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18.11.2020

Hello, I am having trouble with this question, can you help me please?

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16.01.2024, solved by verified expert

Nitin Arora

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Answer:

165 degrees

Step-by-step explanation:

A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. The formula for finding the sum of the measure of the interior angles is (n - 2) * 180.

Therefore each angle = (n - 2) * 180 / n

Here n= 24

Therefore each angle = (24-2)*180/24 = 165

Thus, measure of each interior angle = 165 degrees

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Mathematics

Hello, I m having trouble with this question.

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P Answered by Specialist

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Hello, I'm having trouble with this question.

Mathematics

Hello everyone, I m just having trouble on a question for my Calculus work. Does anyone know where to start with this problem? Any help would be greatly appreciated!

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P Answered by Specialist

sin(8w)/1024 -sin(4w)/128 +3w/128

Step-by-step explanation:

No doubt there are a variety of formulas and identities that can be used. Absent knowledge of those, I found it convenient to rewrite the integrand using Euler's formula. It tells you ...

$\sin(x)=\dfrac{e^{ix}-e^{-ix}}{2i},\quad\cos(x)=\dfrac{e^{ix}+e^{-ix}}{2}$

After some only slightly messy algebra, we find ...

$\cos^4(w)\sin^4(w)=\dfrac{\cos(8w)-4\cos(4w)+3}{128}$

Then the integral becomes straightforward:

$\displaystyle \int{\cos^4(w)\sin^4(w)}\,dw=\int{\dfrac{\cos(8w)}{128}}\,dw-\int{\dfrac{\cos(4w)}{32}}\,dw+\dfrac{3}{128}\int{}\,dw\\\\=\boxed{\dfrac{\sin(8w)}{1024}-\dfrac{\sin(4w)}{128}+\dfrac{3w}{128}}$

Additional comment

The slightly messy algebra involves the identities ...

(a+b)(a-b) = a² -b²

(a -b)⁴ = a⁴ -4a³b +6a²b² -4ab³ +b⁴

Mathematics

Hello everyone, I m just having trouble on a question for my Calculus work. Does anyone know where to start with this problem? Any help would be greatly appreciated!

Step-by-step answer

P Answered by Specialist

sin(8w)/1024 -sin(4w)/128 +3w/128

Step-by-step explanation:

No doubt there are a variety of formulas and identities that can be used. Absent knowledge of those, I found it convenient to rewrite the integrand using Euler's formula. It tells you ...

$\sin(x)=\dfrac{e^{ix}-e^{-ix}}{2i},\quad\cos(x)=\dfrac{e^{ix}+e^{-ix}}{2}$

After some only slightly messy algebra, we find ...

$\cos^4(w)\sin^4(w)=\dfrac{\cos(8w)-4\cos(4w)+3}{128}$

Then the integral becomes straightforward:

Additional comment

The slightly messy algebra involves the identities ...

(a+b)(a-b) = a² -b²

(a -b)⁴ = a⁴ -4a³b +6a²b² -4ab³ +b⁴

Mathematics

Hello everyone, I m just having trouble on two questions for my Calculus work. I need to solve them using trig substitution to eliminate the root. Does anyone know where to start with this problem? Any help would be greatly appreciated!

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P Answered by Specialist

The main idea is to exploit the trigonometric identity,

sin²(θ) + cos²(θ) = 1

2. For an integral containing 16 - 81x², you might substitute x = 4/9 sin(θ) (with differential dx = 4/9 cos(θ) dθ, but without an actual integral to work with this isn't really important). Then

16 - 81x² = 16 - 81 (4/9 sin(θ))²

… = 16 - 81 (16/81 sin²(θ))

… = 16 - 16 sin²(θ)

… = 16 (1 - sin²(θ))

… = 16 cos²(θ)

so that in the root expression, we would end up with

$\left(16 - 81x^2\right)^{7/2} = \left(16\cos^2(\theta)\right)^{7/2} = 2^{14} |\cos(\theta)|^7$

since (ab)^c=a^cb^c for all real a, b, and c; $16^{7/2}=\left(2^4\right)^{7/2}=2^{14}$ ; and $\sqrt{x^2}=|x|$ for all real x.

The goal is to replace x with some multiple of sin(θ) that makes the coefficients factor out like they did here, which then lets you reduce 1 - sin²(θ) to cos²(θ).

And don't be discouraged by the absolute values; in the context of a definite integral, there are things that can be done to remove them or otherwise simplify absolute value expressions.

3. Substitute z = 1/√8 sin(θ) (so that dz = 1/√8 cos(θ) dθ). Then

1 - 8z² = 1 - 8 (1/√8 sin(θ))²

… = 1 - 8 (1/8 sin²(θ))

… = 1 - sin²(θ)

… = cos²(θ)

so that

$\left(1-8z^2\right)^{3/2} = \left(\cos^2(\theta)\right)^{3/2} = |\cos(\theta)|^3$

English

Hello everyone! So i have a story i need to write about an act of courage and I ve completed most of it already, but I m having a bit of trouble coming up with ideas for the next part. if you don t mind, would you kindly please read what I have so far and give me ideas on what could happen next? (The beginning was too short even though it was an act of courage but I have to make the next part an even BIGGER act of courage.) In a small town in Eastern Texas, Sarah was walking home from school when she saw a fight that was occurring at the back of

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P Answered by Specialist

you should write about her and the young boy she met earlier going out on an adventure to look for her mother

Explanation:

English

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P Answered by Master

you should write about her and the young boy she met earlier going out on an adventure to look for her mother

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Mathematics

hello! i ve been having a bit of trouble with my homework! i d appreciate it if one of you people could help me out! (this is a middle school mathematics homework question)

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P Answered by Master

The ( simplified ) expression is 7x - 8

Step-by-step explanation:

We are given the expression ( 2x + $\frac{ 1 }{ 2 }$ ) + ( 5x - 8 $\frac{ 1 }{ 2 }$ ),

$( 2x + \frac{ 1 }{ 2 } ) + ( 5x - 8 \frac{ 1 }{ 2 } ) - remove ( )\\,\\2x + \frac{ 1 }{ 2 } + 5x - 8 \frac{ 1 }{ 2 } - combine like terms,\\\\2x + 5x + \frac{ 1 }{ 2 } - 8 \frac{ 1 }{ 2 } - add / subtract,\\\\Simplified Expression ; 7x - 8$