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3 years ago

F

Mathematics

1 answer:

Stells [14]3 years ago

7 0

Answer:

$x = 34.8^\circ$

Step-by-step explanation:

Given

See attachment for triangle

Required

Find x

To do this, we simply apply sin formula which is:

$sin(\theta) = \frac{Opposite}{Hypotenuse}$

In this case, it is:

$sin(x) = \frac{8}{14}$

$sin(x) =0.5714$

Take arcsin of both sides

$x = sin^{-1}(0.5714)$

$x = 34.84791$

$x = 34.8^\circ$ --- approximated

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What are the fourth roots of 6+6√(3i) ?

Helen [10]

Answer:

Step-by-step explanation:

The genral form of a complex number in rectangular plane is expressed as z = x+iy

In polar coordinate, z =rcos ∅+irsin∅ where;

r is the modulus = √x²+y²

∅ is teh argument = arctan y/x

Given thr complex number z = 6+6√(3)i

r = √6²+(6√3)²

r = √36+108

r = √144

r = 12

∅ = arctan 6√3/6

∅ = arctan √3

∅ = 60°

In polar form, z = 12(cos60°+isin60°)

z = 12(cosπ/3+isinπ/3)

To get the fourth root of the equation, we will use the de moivres theorem; zⁿ = rⁿ(cosn∅+isinn∅)

z^1/4 = 12^1/4(cosπ/12+isinπ/12)

When n = 1;

z1 = 12^1/4(cosπ/3+isinn/3)

z1 = 12^1/4cis(π/3)

when n = 2;

z2 = 12^1/4(cos2π/3+isin2π/3)

z2 = 12^1/4cis(2π/3)

when n = 3;

z2 = 12^1/4(cosπ+isinπ)

z2 = 12^1/4cis(π)

when n = 4;

z2 = 12^1/4(cos4π/3+isin4π/3)

z2 = 12^1/4cis(4π/3)

8 0

3 years ago

PLS ANSWER ASAP Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to

irina [24]

The correct answer is c. 16.6

Explain

The triangle left side
Opposite side= hypotheses x sin 0

Plugin

Opposite side = 39 x sin 43

39 x 0.68

26.60

The right side

Opposite side = adjective side x tan0

Opposite side = 26.60 x tan 32

26.60 x 0.62

X= 16.6

Hope this help you :D

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4 years ago

100 POINTS AND BRAINLIEST

zysi [14]

Answer:

8 square units and $\frac{40}{3}$ square units