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3 years ago

Express the complex number in trigonometric form. square root of 3+2i

1 answer:

8 0

$\bf \begin{array}{llll}
\sqrt{3}&,&2i\\
\uparrow &&\uparrow \\
a&&b
\end{array}\implies r[cos(\theta )+i\ sin(\theta )]\qquad 
\begin{cases}
r=\sqrt{a^2+b^2}\\
\theta =tan^{-1}\left( \frac{b}{a} \right)
\end{cases}
\\\\\\
r=\sqrt{(\sqrt{3})^2+(2)^2}\implies r=\sqrt{3+4}\implies r=\sqrt{7}
\\\\\\
\theta =tan^{-1}\left( \frac{2}{\sqrt{3}} \right)\implies \theta \approx 49.10660535^o\textit{ or just 49 rounded up}\\\\
-------------------------------\\\\
\sqrt{3},2i\implies \sqrt{7}[cos(49^o)+i\ sin(49^o)]$

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Cs.

kykrilka [37]

Answer:

Length of rectangle = 16 cm

Width of rectangle = 4 cm

Step-by-step explanation:

Given:

Area of rectangle = 64 cm²

Find:

Length and width

Computation:

Assume;

Length of rectangle = a

So,

Width of rectangle = a -12

Area of rectangle = l x b

So,

a(a-12) = 64

a² - 12a - 64 = 0

a² - (16-4)a - 64 = 0

a² - 16a+ 4a - 64 = 0

a (a-16) + 4(a-16)= 0

(a-16)(a+4) = 0

a= 16 , a = -4

So,

Length of rectangle = 16 cm

Width of rectangle = a -12

Width of rectangle = 16 -12

Width of rectangle = 4 cm

3 0

2 years ago

Write a vector equation of the line that passes through point P(-4,11) and is parallel to a=[-3,8]. Then write parametric equati

Assoli18 [71]

Answer:

$\vec l = (-4, 11) + t\cdot (-3,8)$ , $x = -4 - 3\cdot t$ and $y = 11 + 8\cdot t$

Step-by-step explanation:

The vector equation of the line is:

$\vec l = \vec P + t \cdot \vec A$

$\vec l = (-4, 11) + t\cdot (-3,8)$

The parametric equations of the line are:

$x = -4 - 3\cdot t$ and $y = 11 + 8\cdot t$

4 0

3 years ago

The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown. What is the function written in vertex form?

pychu [463]

F(x) = 5(x + 4) – 80
f(x) = 5(x + 8) – 80
f(x) = 5(x + 4)2 – 80
f(x) = 5(x + 8)2 – 80

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2 years ago

The quotient of a number and 3 decreased by 121 is -164. Select the solution to the sentence shown.

docker41 [41]

Its algebra. The original equation is $\frac{x}{3} -121 = -164$

To solve for a variable, we reverse the order of operations, beginning with addition/subtraction, and then multiplication/division. To remove a number from one side, we must do the opposite to the other side. In this case, to get rid of the -121 we must add 121 to the -164. This gives us -43. Then, to get the x by itself, we must multiply the other side by 3. -43*3=129

When we are doing the opposite of an operation to the other side, we are really reversing the operation and, to keep both sides equal, we must do whatever we have done to one side to the other side. So when we have -121, we add 121 as it equals 0, therefore it is gone. Since a equation must be balanced, we have to do what we did to the other side (adding 121).

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3 years ago

Select the correct answer.

nordsb [41]

Answer:

A. The graph is a line that goes through the points (9,0) and (0,6).

Step-by-step explanation:

Given

$4x + 6y = 36$