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3 years ago

Simplify.

1 answer:

8 0

First off, nicely done on the exponents. You'd be surprised on how bad some look ,:D

a)
$(3xy^{3})(2x^{2}y)\\ (3*2)(x*x^{2})(y^{3}*y)\\\\ 6x^{3}y^{4}$

b)
$2y(2y+3y^{2})-y^{2}(3-y)\\ (4y^{2}+6y^{3}) + (-3y^{2}+y^{3})\\ (6y^{3}+y^{3})+(4y^{2}-3y^{2})\\ 7y^{3}+y^{2}\\\\ y^{2}(7y+1)$

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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

Match the answer with the question

vlada-n [284]

Answer:

18219

Step-by-step explanation:

7 0

3 years ago

Point B is the midpoint of AC, and point C is the midpoint of AD. If CD=12, what is AB?

Sliva [168]

Answer: AB = 6

Step-by-step explanation:

If CD = 12 , AC also = 12

B is the midpoint of AC so one side = 6

AB is one side of AC , so AB = 6

I am not a professional, I am simply using prior knowledge!

Note- It would mean the world to me if you would mark me brainliest!

4 0

3 years ago

April has only consumed one glass of wine, so her body isn't affected by the alcohol because short-term effects only begin with

MrMuchimi

ANSWER: False

This is false because alcohol can have effect as soon as the first drink, depending on the type of person you are.

For example, if your parents drank, and you were born early (a preemie) this can affect your ability to drink.

Hope this helps! ^^

4 0

3 years ago

Read 2 more answers

The range of which function is (2, infinity)? y = 2x y = 2(5x) y = 5x 2 y = 5x 2

vova2212 [387]

The function which has range (2, infinity) from the provided function is y = 5ˣ +2. Option 4 is correct.

<h3>What is range of function?</h3>

Range of a function is the set of all the possible output values which are valid for that function.

The function whose range is (2, ∞) has to be find out.

The first function given in the problem is,

$y=2^x$

This function has the periodic function with period of logarithmic function and the range of this function is all the real number. This is not the correct option.

The second function given in the problem is,

$y=2(5)^x$

This function has the periodic function with period of logarithmic function and the range of this function is all the real number. This is not the correct option.

The fourth function given in the problem is,

$y=(5)^x+2$

This function is translated 5 units up to the function 5ˣ which has the range (0,∞).

Thus, the range of this function is (2, ∞).

Hence, the function which has range (2, infinity) from the provided function is y = 5ˣ +2. Option 4 is correct.

Learn more about range of the function here;

brainly.com/question/2264373

5 0

2 years ago