A 400 meters running track has two straight sections, each of length 120 meters and two semicircular ends. calculate the total length of the of the curved sections of the track.​

The result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

The expression is given as:

[tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex]

Express [tex]\sin^2(\theta)[/tex] as [tex]1 - \cos^2(\theta)[/tex].

So, we have:

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = (1- \cos^2(\theta)) * (1 + \cos(\theta))[/tex]

Open the bracket

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = 1 + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

Express 1 as cos°(Ф)

[tex]\sin^2(\theta) * (1 + \cos(\theta)) = cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

Hence, the result of expanding the trigonometry expression [tex]\sin^2(\theta) * (1 + \cos(\theta))[/tex] is [tex]cos^0(\theta) + \cos(\theta) - \cos^2(\theta) - \cos^3(\theta)[/tex]

Read more about trigonometry expressions at:

https://brainly.com/question/8120556

#SPJ1

Volume of a Rectangular Prism = length x width x height

Volume = 20

Length = 2

Width = 2

Height = d

20 = 2 x 2 x d

20 = 4 x d

d = 5

Answer: d = 5 centimeters

Hope this helps!

Answer:

d = 5 cm

Step-by-step explanation:

Volume of a rectangular prism: L*W*H

Substitute the values above into the formula:

V = L*W*H

20 = 2*2*d

20 = 4d

/4    /4

5 = d

Therefore, the value of d is 5 cm.

Hope this helps!

Answer:

Equation = [tex]\frac{3}{4}[/tex] x - 2 = [tex]\frac{5}{12}[/tex]

First: [tex]\frac{3}{4}[/tex] x = [tex]\frac{5}{12}[/tex] + 2

Then: [tex]\frac{3}{4}[/tex] x = [tex]\frac{29}{12}[/tex]

Answer: x = [tex]\frac{29}{9}[/tex] —> 9x = 29

—-

Have a nice day!!

Answer:

4.03 < 16.5

Step-by-step explanation:

Four and three hundreths = 4.03

sixteen and five-tenths = 16.5

4.03 < 16.5

Answer:A

Step-by-step explanation:

the correct choice is: B. The numbers in the pattern are odd.

To determine if the numbers in the pattern are even, odd, or alternate between even and odd, let's examine the first few numbers in the pattern:

First number: 41

Second number: 41 - 4 = 37

Third number: 37 - 4 = 33

Fourth number: 33 - 4 = 29

As we can see, the numbers in the pattern are decreasing by 4 in each step. The first number (41) is odd, and subsequently, each number is decreasing by an even value (4). Therefore, all the numbers in the pattern will be odd.

So, the correct choice is:

B. The numbers in the pattern are odd.

Learn more about pattern here

https://brainly.com/question/11170254

#SPJ2

Answer:

165 divided by 11 = 15

154 divided by 14 = 11

306 divided by 17 = 18

322 divided by 14 = 23

Answer: [tex]b^{2}(1-21a^{3})[/tex]

Step-by-step explanation:

[tex]b^{2} - 21a^{3} b^{2} \\b^{2}(1-21a^{3})[/tex]

Answer: 20,-13

Step-by-step explanation:

We can rewrite the problem as an equation. This equation is x(x-7)=260 (x being the mystery number). We can simply this into x^2 -7x=260. We can then rewrite this as x^2 -7x -260=0. We need to find the roots of this quadratic, which are -13 and 20. You can find this by factoring the quadratic.

A population about which we want to get some information is called the sample.

This is a portion of a population that is known to contain several parts of the population. The information that is gotten from the sample would be used to draw conclusion about the entire information.

Therefore from the definition above the answer to the question is the population sample.

Read more on the population sample here:

https://brainly.com/question/17831271

#SPJ1

a) Triangle A is rotated 90 degrees anticlockwise about (-1,0) to give triangle A'.

Triangle A' is then reflected in the line y=0 to give triangle A''.

b) Rotation

a) Triangle A is rotated 90 degrees anticlockwise about (-1,0) to give triangle A'. Triangle A' is then reflected in the line y=0 to give triangle A''.

b) Rotation

Given,

Triangles A , A' , A'' .

Here,

The triangles are rotated and reflected to get different triangles .

Firstly ,

Triangle A is made to be rotated by 90° in anticlockwise direction at point (-1 , 0) .

To get A'' triangle A' is reflected from horizontal axis.

Triangle A maps into triangle A'' by rotation .

Know more about triangle transformation,

https://brainly.com/question/31241624

#SPJ2

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Let [tex]z=r(\cos\theta+i\sin\theta)[/tex] be a complex number, where [tex]n[/tex] is an integer and [tex]n\geq 1[/tex]. By DeMoivre's Theorem, if [tex]z^n=r^n(\cos\theta+i\sin\theta)^n[/tex], then [tex]z^n=r^n(\cos n\theta+i\sin n\theta)[/tex].

Hence, we must first convert from rectangular to polar form:

[tex]z=-1-i\\\\r=\sqrt{a^2+b^2}\\\\r=\sqrt{(-1)^2+(-1)^2}\\\\r=\sqrt{1+1}\\\\r=\sqrt{2}[/tex]

[tex]\displaystyle \theta=\tan^{-1}\biggr(\frac{y}{x}\biggr)\\\\\theta=\tan^{-1}\biggr(\frac{-1}{-1}\biggr)\\ \\\theta=\tan^{-1}(1)\\\\\theta=45^\circ[/tex]

Therefore, the rectangular form for the complex number is [tex]z=\sqrt{2}(\cos45^\circ+i\sin45^\circ)[/tex], and now we can apply DeMoivre's Theorem to raise the complex number to the 10th power:

[tex]z=\sqrt{2}(\cos45^\circ+i\sin45^\circ)\\\\z^{10}=\sqrt{2}^{10}(\cos45^\circ+i\sin45^\circ)^{10}\\\\z^{10}=2^5(\cos10\cdot45^\circ+i\sin10\cdot45^\circ)\\\\z^{10}=32(\cos450^\circ+i\sin450^\circ)\\\\z^{10}=32(0+i)\\\\z^{10}=32i[/tex]

Therefore, [tex]z^{10}=32i[/tex] in rectangular form.

Problem 2

[tex]3\:\text{cis}\:90^\circ=3(\cos90^\circ+i\sin90^\circ)=3(0+i)=3i[/tex]

Therefore, [tex]3\:\text{cis}\:90^\circ=3i[/tex] in rectangular form.

Answer:

0.0109056604

that is the answer, I used a calculator

A mean is an arithmetic average of a set of observations. The score of the student is equal to 63.4.

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

Given the mean score was 75, while the standard deviation was 8. Therefore, the score of the student is,

Scre of the student = μ - 1.45σ = 75 - 1.45(8) = 63.4

Hence, the score of the student is equal to 63.4.

Learn more about Mean:

https://brainly.com/question/16967035

#SPJ1

Answer:

Step-by-step explanation:

The solution to a one-variable inequality can be graphed on a number line. The number line is shaded where the values satisfy the inequality. Boundaries of shaded regions are marked by points that are either a solid dot, or an open circle, depending on whether the point is included in the solution or not.

__

Here, the inequality tells us any value of x that is less than or equal to -1 will satisfy the inequality. Since -1 is part of the solution set, that boundary point will be marked with a solid dot. Values less than -1 are shown on a number line to the left of the point marked -1.

The graph will be a solid dot at x=-1, and shading to its left.

__

Possible solutions are any values less than or equal to -1. Some are ...

  -1

  -1.073

  -429

The list of the set of dimension for fencing the building around a rectangular plot of land is 10.5 meters and 21 meters.

area of rectangle = lw

where

Therefore,

perimeter = 2w+ l

42 = 2w + l

l = 42  - 2w

Hence,

area = w(42 - 2w)

180 = 42w - 2w²

-2w² + 42w - 180 = 0

-w² + 21w - 90 = 0

The dimension w can be found as follows;

w = - b / 2a

where

w = - 21 / 2 ×  -1

w = 10.5 meters

Then,

l = 42  - 2w

l = 42 - 2(10.5)

l = 21 meters

Therefore, the dimensions are 10.5 meters and 21 meters.

learn more on rectangle here: https://brainly.com/question/15536011

#SPJ1

The tangent is the ratio of the perpendicular and the base of the right triangle. Then tan A will be x/y.

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

The right-angle triangle ΔABC is given.

The angle ∠C is 90°.

And the perpendicular is x, the base is y, and the hypotenuse is z.

Then the value of the tangent of angle ∠A will be

The tangent is the ratio of the perpendicular and the base of the right triangle.

tan A = x/y

More about the trigonometry link is given below.

https://brainly.com/question/22698523

#SPJ1

Answer:

1.45

Step-by-step explanation:

weight of all books= 14×1.1= 15.4

weight of all duster=7×0.2= 1.4

weight of books and duster= 15.4+1.4=16.8

weight of the empty box = 18.25-16.8=1.45

Answer:

75.96°

Step-by-step explanation:

22.5 = 1.5x

x = 22.5/1.5

x = 15

hope it helps...!!!

Answer:

x = 15

Step-by-step explanation:

1.5x = 22.5

x = 22.5/1.5

assuming your finding x

Answer:

answer = 12

Step-by-step explanation:

Let the smallest number be x

So

X+(x+2)+(x+4)+(x+6)=60

4x+12=60

4x=48

X=12

Answer:

€ 1800

Step-by-step explanation:

x - 20% of x = 1440

x - 20x/100 = 1440

x - x/5 = 1440

(5x - x)/5 = 1440

4x/5 = 1440

therefore x = 1440 × 5/4 [ transpose 4/5 to right hand side ]

x = 360 × 5

= € 1800

Answer:

10.672hrs ( maybe)

Step-by-step explanation:

A can complete the work in 20 hrs then 1/3 part can be completed in 20*1/3=6.67hrs

B can complete the 1/4 part of the work in same time then B can complete hole work in 6.67*4=26.68 hrs

B can complete the 1/5 part of work in 26.67/5=5.336hrs

according to question C can complete 1/2part of work in same time then the whole work can complete in

2*5.336=10.672hrs

A real-life situation that can be modeled by a function is that Bob has 20 pens and buys extra 5 pens weekly.

It should be noted that a function simply means an expression that shows the relationship between the variables.

In this case, a real-life situation that can be modeled by a function is that Bob has 20 pens and buys extra 5 pens weekly.

The function will be:

= 20 + 5w

where w represents the number of weeks.

Learn more about functions on:

https://brainly.com/question/4025726

#SPJ1

Answer:

The rule a+b=b+a, for all real numbers a,b, is the commutative law for addition. The fact that we can have g∘h≠h∘g, for some functions g,h, says that composition of functions is not commutative. Composition of functions is not the same as multiplication of functions: f=h∘gmeansf(x)=h(g(x))j=h⋅gmeansj(x)=h(x)g(x).

Answer:

so the next 2 sequences would be 60 and 62

Step-by-step explanation:

The next two terms in the given arithmetic sequence are 60 and 62.

The arithmetic sequence is given as follows:

20, 32, 42, 50, 56, ?

To find the next two terms in the sequence, let's analyze the pattern:

The sequence increases by the following increments:

12, 10, 8, 6

We can observe that the increments are decreasing by 2 each time.

To find the next two terms, we can continue this pattern:

Increment: 4 (6 - 2)

Increment: 2 (4 - 2)

Adding the increments to the previous terms:

56 + 4 = 60

60 + 2 = 62

Therefore, the next two terms in the arithmetic sequence are 60 and 62.

Learn more about arithmetic sequence here:

brainly.com/question/21961097

#SPJ4

Answer:

£225

Step-by-step explanation:

[For percentage increase, add the percentage with 100, for percentage decreases substract the percentage from 100.]

100 + 25 = 125%

[tex]\frac{125}{100}[/tex] × 180 = £225