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3 years ago

Simplify the following expression into the form a + bi, where a and b are rational numbers. (4-i)(-3+7i)-7i(8+2i), please help

Mathematics

2 answers:

olganol [36]3 years ago

8 0

Answer:

9-25i is the answer

atroni [7]3 years ago

7 0

9-25i is the answer to your question

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Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Leni [432]

Answer: $\dfrac{2x^2-1}{x(x^2-1)}$

Step-by-step explanation:

The given function : $y=\ln(x(x^2 - 1)^{\frac{1}{2}})$

$\Rightarrow\ y=\ln x+\ln (x^2-1)^{\frac{1}{2}}$ [ $\because \ln(ab)=\ln a +\ln b$ ]

$\Rightarrow y=\ln x+\dfrac{1}{2}\ln (x^2-1)}$ [ $\because \ln(a)^n=n\ln a$ ]

Now , Differentiate both sides with respect to x , we will get

$\dfrac{dy}{dx}=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})\dfrac{d}{dx}(x^2-1)$ (By Chain rule)

[Note : $\dfrac{d}{dx}(\ln x)=\dfrac{1}{x}$ ]

$\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x-0)$

[ $\because \dfrac{d}{dx}(x^n)=nx^{n-1}$ ]

$=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x) = \dfrac{1}{x}+\dfrac{x}{x^2-1}\\\\\\=\dfrac{(x^2-1)+(x^2)}{x(x^2-1)}\\\\\\=\dfrac{2x^2-1}{x(x^2-1)}$

Hence, the derivative of the given function is $\dfrac{2x^2-1}{x(x^2-1)}$ .

8 0

3 years ago

Please answer both thank you

jeyben [28]

Answer:

Solution given;

male=15

female=27

1st term=5*3

2nd term=3*3*3

now

Highest common factor=3

The maximum number of groups that the teacher can make is 3.

and each team contains 5 male and 9 female.

7 0

3 years ago

What is the value of 6/x +2c^2, when x= 3? O 8 O 11 O 14 20

yarga [219]

Answer:

the answer is 11

Step-by-step explanation:

dont know

3 0

3 years ago

PLEASE I NEED HELP!!!!!!!!

leonid [27]

Use distributive property in order to find the equivalent pieces of oi

5 0

3 years ago

Can someone help me with this I don't understand and please explain the answer

lukranit [14]

(2^6)=1
take log on both sides,
xlog(2^6)=log(1)=0
=>
x=0, since log(2^6)>0

5^0=1
there is no value of x appearing in the equation, so x can be any valid number.

5 0

3 years ago