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3 years ago

Convert the polar representation of this complex number into its standard form: z=8(cos240degrees + isin 240degrees)

Mathematics

1 answer:

ollegr [7]3 years ago

5 0

Answer:

Step-by-step explanation:

The standard form of a complex number is a + bi. where

$a=rcos\theta$ and $b=rsin\theta$

Putting these together to get the form that you have right now gives you

$(rcos\theta+rsin\theta i)$ and you have the r factored out. If you want to find out what a is then in a + bi, find out what 8cos(240) is on your calculator.

8cos(240) = -4

Likewise for b:

8sin(240) = -6.9

Putting these together in standard form gives you -4 - 6.9i

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Mr. Collins is constructing a fence around his property. He already has 25 sections up and plans to add 8 sections each Saturday

AURORKA [14]

Hi!

So, we know the Mr. Collins already has 25 sections. So let's write an equation.

25 + 8s
(s = Saturday)

Now our value for s in this equation is 15. So put in the value..

25 + 8 · 15
25 + 120
145

The answer is 145

Hope this helps! :)

4 0

3 years ago

Convert 23cm in the inches(round off to the nearest inch)

sammy [17]

Answer:

9.055

Step-by-step explanation:

4 0

3 years ago

A line passes through the points (–6, 4) and (–2, 2). Which is the equation of the line?

insens350 [35]

Answer:

y=-1/2x+1

Step-by-step explanation:

We can use the points to find the slope of the line.

Equation: y₂-y₁/x₂-x₁

2-4/-2-(-6)

2-4/-2+6

-2/4

-1/2 is the slope of the line

So the equation is y=-1/2x+b

We can substitute one of the x-coordinates and the matching y-coordinate into this equation:

2=-1/2*(-2)+b

2=1+b

1=b

b=1

Therefore, the equation is y=-1/2x+1

5 0

3 years ago

Solve the given inequality :

tigry1 [53]

Answer:

x < -5 or x = 1 or 2 < x < 3 or x > 3

Step-by-step explanation:

Given rational inequality:

$\dfrac{(x-1)^2(x-2)^3}{(x^2-5x+6)^2(x+5)}\geq 0$

$\textsf{Factor }(x^2-5x+6):$

$\implies x^2-2x-3x+6$

$\implies x(x-2)-3(x-2)$

$\implies (x-3)(x-2)$

Therefore:

$\dfrac{(x-1)^2(x-2)^3}{(x-3)^2(x-2)^2(x+5)}\geq 0$

Find the roots by solving f(x) = 0 (set the numerator to zero):

$\implies (x-1)^2(x-2)^3=0$

$\implies (x-1)^2=0\implies x=1$

$\implies (x-2)^3=0 \implies x=2$

Find the restrictions by solving f(x) = undefined (set the denominator to zero):

$\implies (x-3)^2(x-2)^2(x+5)=0$

$\implies (x-3)^2=0 \implies x=3$

$\implies (x-2)^2=0 \implies x=2$

$\implies (x+5)=0 \implies x=-5$

Create a sign chart, using closed dots for the roots and open dots for the restrictions (see attached).

Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.

Test values: -6, 0, 1.5, 2.5, 4

For each test value, determine if the function is positive or negative:

$f(-6)=\dfrac{(-6-1)^2(-6-2)^3}{(-6-3)^2(-6-2)^2(-6+5)}=\dfrac{(+)(-)}{(+)(+)(-)}=+$

$f(0)=\dfrac{(0-1)^2(0-2)^3}{(0-3)^2(0-2)^2(0+5)}=\dfrac{(+)(-)}{(+)(+)(+)}=-$

$f(1.5)=\dfrac{(1.5-1)^2(1.5-2)^3}{(1.5-3)^2(1.5-2)^2(1.5+5)}=\dfrac{(+)(-)}{(+)(+)(+)}=-$

$f(2.5)=\dfrac{(2.5-1)^2(2.5-2)^3}{(2.5-3)^2(2.5-2)^2(2.5+5)}=\dfrac{(+)(+)}{(+)(+)(+)}=+$

$f(4)=\dfrac{(4-1)^2(4-2)^3}{(4-3)^2(4-2)^2(4+5)}=\dfrac{(+)(+)}{(+)(+)(+)}=+$

Record the results on the sign chart for each region (see attached).

As we need to find the values for which f(x) ≥ 0, shade the appropriate regions (zero or positive) on the sign chart (see attached).

Therefore, the solution set is:

x < -5 or x = 1 or 2 < x < 3 or x > 3

As interval notation:

$(- \infty,-5) \cup x=1 \cup (2,3) \cup(3,\infty)$

4 0

2 years ago

Translate the sentence into an equation.

murzikaleks [220]

Answer:

9 - 5x = 7

Step-by-step explanation:

Nine (9) less (-) then the product (*) of 5*x, equals (=) to 7

9 - 5x = 7

3 0

2 years ago