Determine if the following relation is a function or not

Here Is your answer!!!!

Answer:

In order of increasing angle measure, the fourth roots of -3 + 3√3·i are presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left({-\dfrac{\pi}{12} } \right) + i \cdot sin\left(-\dfrac{\pi}{12} } \right) \right][/tex]

[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{5 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{5 \cdot\pi}{12} } \right) \right][/tex]

[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{11 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{11 \cdot\pi}{12} } \right) \right][/tex]

[tex]\sqrt[4]{6} \cdot \left[cos\left({\dfrac{17 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{17 \cdot\pi}{12} } \right) \right][/tex]

Step-by-step explanation:

The root of a complex number a + b·i is given as follows;

r = √(a² + b²)

θ = arctan(b/a)

The roots are;

[tex]\sqrt[n]{r}[/tex]·[cos((θ + 2·k·π)/n) + i·sin((θ + 2·k·π)/n)]

Where;

k = 0, 1, 2,..., n -2, n - 1

For z = -3 + 3√3·i, we have;

r = √((-3)² + (3·√3)²) = 6

θ = arctan((3·√3)/(-3)) = -π/3 (-60°)

Therefore, we have;

[tex]\sqrt[4]{-3 + 3 \cdot \sqrt{3} \cdot i \right)} = \sqrt[4]{6} \cdot \left[cos\left(\dfrac{-60 + 2\cdot k \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-60 + 2\cdot k \cdot \pi}{4} \right) \right][/tex]

When k = 0, the fourth root is presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 0 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 0 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({-\dfrac{\pi}{12} } \right) + i \cdot sin\left(-\dfrac{\pi}{12} } \right) \right][/tex]

When k = 1 the fourth root is presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 1 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 1 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{5 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{5 \cdot\pi}{12} } \right) \right][/tex]

When k = 2, the fourth root is presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 2 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 2 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{11 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{11 \cdot\pi}{12} } \right) \right][/tex]

When k = 3, the fourth root is presented as follows;

[tex]\sqrt[4]{6} \cdot \left[cos\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 3 \cdot \pi}{4} \right) + i \cdot sin\left(\dfrac{-\dfrac{\pi}{3} + 2\cdot 3 \cdot \pi}{4} \right) \right] \\= \sqrt[4]{6} \cdot \left[cos\left({\dfrac{17 \cdot \pi}{12} } \right) + i \cdot sin\left(\dfrac{17 \cdot\pi}{12} } \right) \right][/tex]

Answer:

Step-by-step explanation:

Just took the test.

1) 4sqrt6 cis(pie/6)

2) 4sqrt6 cis (2pie/3)

3) 4sqrt6 cis(7pie/6)

4) 4sqrt6 cis (5pie/3)

Answer:

use Pythagorean theorem:

[tex]a^2+b^2=c^2\\9^2+12^2=18^2\\81+144=324\\225\neq 324[/tex]

it's not a right triangle

Answer:

16

Step-by-step explanation:

The area of a triangle is

A =1/2 bh  where b is the base length  and h is the height

Substitute the values in

69.6 = 1/2 ( 8.7) * p

69.6 = 4.35p

Divide each side by 4.35

69.6/4.35 = p

16 = p

The formula for the area of a triangle is: A = 1/2 * base * height.

Using this formula, let's plug in what we know.

69.6 = 1/2 * 8.7 * height

Next, we'll go ahead and get rid of that 1/2 by multiplying everything by its reciprocal, 2.

139.2 = 8.7 * height

Then, all that's left is to divide both sides by 8.7.

Height = 16 yards

Hope this helps!! :)

Step-by-step explanation:

(I) A number which can be expressed in the form m/n, where m and n are integers and n is not equal to zero, is called a Rational Number .

(ii) If the integers m and n have no common divisor other than 1 and n is positive, then the rational number m/n is said to be in the Simplest form .

(iii) Two rational numbers are said to be equal, if they have the same Simplest form .

(iv) If m is a common divisor of x and y, then x/y = (x ÷ k)/( y ÷ k) .

(v) The standard form of -1 is -1/1

(vi) If m/n is a rational number, then n cannot be 0

(vii) Two rational numbers with different numerators are equal, if their numerators are in the same ratio as their denominators.

Answer:

6761/320

Step-by-step explanation:

[(51/2)÷32/3]+14/5

=6761/320

Answer:3

Step-by-step explanation:

Answer:

Median: 10

Mean: 9

Range: 15

Step-by-step explanation:

Have a good day :)

Answer:

B.   y = 10(2)^x

Step-by-step explanation:

y = ab^x

to find "b" divide the function at x = 3 by the function at x = 2

80 = ab^3

——————

40 = ab^2

This results in

2 = b

to find "a" plug pickany value of x

using x = 2

40 = a(2²)

40 = a(4)

a = 10

With a = 10 and b = 2 the exponential function y = ab^x is

y = 10(2)^x

Answer: 88 gallons

Step-by-step explanation:

Every 2 vanillas = 11 chocolates

so 16 vanillas = 88 chocolates

i did this by multiplying both numbers by 8

sorry if this is wrong

Answer:

D) 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

log(3) = 0.477

log(8.2) = 0.913

log(0.04) = -1.397

Answer:

So the answer would be 9

Step-by-step explanation:

3*6=9

Consider that,

x^2+4x+4 = (x+2)(x+2)

x^2+7x+10 = (x+2)(x+5)

Dividing those expressions leads to

(x^2+4x+4)/(x^2+7x+10) = (x+2)/(x+5)

The intermediate step that happened is that we have (x+2)(x+2) all over (x+2)(x+5), then we have a pair of (x+2) terms cancel as the diagram indicates (see below). This is where the removable discontinuity happens. Specifically when x = -2. Plugging x = -2 into (x+2)/(x+5) produces an output, but it doesn't do the same for the original ratio of quadratics. So we must remove x = -2 from the domain.

Answer:

1250 Meters

Step-by-step explanation:

75 kilometers divided by 60 minutes is 1.25 kilometers per minute.

1 kilometer = 1000 meters

Answer:

75km/hr =75000

60 sec =1min,60 min=1hr

75000÷60=1250m

Answer:

X=275.8

Step-by-step explanation:

This polygon is 10 sides

The sum of all angles in a Decagon is 1,440

5x-61=1,440

+61 +61

5x=1,379

— ———

5 5

X=275.8

Answer:

I'm not in 7th grade but 7th grade was not the year for me lol

Step-by-step explanation:

sh. it was wild XD

Answer:

not in 7th grade

Step-by-step explanation:

but teachers gotta help out students a little more dude

Answer:

54

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Answer:

A- Quadrant one.

B- Quadrant three.

Step-by-step explanation:

So, the quadrants go counter-clockwise, starting at the top right which is Quadrant one. Therefore, A is in one. Using that information, we can assume that B is in Quadrant three.

Answer:

[tex]\cot 330^{\circ} = -\sqrt{3}[/tex]

Step-by-step explanation:

The cotangent function can be rewritten by trigonometric relations, that is:

[tex]\cot 330^{\circ} = \frac{1}{\tan 330^{\circ}} = \frac{\cos 330^{\circ}}{\sin 330^{\circ}}[/tex] (1)

By taking approach the periodicity properties of the cosine and sine function (both functions have a period of 360°), we use the following equivalencies:

[tex]\sin 330^{\circ} = \sin (-30^{\circ}) = -\sin 30^{\circ}[/tex] (2)

[tex]\cos 330^{\circ} = \cos (-30^{\circ}) = \cos 30^{\circ}[/tex] (3)

By (2) and (3) in (1), we have following expression:

[tex]\cot 330^{\circ} = -\frac{\cos 30^{\circ}}{\sin 30^{\circ}}[/tex]

If we know that [tex]\sin 30^{\circ} = \frac{1}{2}[/tex] and [tex]\cos 30^{\circ} = \frac{\sqrt{3}}{2}[/tex], then the result of the trigonometric expression is:

[tex]\cot 330^{\circ} = -\frac{\frac{\sqrt{3}}{2} }{\frac{1}{2} }[/tex]

[tex]\cot 330^{\circ} = -\sqrt{3}[/tex]

The exact value of cot 330° with a rational denominator is √3.

To find the exact value of cot 330°, we can first determine the reference angle. The reference angle for 330° is 30°, as it is the angle between the terminal side of 330° and the x-axis.

Cotangent (cot) is the reciprocal of the tangent function, so we need to find the tangent of the reference angle, which is tan 30°. The tangent of 30° is √3/3.

Since cot is the reciprocal of tan, the cotangent of 330° is the reciprocal of √3/3, which is 3/√3.

To rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is √3.

(3/√3) x (√3/√3) = 3√3/3

Simplifying further, we can cancel out the common factor of 3:

(3√3/3) = √3

Therefore, the exact value of cot 330° with a rational denominator is √3.

To learn more about trigonometric identities;

https://brainly.com/question/24377281

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Answer:

10

Step-by-step explanation:

5x2

Given:

The figure of an algebraic tiles model of an inequality.

To find:

The inequality for the given model.

Solution:

On the left hand side of the inequality sign in the model we have 8 tiles of x and 12 tiles of 1. So,

[tex]LHS=8(x)+12(1)[/tex]

[tex]LHS=8x+12[/tex]

On the right hand side of the inequality sign in the model we have 12 tiles of -1. So,

[tex]RHS=12(-1)[/tex]

[tex]RHS=-12[/tex]

Now, the inequality for the given model is:

[tex]8x+12\geq -12[/tex]

Therefore, the required inequality for the given model is [tex]8x+12\geq -12[/tex].

Step-by-step explanation:

Hoping this will help you on your journey through brainly!

Answer: 37

8(4)+11-3(2)

32+11-6

43-6

37