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2 years ago

Consider the set of points defined by z = 5 cos(theta) + 3i sin(theta).

Mathematics

1 answer:

vitfil [10]2 years ago

4 0

Answer:

This is an ellipse.

Step-by-step explanation:

$z=5cos(\theta)+3isin(\theta)$

Applying the angle values in intervals of right angles (90°), the resulting set of values for z are:

$\theta = 0,90,180,270,360$

$z=5,3i,-5,-3i,5$ (again)

If you look at the plot, you will observe how these values represent points in the xy plain. All of them belong to either the x or the y axis.

The resulting figure for the whole set of values of $\theta$ is in fact an ellipse.

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Answer question in the picture

m_a_m_a [10]

Answer:

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2 years ago

[20points][Precal] Find the cross product of -(3/4)V and (1/2)w if v = <-2, 12, -3> and w = <-7, 4, -6>

Lana71 [14]

$\mathbf v=\langle-2,12,-3\rangle=-2\,\vec i+12\,\vec j-3\,\vec k$
$-\dfrac34\mathbf v=\dfrac32\,\vec i-9\,\vec j+\dfrac94\,\vec k$

$\mathbf w=\langle-7,4,-6\rangle=-7\,\vec i+4\,\vec j-6\,\vec k$
$\dfrac12\mathbf w=-\dfrac72\,\vec i+2\,\vec j-3\,\vec k$

$-\dfrac34\mathbf v\times\dfrac12\mathbf w=\begin{vmatrix}\vec i&\vec j&\vec k\\\frac32&-9&\frac94\\-\frac72&2&-3\end{vmatrix}$
$=\left((-9)\times(-3)-\dfrac94\times2\right)\,\vec i-\left(\dfrac32\times(-3)-\dfrac94\times\left(-\dfrac72\right)\right)\,\vec j+\left(\dfrac32\times2-(-9)\times\left(-\dfrac72\right)\right)\,\vec k$
$=\dfrac{45}2\,\vec i-\dfrac{27}8\,\vec j-\dfrac{57}2\,\vec k=\left\langle\dfrac{45}2,-\dfrac{27}8,-\dfrac{57}2\right\rangle$

6 0

3 years ago

There is a bowling ball with a diameter of 216 mm and a baseball with a diameter of 74 mm. Find how many times greater the volum

zmey [24]

Bowling ball radius = 108 mm
Sphere Volume = 4/3 • π • r³
bowling ball volume = 4/3 * PI * 108^3
bowling ball volume = 5.2767e+6
 bowling ball volume = 5,276,669 cubic mm

baseball radius = 37 mm
baseball volume = 4/3 * PI * 37^3
baseball volume = 4/3 * PI * 37^3
 baseball volume = 212,174 cubic mm

bowling ball greater than baseball by a factor of:

5,276,669 / 212,174 = 24.8694450477 
answer is D

6 0

3 years ago

If one side of a square notebook measures 20 cm, what is the area of the front cover of the notebook?

fgiga [73]

Area is defined as a product of sides when we talk about squares.

$A=a\cdot a=20\cdot20=\boxed{400}$

The area of the front cover of notebook is 400 centimetres squared.

Hope this helps.

r3t40

6 0

3 years ago

Read 2 more answers

What is x in the equation 3(x-7);33-21

Andru [333]

3x-21=12

add 21 to both sides to get 3x alone.

3x=33

divide both sides by 3

and you get:

x=11

6 0

3 years ago