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3 years ago

6

If the following system of equations was written as a matrix equation in the form AX = C, and matrix A was expressed in the form

[a c b d] , find the value of a - b + c + d.
5x + 7y = 7
3x - 2y = 9

My main problem is understanding which numbers are a, b, c, and d.

1 answer:

FrozenT [24]3 years ago

6 0

That's what I came up with. Still not sure of my answer.

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Suppose a and b are both non zero real numbers. Find real numbers c and d such that 1/a+ib= c+id

Thepotemich [5.8K]

$\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

Explanation

$\frac{1}{a+bi}=c+di$

Step 1

multiplicate by the conjugate

$\begin{gathered} \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(bi)^2} \\ \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(-b^2)}=\frac{a-bi}{a^2+b^2} \end{gathered}$

notice that

$\begin{gathered} \frac{1}{a+bi}=\frac{a-bi}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i \\ \frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i=c+di \\ so \\ \end{gathered}$ $\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

I hope this helsp you

6 0

1 year ago

The surface area for a rectangular prism with a square base is SA=2s2+4sh. What is the surface area if s=3 and h=5?

Zigmanuir [339]

Answer:

The surface area is 78 unit square.

Step-by-step explanation:

Given : The surface area for a rectangular prism with a square base is $SA=2s^2+4sh$ .

To find : What is the surface area if s=3 and h=5?

Solution :

The surface area for a rectangular prism with a square base is $SA=2s^2+4sh$

Substitute, s=3 and h=5

$SA=2(3)^2+4(3)(5)$

$SA=2\times 9+4\times 15$

$SA=18+60$

$SA=78$

Therefore, The surface area is 78 unit square.

7 0

3 years ago

Answers plz<br> i don’t get it

masha68 [24]

The third option has the highest value

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What is 62394 rounded to the nearest ten

Semmy [17]

Answer:

62390

Step-by-step explanation:

you have to round up if it's 5 or more and round down if it's less.

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