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3 years ago

Express the complex number 6 in complex trigonometric form.

Mathematics

2 answers:

Tanzania [10]3 years ago

8 0

Hello,

6=6*(cos 0 +i *sin 0)

anyanavicka [17]3 years ago

7 0

Answer:

6(cos 0° + sin 0° . i)

Step-by-step explanation:

The trigonometric form formula is a combination of the following formulas:

Binomic: a + bi

Polar: rα

Giving as a result the formula: r (cos α + sin α · i)

Where,

r = module

α = angle

In the given case, the complex number is 6, where

Binomic form: 6 + 0i

Where a = 6 and b = 0

We must calculate the module (r) and the angle (α).

$r=\sqrt{a^{2} +b^{2}} =\sqrt{6^{2} +0^{2}}=\sqrt{36}=6$

α = $tan^{-1}(0)$ = 0°

Since r=6 and α=0°, then the trigonometric form is

r(cos α + sin α · i) = 6(cos 0° + sin 0° . i)

Hope this helps!

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A rocket is shot straight up into the air with an initial velocity of 500 ft per second and from a height of 20 feet above the g

iragen [17]

The height of the rocket above the ground after $t$ seconds is given by the equation : $H= -16t^2+Vt+h$ , where $V$ is the initial velocity and $h$ is the initial height.

Given that, $V= 500 ft/second$ and $h= 20 ft$

So, the equation will become: $H= -16t^2 +500t+20$

A) For finding the height of the rocket 3 seconds after the launch, we will plug $t=3$ into the above equation. So....

$H= -16(3)^2+500(3)+20\\ \\ H= -16(9)+1500+20\\ \\ H= -144+1500+20=1376$

So, the height of the rocket 3 seconds after the launch is 1376 feet.

B) When the rocket at a height of 400 feet, then we will plug $H= 400$

$400=-16t^2+500t+20\\ \\ 16t^2-500t-20+400=0\\ \\ 16t^2-500t+380=0\\ \\ 4(4t^2-125t+95)=0\\ \\ 4t^2-125t+95=0$

Using quadratic formula, we will get......

$t= \frac{-(-125)+/-\sqrt{(-125)^2-4(4)(95)}}{2(4)}\\ \\ t= \frac{125+/-\sqrt{14105}}{8}\\ \\ t= 30.4705... \\ and \\ t= 0.7794...$

So, after 0.7794...seconds and 30.4705...seconds the rocket is at a height of 400 feet above the ground.

C) The time duration that the rocket remains in the air means we need to find the time taken by the rocket to reach the ground. When it reaches the ground, then $H=0$ . So.....

$0=-16t^2+500t+20\\ \\ -4(4t^2-125t-5)=0\\ \\ 4t^2-125t-5=0$

Using quadratic formula, we will get.....

$t= \frac{-(-125)+/-\sqrt{(-125)^2-4(4)(-5)}}{2(4)}\\ \\ t= \frac{125+/-\sqrt{15705}}{8}\\ \\ t=31.2899...\\ and\\ t= -0.0399...$

(Negative value is ignored as time can't be in negative)

So, the rocket will remain in the air for 31.2899... seconds.

5 0

4 years ago

3. Use Structure Ana drew a plan for a

shtirl [24]

Answer:

(5.5, -3.5)

Step-by-step explanation:

As you can see in the figure, the fourth vertex is (5.5, -3.5)

If you observe carefully the vertex given, you will see that there are two vertex with same coordinates in x axis:

(-1.2, -3.5),
(-1.2, 4.4),

And one vertex has other coordinate in x axis, it is: (5.5, 4.4)

To form a rectangle, you need a fourth vertex that will have same coordinate in x than (5.5, 4.4) and same coordinate in y axis as (-1.2, -3.5),

Then the fourth vertex coordinate is (5.5, -3.5)

7 0

3 years ago

Leah is 5 1/2 feet tall Leah's sons height is 2/3 her height. What is s, her sons height, in feet?

N76 [4]

Her son is about 3 feet tall

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4 years ago

Why is 1/2 not useful as a benchmark to compare 5/8 and 9/10?

pentagon [3]

1/2 would not be a useful benchmark to compare these 2 fractions because both of them are greater than half. The benchmark fraction 1/2 is most useful when one fraction is less than half and the other more than 1/2. 5/8 is more than 4/8(1/2), and 9/10 is more than 5/10(1/2).

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3 years ago

Read 2 more answers

Hello please help i’ll give brainliest

Nikitich [7]

Answer:

None. The movement of these tectonic plates is likely caused by convection currents in the molten rock in Earth’s mantle below the crust.

Step-by-step explanation:

Plate tectonics is the scientific theory explaining the movement of the earth’s crust. It is widely accepted by scientists today. Recall that both continental landmasses and the ocean floor are part of the earth’s crust, and that the crust is broken into individual pieces called tectonic plates (Fig. 7.14). The movement of these tectonic plates is likely caused by convection currents in the molten rock in Earth’s mantle below the crust. Earthquakes and volcanoes are the short-term results of this tectonic movement. The long-term result of plate tectonics is the movement of entire continents over millions of years (Fig. 7.18). The presence of the same type of fossils on continents that are now widely separated is evidence that continents have moved over geological history.

Information found on:

https://manoa.hawaii.edu/exploringourfluidearth/node/1348#:~:text=Plate%20tectonics%20is%20the%20scientific,movement%20of%20the%20earth's%20crust.&text=The%20movement%20of%20these%20tectonic,results%20of%20this%20tectonic%20movement.

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3 years ago