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3 years ago

What is the sum of the complex numbers 6+5i and 8+3i2? (NOTE: −1‾‾‾√=i )

Mathematics

1 answer:

Ahat [919]3 years ago

4 0

Answer:

11 + 5i

Step-by-step explanation:

6 + 5i + 8 + 3i² =

= 6 + 8 + 3(-1) + 5i

= 14 - 3 + 5i

= 11 + 5i

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Prove: cot(x) sec^4(x) = cot(x) +2tan(x) + tan^3(x)

masha68 [24]

$\bf cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\qquad\qquad 
sec(\theta)=\cfrac{1}{cos(\theta)}\quad\qquad 1+tan^2(\theta)=sec^2(\theta)\\\\\\
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}
\qquad \qquad cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\\\\
-------------------------------\\\\
cot(x)sec^4(x)=cot(x)+2tan(x)+tan^3(x)\\\\
-------------------------------\\\\$

$\bf \textit{so, let's do the left-hand-side}\\\\
cot(x)sec^2(x)sec^2(x)\implies cot(x)[1+tan^2(x)][1+tan^2(x)]
\\\\\\
cot(x)[1^2+2tan^2(x)+tan^4(x)]
\\\\\\
cot(x)+2tan^2(x)cot(x)+tan^4(x)cot(x)
\\\\\\
cot(x)+2\cdot \cfrac{sin^2(x)}{cos^2(x)}\cdot \cfrac{cos(x)}{sin(x)}+\cfrac{sin^4(x)}{cos^4(x)}\cdot \cfrac{cos(x)}{sin(x)}
\\\\\\
cot(x)+2\cdot \cfrac{sin(x)}{cos(x)}+\cfrac{sin^3(x)}{cos^3(x)}\implies \boxed{cot(x)+2tan(x)+tan^3(x)}$

8 0

3 years ago

Write 10 toolbars on the keyboard

posledela

Answer:

WINKEY + D. ...

WINKEY + SPACE. ...

SHIFT + Mouse Click on a taskbar button. ...

CTRL + SHIFT + Mouse Click on a taskbar button. ...

SHIFT + Right Mouse Click on a taskbar button. ...

SHIFT + Right Mouse Click on a grouped taskbar button. ...

CTRL + Mouse Click on a grouped taskbar button. ...

WINKEY + T.

ctrl + X = cut

ctrl + c = copy

make me brainliest

3 0

3 years ago

You have a $3175 student loan. Suppose you pay the loan off in two and a half years (30 months). Estimate your monthly payment b

finlep [7]

Answer:

$106

Step-by-step explanation:

The formula given for Monthly payment of a loan =

P × [ r (1 + r)/(1 + r)^n - 1

Where

r = interest rate

n = number of monthly payments

P = Present value of the loan

From the question,

r = interest rate, we were told to ignore hence, r = 0

P = $3,175

n = 30

Hence,

Amount to be paid monthly = P/n

= $3175/30

= $105.83

Approximately to the nearest dollars

= $106

6 0

3 years ago

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tia_tia [17]

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8 0

3 years ago

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Determine the zeros of f(x)=x^3+7x^2+10x-6

igor_vitrenko [27]

Hello,
x^3+7x^2+10x-6=x^3+3x^2+4x^2+12x-2x-6
=x²(x+3)+4x(x+3)-2(x+3)
=(x+3)(x²+4x-2)
=(x+3)(x+2-√7)(x+2+√7)

zeroes={-3,-2+√7,-2-√7}

4 0

3 years ago