For the complex number z = (5sqrt(3))/4 - 5/4 * i what is the polar form

============================================================

Explanation:

I'm going to relabel the figure as triangle ABC.

As the instructions mention, we'll use the law of cosines to find the missing side.

Use these facts to find side c

c^2 = a^2 + b^2 - 2*a*b*cos(C)

c^2 = 147^2 + 166^2 - 2*147*166*cos(50)

c^2 = 17794.393497

c = sqrt(17794.393497)

c = 133.395628

c = 133

Answer: 3ln4 + 3lna

Step-by-step explanation:

[tex]\ln (4a)^{3}\\=3 \ln 4a\\=3(\ln 4+\ln a)\\=\boxed{3\ln 4+3\ln a}[/tex]

Answer:

C and second one is A

Answer:

2.08

Step-by-step explanation:

[tex]sin^{-1} 4/5 = 53.13\\tan 53.13 = 1.33\\cot 53.13 = 0.75\\1.33 + 0.775 = 2.08[/tex]

Answer:

The answer is 2

Step-by-step explanation:

[tex]Cot(x)=\frac{1}{tan(x)} =\frac{Cos(x)}{Sin(x)}[/tex]

[tex]Tan(x) = \frac{Sin(x)}{Cos(x)}[/tex]

[tex]Cos(\frac{\pi }{2} -x)=sin(x)[/tex]

This means that
[tex]\frac{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+\frac{\sin \left(\frac{4}{5}\right)}{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}[/tex]

This will be a long one to solve
-> apply cos identity to right side

[tex]\frac{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+\frac{\sin \left(\frac{4}{5}\right)}{\cos \left(\frac{\pi }{2}\right)\cos \left(\frac{4}{5}\right)+\sin \left(\frac{\pi }{2}\right)\sin \left(\frac{4}{5}\right)}[/tex]

-> simplify according to unit circle

[tex]\frac{\cos \left(\frac{\pi }{2}-\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+1[/tex]

->apply cos identity again

[tex]\frac{\cos \left(\frac{\pi }{2}\right)\cos \left(\frac{4}{5}\right)+\sin \left(\frac{\pi }{2}\right)\sin \left(\frac{4}{5}\right)}{\sin \left(\frac{4}{5}\right)}+1[/tex]

If you apply for unit circle numbers,

you will get 2

I do not recommend using a calculator for these questions, but instead, turn the form into [tex]sin\frac{\pi }{2}[/tex] other base unit circle locations, and most likely this is the method that your teacher counts as "right."
when using a calculator, it tends to "round" the number, which result in a inaccurate answer

Based on the calculations, the surface area (SA) of a cylinder is equal to: B.  2,813.44 in.²

Mathematically, the surface area (SA) of a cylinder can be calculated by using this formula:

SA = 2πrh + 2πr²

Where:

The dimensions of this new cylinder would be equal to:

Radius = 8 × 2 = 16 in.

Height = 6 × 2 = 12 in.

Substituting the given parameters into the formula, we have;

SA = (2 × 3.14 × 16 × 12) + 2 × 3.14 × 16²

SA = 1,205.76 + 1,607.68

SA = 2,813.44‬ square inches.

Read more on surface area here: https://brainly.com/question/26396269

#SPJ1

Complete Question:

If the dimensions of the following cylinder are doubled, what will be the surface area of the new cylinder? Radius: 8 in and Height: 6 in.

Group of answer choices.

A. 1,406.72 in.²

B.  2,813.44 in.²

C. 1,607.68 in.²

D. 5,626.88 in.²

Answer:

2.3333 ≈ 2

Step-by-step explanation:

The first step is the 1/6 because you are only counting the value 4 not the other ones like 1,2,3,5,6. So then that is 0.1666666. Then you multiply it by 14 which is rounded to 2. I can tell you are a 6th grader.

DISCLAIMER: THIS ANSWER MAY BE FALSE BECAUSE THERE IS NO PICTURE ATTACHED TO THIS POST. THUS, NEXT TIME YOU SHOULD UPLOAD A PICTURE. THIS IS ONLY A GUESS NOT A REAL ANSWER.

Answer:

8000.

Step-by-step explanation:

um I said so you don't need no step by step.

Answer:

B) Angle D is congruent to Angle P

Step-by-step explanation:

In order for the triangles to be congurent due to ASA, we need to know two pairs of congruent angles and one pair of congruent sides. We have one pair of sides and angles, so we only need another angle pair, therefore eliminating C and D, which are giving sides. If we chose option A we would get SAA property since it's supposed to be read clockwise. The only option left is option B.

Have a nice day!

All solutions to the equation 3 cos (5t) + 3 = 2 in the interval from 0 to π will be 0.3821, 0.2462, and 0.8745. Then the correct option is A.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The equation is given below.

3 cos (5t) + 3 = 2

By simplifying the equation, then we have

3 cos 5t = -1

   cos 5t = -1/3

Then the value of t will be

5t = 1.91063, 1.12096, 4.3725

 t = 0.3821, 0.2462, 0.8745

Then the correct option is A.

More about the trigonometry link is given below.

https://brainly.com/question/22698523

#SPJ1

The value of k based on the information given will be k = 2.

It should be noted that the line of f(x) passes through the point (-4, 0) and (0, 4). The line of g(x) goes through (-2, 0) and (0, 4).

The slope of x will be:

= (4 - 0)/(0 + 4)

= 4/4

= 1

By using slope point form, y = kx + 4.

Substitute x = 2.

g(-2) = -2k + 4 = 0

2k = 4

k = 4/2 = 2

Learn more about slope on:

brainly.com/question/13657991

#SPJ1

Explanation:

The solution set for a system of equation is the set of points where the graphs of the equations intersect.

__

A system will have one solution if there is a single point of intersection of the graphs of the equations.

A system will have no solutions if the graphs have no points of intersection.

A system will have an infinite number of solutions if the graphs intersect at an infinite number of points.

_____

When the equations are linear equations, their graphs are straight lines. If the lines have different slopes, they must intersect at exactly one point: there will be one solution.

If the lines have the same slope, there are two possibilities:

The attached graph illustrates these cases.

Answer:

6 cm^2

Step-by-step explanation:

Area of Rectangle is L*W

L=3 and W=2

3*2=6

The expression that allows us conclude parts of congruent triangles are congruent to each other is corresponding parts of Congruent Triangles are congruent

A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees. Two triangles are congruent when they have exactly the same three sides and exactly the same three angles.

To learn more about triangles, please check: https://brainly.com/question/22949981

#SPJ1

Answer:

b = 17.318    height = 23.318 ft

Step-by-step explanation:

This IS very similar to the other one, Emily..... Have you tried to solve it the same way?

b =   152 tan 6.5  = 17.318 ft      (using a calculator)

    add the height of the victim's head (6 ft)

17.318 + 6 = 23.318 ft

Answer:

[tex]\textsf{A)} \quad 5u^3-2u^2+5u+8[/tex]

Step-by-step explanation:

Given expression:

[tex](-2u^3+5u-1)+(7u^3-2u^2+9)[/tex]

Remove parentheses:

[tex]\implies -2u^3+5u-1+7u^3-2u^2+9[/tex]

Collect like terms:

[tex]\implies -2u^3+7u^3-2u^2+5u-1+9[/tex]

Combine like terms:

[tex]\implies 5u^3-2u^2+5u+8[/tex]

Option A

The range of the function is {-34, -2, -20}

The function is given as:

f(x) = -2x^2 - 2

The domain is {-4, 0, 3}

Substitute the domain values in the function.

f(-4) = -2(-4)^2 - 2 = -34

f(0) = -2(0)^2 - 2 = -2

f(3) = -2(3)^2 - 2 = -20

This means that the range of the function is {-34, -2, -20}

Read more about range at:

https://brainly.com/question/10197594

#SPJ1

Step-by-step explanation:

standard form is given by Ax × By = C

hence the answer would be

5x + 8y = 24

comment if you still have any doubts :)

Answer:

5x + 8y = 24

Step-by-step explanation:

Given :

[tex]y=-\frac{5x}{8} +3[/tex]

……………………

[tex]y=-\frac{5x}{8} +3[/tex]

[tex]\Longleftrightarrow 8\times y=8\times (-\frac{5x}{8} +3)[/tex]

[tex]\Longleftrightarrow 8y=-5x+24[/tex]

[tex]\Longleftrightarrow 5x+8y=24[/tex]

[tex]\\ \rm\Rrightarrow \sum^{60}_{n=1}3n[/tex]

It will form a arithmetic sequence as

[tex]\\ \rm\Rrightarrow 3(1)+3(2)+3(3)\dots 3(60)[/tex]

So

Summation

[tex]\\ \rm\Rrightarrow \dfrac{n}{2}(a+\ell)[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{60}{2}(3+180)[/tex]

[tex]\\ \rm\Rrightarrow 30(183)[/tex]

[tex]\\ \rm\Rrightarrow 5490[/tex]

Option D

Answer:

[tex]\mathsf {5,490}[/tex]

Step-by-step explanation:

[tex]\textsf {Given :}[/tex]

[tex]\lim_{1 \to \660} \sum3n[/tex]

[tex]\textsf {Finding the necessary :}[/tex]

[tex]\textsf {1. first term (a)}[/tex]

[tex]\implies \mathsf {a = 3(1) = 3}[/tex]

[tex]\textsf {2. final term}[/tex] [tex]\mathsf {(a_n)}[/tex]

[tex]\implies \mathsf {a_n = 3(60) = 180}[/tex]

[tex]\textsf {3. common difference (d)}[/tex]

[tex]\implies \mathsf {a_2 = 3(2) = 6}[/tex]

[tex]\implies \mathsf {d = a_2 - a_1 = 6 - 3 = 3}[/tex]

[tex]\textsf {Finding the sum of the series :}[/tex]

[tex]\implies \mathsf {S_n =\frac{n}{2}(a + a_n) }[/tex]

[tex]\implies \mathsf {S_6_0 = \frac{60}{2} (3 + 180)}[/tex]

[tex]\implies \mathsf {S_6_0 = 30 \times 183}[/tex]

[tex]\implies \mathsf {S_6_0 = 5,490}[/tex]

The area of a 2D form is the amount of space within its perimeter. The lateral area of the right prism is 120 cm².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Given the perimeter of the base of the right prism is 20 cm, while the lateral height is 6 cm. Therefore, the lateral area of the right prism is,

Lateral Area of Right Prism = 6cm × 20cm = 120cm²

Hence, the lateral area of the right prism is 120 cm².

Learn more about the Area:

https://brainly.com/question/1631786

#SPJ1

Answer:

x+3x+2x=180(sum of triangle)

6x=180

x=180/6

x=30

again

3x=3×30=90

2x=2×30=60

The function that has the same domain as y= 2√x is (a) y = √2x

The function is given as:

y= 2√x

The above function is a square root function.

All square root functions have the same domain when they are not translated.

This means that

y = √2x has the same domain as y= 2√x  because it is not translated

Read more about domain at:

https://brainly.com/question/1770447

#SPJ1

Answer:

37

20

C

a

→

37

19

K

+

0

+

1

e

This equation shows us the parent atom, which is calcium-37. The mass number is written above the atomic number for the atom. The arrow indicates the decay process with the products to the right of the arrow. The products are an atom of potassium-37 and a positron, which is similar to an electron but it carries a charge of +1 instead of a charge of -1. We can see that the transition of a proton to a neutron in positron decay decreases the atomic number of the atom from 20 to 19, but the mass number of 37 remains the same.

Step-by-step explanation:

Answer:

37

20

C

a

→

37

19

K

+

0

+

1

e

Step-by-step explanation:

If the original pendulum completed one swing every 1.5 seconds. How long should the new pendulum be is: C. 55.9 centimeters.

Using this formula

T=2π√I/g

Where:

T=1.5 seconds

l =length of pendulum

g= acceleration of gravity=9.8m/s²

Let plug in the formula

1.5 seconds=2π√I/9.8

l/9.8=0.05699

l=0.05699×9.8

l=0.5585

l=55.9 centimeters (Approximately)

Therefore How long should the new pendulum be is: C. 55.9 centimeters.

Learn more about How long should the new pendulum be here:https://brainly.com/question/11616656

#SPJ1

Answer:

4/5

Step-by-step explanation:

First, we know that we have 5 envelopes. So the denominator of the probability is going to be x/5. We then realize that only one envelope has the car, so the probability of that is 1/5. If we subtract 1/5 from the probability of choosing an envelope (5/5), we get 5/5-1/5=4/5.

Step-by-step explanation:

I don't see question 1 and 2.

but it did be way for you : the distance from the verge of a circle to a point on the circle is always the radius.

that is the whole concept of a circle : it is the line (or curve) of all points that have the same, constant distance r from a single point.

The letter that will be on the side opposite D is letter B

The attached image represents the missing piece in the question

The opposite sides of a cube always have a face in between them, when represented as a net.

From the attached image, the adjacent sides are:

A B C D

F C E

The opposite sides as represented above are;

A and C

B and D

F and E

Hence, the letter that will be on the side opposite D is letter B

Read more about cubes at:

https://brainly.com/question/1972490

#SPJ1

The system of equations that have a solution of (-2,-2,-2) is (b) x + 2y = -6, y + 2z = -6 and x - y - z = 2

The attached figure represents the proper format of the equations.

The solution is given as:

(x,y,z) = (-2,-2,-2)

To determine the system of equation, we simply substitute the values of x, y and z in the equations in the options.

So, we have:

Option 1:

x + y = 0

y - z = -2

x + y - z = -4

Evaluate

x + y = 0

-2 - 2 = 0 --- False

This means that this system of equations do not have a solution of (-2,-2,-2)

Option 2:

x + 2y = -6

y + 2z = -6

x - y - z = 2

Evaluate

x + 2y = -6

-2 + 2 * -2 = -6 --- True

y + 2z = -6

-2 + 2 * -2 = -6 ---- True

x - y - z = -2

-2 + 2 + 2 = 2

This means that this system of equations have a solution of (-2,-2,-2)

Read more about system of equations at:

https://brainly.com/question/14323743

#SPJ1

The true statement about the graph is that there is a hole at x = 3 and an asymptote at x = -1.

The expression in the denominator is x^2-2x-3

x² - 2x-3 ≠0

-3 = +1 -4

(x²-2x+1)-4 ≠0

(x²-2x+1)=(x-1)²

(x-1)² - (2)² ≠0

∴a²-b² =(a-b)(a+b)

(x-1-2)(x-1+2) ≠0

(x-3)(x+1) ≠0

x≠3 for all x≠ -1

There is a hole at x=3 and an asymptote at x= -1, so Option B is wrong

Asymptote:

x-3/x^2-2x-3

We know that denominator is equal to (x-3)(x+1)

x-3/(x-3)(x+1)

x-3 will be cancelled out by x-3

1/x+1

We have asymptote at x=-1 and hole at x=3, therefore the correct option is A.

Learn more about graph on:

https://brainly.com/question/19040584

#SPJ1

Answer:

[tex]\csc A - \sec A = \dfrac 83 + \dfrac{8}{\sqrt{55}}\\\\\csc A - \sec A = \dfrac 83 - \dfrac{8}{\sqrt{55}}[/tex]

Step by step explanation:

[tex]\text{Given that,}\\\\~~~~~~\sin A = \dfrac 38 \\\\\implies \sin^2 A = \dfrac 9{64}\\\\\implies 1 - \cos^2 A = \dfrac{9}{64}\\\\\implies \cos ^2 A = 1 - \dfrac 9{64}\\\\\implies \cos^2 A = \dfrac{55}{64}\\\\\implies \cos A =\pm\sqrt{\dfrac{55}{64}}\\ \\\implies \cos A = \pm\dfrac{\sqrt{55}}8\\\\[/tex]

[tex]\implies \dfrac 1{\cos A} = \pm\dfrac{8}{\sqrt{55}}[/tex]

[tex]\text{Now,}\\\\\csc A - \sec A\\\\=\dfrac{1}{\sin A}- \dfrac{1}{\cos A}\\\\=\dfrac 83 -\left(\pm \dfrac 8{\sqrt {55}} \right)\\ \\\text{Hence,}\\\\\csc A - \sec A = \dfrac 83 + \dfrac{8}{\sqrt{55}}\\\\\csc A - \sec A = \dfrac 83 - \dfrac{8}{\sqrt{55}}[/tex]