y}\end{array}\right]$

which is the matrix viasualization of $z\cdot\tilde{z}.$

B) Since the usual matrix operations are consisten with the usual addition and multiplication rules in the complex numbers, we can use them to find the multiplicative inverses of a complex number $z=x+iy$ .

We are looking for the complex number $z^{-1}=(x+iy)^{-1}$ which in terms of matrices is equivalent to find the matrix

$\left[\begin{array}{cc}x&y\\-y & x\end{array}\right]^{-1}= \dfrac{1}{x^{2}+y^{2}} \left[\begin{array}{ccc}x&-y\\y&x\end{array}\right]$

Hence,

$z^{-1}=\dfrac{1}{x^2 +y^2} (x-iy)=\dfrac{1}{|z|^2}(x-iy)$

6 0

3 years ago

3. The graph at the right shows

Rudiy27

Answer:

30 miles

Step-by-step explanation:

there is three miles per day so u count by 3 up to ten days and you’ll get 30 (10,30) option c

3 0

3 years ago

The initial size of the population is 300. After 1 day the population has grown to 800. Estimate the population after 6 days. (R

Cloud [144]

Solution :

Given initial population = 300

Final population after 1 day = 800

Number of days = 6

∴ $\frac{dP}{dt} =kt^{1/2}$

P(0) = 300 P(1) = 300

We need to find P(8).

$dP = kt^{1/2} dt$

$\int 1 dP = \int kt^{1/2} dt$

$P(t) = k \left(\frac{t^{3/2}}{3/2}\right)+c$

$P(t)= \frac{2k}{3}t^{3/2} + c$

When P(0) = 300

$300 = \frac{2k}{3} (0)^{3/2} + c$

∴ c = 300

∴ $P(t)= \frac{2k}{3}t^{3/2} + 300$

When P(1) = 800

$800 = \frac{2k}{3} (1)^{3/2} + 300$

$500 = \frac{2k}{3}$

∴ k = 750

$P(t)= 500t^{3/2} + 300$

So, P(8) is

$P(t)= 500(8)^{3/2} + 300$

= 11,614

So the population becomes 11,614 after 8 days.

8 0

3 years ago

Simplify -2[9 - (x + 7)]

tiny-mole [99]

Hey there! $-2[9 - (x + 7)] \\ \\ \\( -2(9) + -2(-x) + -7) \\ \\ -2(9) +-2(-x) + -2 (-7) \\ \\ \\ -2(9) = -18 \\-2(-x) = 2x \\ -2(-7) = 14 \\ \\ \\ -18 + 2x + 14 \\ \\ \\ \\ Combine \\ like\\ terms: -18 , 14 \\ \\ \\ -18 +14 = -4 \\ \\ \\ \\ Answer: 2x - 4 \\ \\ \\ \\ \\ \\ Good\\ luck \\ on \\ your \\ assignment \\ and \\ enjoy \\ your \\ day!$

~ $LoveYourselfFirst:)$

6 0

4 years ago

Read 2 more answers

The stock of Company A lost 2% today to $46.55. What was the opening price of the stock in the beginning of the day?

cluponka [151]

Answer:

$2327.5

Step-by-step explanation:

The stock of company A lost 2% today .

Let the price of the stock at the beginning of the day be A.

Therefore, a 2% loss of A = $46.55

That’s

2% /100% x A = $46.55

0.02 x A = $46.55

Divide both sides by 0.02

0.02/0.02 x A = $46.55/0.02

A = $2327.5

The price of stock at the beginning of the opening day was $2327.5

4 0

3 years ago