If cos of Ф = 2/5, find sin Ф/2 and cos Ф/2. Assume the angles are in the 1st quartile

The required fifth roots of the given complex number as ⁵√3i = ⁵√3·⁵√i.

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib,

where a, and b are real numbers and i is an imaginary number.

The complex number is given in the question following as

3i

We have to determine the fifth roots of the given complex

As per the given question, we have

⇒ ⁵√3i

Apply the radical rule ⁿ√ab = ⁿ√aⁿ·√b,  (Assuming a ≥ 0, b ≥ 0)

⇒ ⁵√3·⁵√i

Thus, the required fifth roots of the given complex number as ⁵√3i = ⁵√3·⁵√i.

Learn more about the complex numbers here:

brainly.com/question/19007885

#SPJ1

The previous length and width are 20 ft and 12 ft, new length and width are 30 ft and 18 ft thus, option (C) is correct.

You must specify the extent of the shape's enlargement when describing one.

The scale factor is the ratio of two dimensions such that one figure is large and another is small.

The scale factor is done due to the unpractical measurement of any figure.

As per the given scale factor 1 in 4ft

Previous length   = 5 × 4 = 20 feet

Previous width = 3 ×4 = 12 ft

As per the given scale factor 1 in 6ft

Previous length = 5×6  = 30 feet

and New width  = 3 × 6 = 18 feet

Hence" the Previous length and width are 20 ft and 12 ft, new length and width are 30 ft and 18 ft".

To learn more about scale factors,

brainly.com/question/22312172

#SPJ1

The complete question is below,

Adenan makes a scale drawing of a rectangular flower box. The length is 5 in., and the width is 3 in. Adenan changes the scale of the drawing from 1 in. : 4 ft to 1 in. : 6 ft. Which statement about the dimensions of the flower box is true?

The length of the flower box under the new scale is 15 ft.

The length of the flower box under the old scale is 30 ft.

The width of the flower box under the old scale is 12 ft.

The width of the flower box under the new scale is 24 ft.

Answer:

63

Step-by-step explanation:

Answer:

2nd ones answer is 13.5 m.

4th ones answer is 600 yard³.

5th ones answer 86400 cm³/m³

Please give 20 point for each question.

The equation to find out his score is above average is  x = 300 - 187

and it is 113.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Jean Conrad is an amateur bowler with an average score of 187. She recently bowled a perfect 300 score.

Let the score above her average score be x,

∴ x = 300 - 187.

x = 113.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ2

The height of the tower is 2358.3 feet

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the height of the tower be = A

Let the base of the tower be at a distance of = 500 feet

Now , the angle of elevation is θ = 78°

The height of David's view = 6 feet above

So , the total height of the tower be = A + height of David's eyes

Now , A right angle triangle is formed between the tower, the angle of elevation of David's eyes and his distance from the tower

And , the opposite side = A

Adjacent side = 500 feet

So , from the trigonometric relations

tan θ = opposite side / adjacent side

tan θ = A / 500

Multiply by 500 on both sides , we get

A = tan θ x 500

Substituting the value for θ

A = tan 78° x 500

A = 4.7046 x 500

A = 2352.3 feet

Now , the total height of the tower = A + height of David's eyes

                                                          = 2352.3 + 6

                                                          = 2358.3 feet

Hence , The height of the tower is 2358.3 feet

To learn more about trigonometric equations click :

https://brainly.com/question/14746686

#SPJ1

Answer: A. 8

Step-by-step explanation: Draw it out like 1 white hat and 1 blue hat

                                                                        1 white blouse    1 blue blouse                                                            

                                                                       1 white short       1 blue short

1 white hat with a blue or white blouse and 1 white short or blue so 4 in total outfits by counting with the hat and the same for the other hat. so 8 outfits. I hope you get my logic :)

Answer:4 and 16

Step-by-step explanation:

4 = 4, 8, 12, 16, 20

16 = 16, 32..

LCM = 16

Answer:

3!

Step-by-step explanation:

Hope this helped ! :D

The population of a town t years from now is given by the formula[tex]P_{t+1} = 1.02(P_t - 550)[/tex]. The current population is 42,000, so there will be approximately 44,031 people in the town 3 years from now.

We are given that the population of the town t years from now is given by the formula

[tex]P_{t+1} = 1.02(P_t - 550)[/tex]

We know that the population of the town is currently 42,000, so we can use this to find the population of the town 1 year from now

P₁ = 1.02(P₀ - 550)

= 1.02(42000 - 550)

= 42669

So there will be 42,669 people in the town 1 year from now.

We can now use this to find the population of the town 2 years from now

P₂ = 1.02(P₁ - 550)

= 1.02(42669 - 550)

= 43349.18 (rounded to 2 decimal places)

So there will be approximately 43,349 people in the town 2 years from now.

Finally, we can use this to find the population of the town 3 years from now

P₃ = 1.02(P₂ - 550)

= 1.02(43349.18 - 550)

= 44031.45 (rounded to 2 decimal places)

So there will be approximately 44,031 people in the town 3 years from now.

To know more about population:

https://brainly.com/question/29044849

#SPJ1

Answer: -800

Step-by-step explanation:

-2(12+8)^2

-2(20)^2

-2(400)

-800

(i think)

Answer:

1/4 of the trip

Step-by-step explanation:

The questions is asking what is 1/2 of 1/2 and that would b 1/4

These sentences are correct among all the given sentences & in terms of a given diagram.

 Corresponding Angles Converse

 Alternate interior Angles Converse

 Alternate Exterior Angles Converse

What are the corresponding angles?

In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance. In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.

We have,

no lines are parallel

Corresponding Angles Converse

Alternate interior Angles Converse

Alternate Exterior Angles Converse

Consecutive interior Angles Converse

By considering the given diagram the correct sentences are:

 Corresponding Angles Converse

 Alternate interior Angles Converse

 Alternate Exterior Angles Converse

Hence, these sentences are correct among all the given sentences & in terms of a given diagram.

To learn more about the corresponding angles visit,

https://brainly.com/question/2009183

#SPJ4

Answer:

Line l is parallel to line n.

Alternate interior angle converse.

Step-by-step explanation:

Angles 8 and 19 are alternate interior angles of lines l and n cut by transversal k.

Since angles 8 and 19 are congruent, then by alternate interior angle converse, lines l and n are parallel.

[tex] \Large{\boxed{\sf | \sf z| = \sf \sqrt{40} = 2\sqrt{10} }} [/tex]

[tex] \\ [/tex]

We are given a complex number in algebraic form, and we would like to find its modulus, |z|.

[tex] \\ \\ [/tex]

[tex] \\ \\ [/tex]

Let's recall that a complex number in algebraic form is written as [tex] \sf z = a + ib [/tex] , where a is its real part and b is its imaginary part.

[tex] \\ [/tex]

The modulus of said complex number is calculated as follows:

[tex] \sf | \sf z| = \sqrt{a^2 + b^2} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

Let's identify our values:

[tex] \sf z = -2 - 6i \Longleftrightarrow z = \underbrace{\sf -2}_{\sf a} + (\underbrace{\sf -6}_{\sf b})i [/tex]

[tex] \\ [/tex]

Now, substitute these values into our formula:

[tex] \sf | \sf z | = \sqrt{(-2)^2 + (-6)^2} = \sqrt{4 + 36} = \boxed{\sf \sqrt{40}} [/tex]

[tex] \\ [/tex]

While this may be optional, the result can be simplified by using the following property:

[tex]\green{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \blue{ \star \: \sf{\boxed{ \sf Product \: rule \: of \: square \: roots\text{:}}}} \\ \\ \sf{ \diamond \: \sqrt{ab} = \sqrt{a} \times \sqrt{b} } \\ \end{array}}\\\end{gathered} \end{gathered}}[/tex]

[tex] \\ [/tex]

[tex] \sf \sqrt{40} = \sqrt{4 \cdot 10} = \sqrt{4} \cdot \sqrt{10} = \boxed{\boxed{\sf 2\sqrt{10}}} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

▪️Learn more about the modulus of a complex number here:

↣https://brainly.com/question/10737199

The equation of the straight line in fully simplified slope-intercept form: [tex]y = 2x-6[/tex]

A straight line is just a straight line with no bends. A straight line is one that has no bends and continues to infinity on both sides.

A straight line's equation is y=mx+c, where m is the gradient and c is the height at which the line crosses the y axis, commonly known as the y -intercept.

The drawn line cut the x-axis at (3,0) and y-axis at (0,-6)

So, the equation of line is:

    [tex]\frac{x}{3} + \frac{y}{-6} = 1[/tex]

or, [tex]\frac{x}{3} - \frac{y}{6} = 1[/tex]

or, [tex]\frac{2x-y}{6} = 1[/tex]

or, [tex]2x-y =6[/tex]

or, [tex]y = 2x-6[/tex]

Thus, slope-intercept form is: [tex]y = 2x-6[/tex]

To know more about straight line refer to:

https://brainly.com/question/25969846

#SPJ1

Using the attached process, the square roots and cube roots are estimated as follows:

1. √15 = 3.81

2. √44 = 6.6.

3. √81 = 9

4. ∛12 = 2.88.

5. ∛125 = 5

6. ∛320 = 6..8

2)The mistake made by Jan is in the place of 17cm we get 13cm by sing Pythagorean theorem. Therefore, perimeter is 30cm.

3) The error of Joshua is that he miscalculated the third length of the triangle.

From the Pythagorean theorem, we have learned that a²+b²=c²

In mathematics, the Pythagorean Theorem  is the fundamental relationship in Euclidean geometry between the three sides of a right triangle. It states that the area of ​​a square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

The attachment depicts the procedure we will use.

The first step is to make a list of all the perfect squares from 1 to 100, followed by all the perfect cubes from 1 to 1000.

1 to 100 perfect squares; 4, 9, 16, 25, 36, 49, 64, 81, 100

1 to 1000 perfect cubes; 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000.

1) √15

The perfect squares that are nearest are 9 and 16.

√9 < √15 < √16

⇒ 3 < √15 < 4

Now, √15 is between 3 and 4.

We can estimate √15  as 3.81

2) √44

The perfect squares that are nearest are 36 and 49.

√36 < √44 < √49

⇒ 6 < √44 < 7

Now,√44 is between 6 and 7.

So, we can estimate √44 as 6.6

3) √81

Because this is a perfect square, the approach used to estimate non-perfect squares does not apply. Thus;√81 = 9

4) ∛12

The perfect cubes that are nearest are 8 and 27

Thus; ∛8 < ∛12 < ∛27

⇒ 2 < ∛12 < 3

Now,√12 is between 2 and 3.

So, we can estimate ∛12 as 2.88.

5) ∛125

Because this is a perfect cube, the approach used to estimate non-perfect squares does not apply. Thus;∛125 = 5

6) ∛320

The perfect cubes that are nearest are 216 and 343

Thus; ∛216 < ∛320 < ∛343

⇒ 6 < ∛320 < 7

Now, ∛320 is between 6 and 7.

So, we can estimate ∛320 as 6..8

2) Perimeter of the triangle=L+L+L

Given, Perimeter=5cm+12cm+17cm

=34cm

The mistake he made wrong is,

By using Pythagorean theorem,

√a²+b²=c²

√5²+12²=c²

√25+144=c²

√169=c²

13=c

Therefore, perimeter of the triangle is 5cm+12cm+13cm=30cm

3) First we calculate the third length of the triangle x.

As the triangle is a right triangle we use Pythagorean theorem.

x²=7²+7²

x²=2(7²)

Squaring on both sides, we get

x=√2(7²)

x=7√2

The other shape in the given figure is square.

Therefore the perimeter P is given by,

P=7+x+x+x+7

So, P=7+7√2+7√2+7√2+7

P=14+21√2

Hence, the error of Joshua is that he miscalculated the third length of the triangle.

From the Pythagorean theorem, we have learned that a²+b²=c².

To know more about Pythagorean theorem, visit:

https://brainly.com/question/14930619

#SPJ1

The 3 side lengths that can form a right triangle are 16, 30, 34

A right triangle (American English) or right-angled triangle (British), or more formally an orthogonal triangle, historically known as a rectangle triangles, is a triangle with one angle that is a right angle (that is, a 90-degree angle), i.e., two sides that are perpendicular.

The hypotenuse is the opposite side of the right angle (side c in the figure). Legs are the sides adjacent to the right angle. Side an is the side adjacent to angle B that is opposed to (or opposite) angle A, whereas side b is the side adjacent to angle A that is opposed to (or opposite) angle A.

By checking the three sides of a triangle are:

16, 30, 34

By using Pythagorean theorem,

√a²+b²=c²

=√16²+30²=34²

=1156=1156

Therefore, the 3 side lengths that can form a right triangle are 16, 30, 34

To know more about right triangle, visit:

https://brainly.com/question/4364353

#SPJ1

The range of the function is {1,-1,10} for function f(x)=2x³−3x .

A relation is a function if it has only One y-value for each x-value.

In a function what can go into a function is called the Domain. What may possibly come out of a function is called the Codomain. What actually comes out of a function is called the Range.

The given function is f(x)=2x³−3x

The domain is {-1,1,2}

Now f(-1)=2(-1)³-3(-1)

=-2+3=1

f(1)=2(1)³-3(1)=2-3=-1

f(2)=2(2)³-3(2)=16-6=10

Hence, the range of the function is {1,-1,10} for  f(x)=2x³−3x .

To learn more on Functions click:

https://brainly.com/question/21145944

#SPJ1

Answer:

27 units

Step-by-step explanation:

12 over 4

36 over x

x = 27

linear equation

Answer:alt  account

Step-by-step explanation:

Answer:

To write this as a sentence, it would be:

10x-6

Step-by-step explanation:

Hope this helps! HAVE A GREAT DAY! :D

10(n) - 6

6 less = -6

THAN the product of 10 and a number

(We can represent a number as n). (Product = multiplication).

10 x n

10(n) - 6

10(n) - 6

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer:

Minimum Value: -5

Maximum Value: -1

Interval is [-5, -1]

Step-by-step explanation:

In math the absolute rule for a function f(x) = |x| ≤ a means that the range of values for x can be -a ≤ x ≤ +a

Use |t+3| instead of x in the above rule with a = 2

|t + 3| ≤ 2

⇒ -2 ≤ t + 3 ≤ 2

Subtract 3 from all parts
⇒            -2 - 3 ≤ t + 3 -3 ≤ 2 - 3
This gives

-5 ≤ t ≤ -1

which are the limits for t.

In interval notation this is
[-5, -1]
Minimum Value:   - 5
Maximum Value:  - 1

The solution to the linear equations y=3/4x-4 and y=-1/2x+11, as shown in the graph in the attachment is: (12, 5).

If the lines that represent the linear equations of a system are graphed, the coordinates of x and y of the point where the two lines intersect is the solution to the system of linear equations.

Given the equations, y = 3/4x - 4 and y = -1/2x + 11, the line of y = 3/4x - 4 is the red line in the image attached below which has a slope of 3/4 and a y-intercept of -4, while the line of y = -1/2x + 11 is the blue line that has a slope of -1/2 and has a y-intercept of 11.

The graph also shows that the lines of both linear equations intersect at (12, 5).

Therefore, the solution to the linear equations is:

Learn more about linear equation graphs on:

https://brainly.com/question/14323743

#SPJ1

Answer:

Below

Step-by-step explanation:

FIRST, note that it has a negative slope   ( goes downhill when reading from L to R) .....this is nice to know to see if you calculate slope correctly:

Find two convenient integer coordinates to calculate slope

 ( 0,2) and  (4,0)  

slope =   (2-0)/(0-4) = m = -1/2

b = y-axis intercept = +2  ( from the graph )

Line equation is  y = mx + b

                               y = -1/2 x + 2

Answer: x=-15

Step-by-step explanation:

First you want to get rid of the fraction.
you multiply by 6 on each side so you get -3x-3=42. After that you add 3 to get 45, and lastly you divide 45 by -3 which gets you -15

The area of the rhombus is 108m²

The area of a rhombus can be defined as the amount of space enclosed by a rhombus in a two-dimensional space. A rhombus is a type of quadrilateral projected on a two dimensional (2D) plane, having four sides that are equal in length and are congruent.

The formula of a rhombus is given as

A = (d₁ * d₂) ÷ 2

where d₁ and d₂ are the diagonals

d₁ = 12m

d₂ = 18m

A = (12 * 18) / 2

A = 108m²

The area is 108 squared meter

Learn more on area of rhombus here;

https://brainly.com/question/26154016

#SPJ1

Translation: How many squared meters does the surface of a rhombus-shaped children's party room whose diagonals measure 12 and 18 meters?

Answer: 64

Step-by-step explanation:

Answer:

(0,0)

Step-by-step explanation:

For this, you need to use the midpoint formula.

(-3) + 3                      2 + (-2)

--------------      ,       ----------------

     2                               2

This leads to:

-3 + 3 = 0 -> 0/2

x = 0

3 + (-3) = 0 -> 0/2

The answer is:

(0, 0)