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1 year ago

Find the cube roots of 8(cos 216° + i sin 216°).

1 answer:

5 0

$z^3=8(\cos216^\circ+i\sin216^\circ)$
$z^3=2^3(\cos(6^3)^\circ+i\sin(6^3)^\circ)$
$\implies z=8^{1/3}\left(\cos\left(\dfrac{216+360k}3\right)^\circ+i\sin\left(\dfrac{216+360k}3\right)^\circ\right)$

where $k=0,1,2$ . So the third roots are

$z=\begin{cases}2(\cos72^\circ+i\sin72^\circ)\\2(\cos192^\circ+i\sin192^\circ)\\2(\cos312^\circ+i\sin312^\circ)\end{cases}$

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Using the side-splitter theorem, which segment length would complete the proportion?

tia_tia [17]

we know that

<u>The Side-Splitter Theorem</u>: States that If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those two sides proportionally

in this problem

$\frac{GH}{HE} =\frac{GJ}{JF}$

therefore

<u>the answer is</u>

The segment length is GJ

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2 years ago

Read 2 more answers

A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally. A piece of climbing equipment at a

Dahasolnce [82]

Answer: The comparison is mentioned below.

Step-by-step explanation:

A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally.

Therefore its slope = length of the equipment vertically / length of equipment horizontally

$m_1$ = 6/4 = 3/2 = 1.5

And, A piece of climbing equipment at a gym is 10 feet high and extends 6 feet horizontally.

Therefore slope, $m_2$ = 10/6 = 5/3=1.67 (approx)

Since, $m_1$ < $m_2$

Thus the slope of equipment first is less than slope of second equipment.

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1 year ago

Read 2 more answers

Which is a solution to the equation? (x −2)(x + 5) = 18 x = −10 x = −7 x = −4 x = −2

Leona [35]

Answer:

Solutions:

$x=-7$

$x=4$

Step-by-step explanation:

$(x-2)(x + 5) = 18$

Expanding the factored form:

$x^2+5x-2x-10=18$

$x^2+3x-28=0$

Factoring the second-degree polynomial:

$(x+7)(x-4)=0$

This is true for

$x=-7 \text{ or } x=4$

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1 year ago

FreezeFrame, a social networking site, sent out a survey in which the users simply click a response to join the sample. One of t

kramer

Answer:

Here, Convenience sampling is used by the poll

Explanation:

Convenience sampling also called as opportunity, grab or accidental sampling is a kind of non-likelihood testing that includes the sample being drawn from that piece of the populace that is near hand. This sort of sampling is most valuable for pilot testing.

Convenience sampling is a procedure used to make sample according to straightforward entry, readiness to be a sample's part , accessibility at a given scheduled slot.

So, this method of sampling is biased and don't results in desired outcomes.

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1 year ago

In triangle XYZ, if angle X is congruent to angle Z, XY = 13x - 21, YZ = 8x - 6, & XZ = x + 4, find x & the measure of e

Naily [24]

Answer:

Given: In triangle XYZ, $\angle X \cong \angle Z$ , XY=13x-21 , YZ=8x-6 and XZ=x+4.

If two angles are congruent if and only if, they measure the same number of degrees.

therefore, from the given condition; $\angle X = \angle Z$ .

Isosceles Triangle : An triangle with two equal sides. The angles opposite the equal sides are also equal.

Therefore, the triangle XYZ is an isosceles triangle, as the base angle $\angle X$ and $\angle Z$ are equal and the sides opposite to these angles are also equal i.e, XY=YZ.

Since, we have XY=YZ ,

⇒ 13x-21 =8x-6 or

13x-8x=21-6 or

5x=15

Simplify:

x=3

Therefore, the sides of an isosceles triangle are:

XY = 13x-21 = $13\cdot 3 -21$ = 39-21 = 18 unit ,

YZ = 8x-6 = $8 \cdot3 -4$ = 24-6 =18 unit,

and XZ = x+4 = 3+4 =7 unit.

Since, the triangle is isosceles, we draw a line from an vertex angle Y of a triangle XYZ which is perpendicular (i.e, of 90 degree angle) to opposite side meets the opposite side at its midpoint i.e, say W.

As W is the midpoint(i.e, it divide the sides into two equal halves),

XW=WZ = $\frac{7}{2} =3.5$ unit

Now, use the Pythagorean theorem, to find the altitude WY.

⇒ $(WY)^2+(WZ)^2=(YZ)^2$

Substitute the value of WZ = 3.5 unit and YZ = 18 unit in above formula to calculate the length of WY;

⇒ $(WY)^2+(3.5)^2=(18)^2$

Simplify:

$(WY)^2=324-12.25=311.75$ or

$WY=\sqrt{311.75}$

On simplify we get;

WY=17.65 unit(approx.)

The vertex angle Y is split into two equal angles, we can find the vertex angle by finding the one of the base angle by using the fact; $Cosine = \frac{Base}{Hypotenuse}$ .