Integrate :-
[tex]:\implies \: \boxed{ \displaystyle \int \sf{ \frac{1}{sin {}^{2} \bigg(\dfrac{x - 2}{3} \bigg) } \: dx }} \: \red\bigstar[/tex]
​

Recall that

[tex]\dfrac{d}{dx}\left[\cot(x)\right] = -\csc^2(x)[/tex]

so that

[tex]\displaystyle \int \frac{dx}{\sin^2\left(\frac{x-2}3\right)} = \int \csc^2\left(\frac{x-2}3\right) \, dx = \boxed{-3 \cot\left(\frac{x-2}3\right) + C}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Your \ exercise \ is \to\int\limits \frac{1}{sin^2\left(\dfrac{x-2}{3}\right) }dx } \end{gathered}$}[/tex]

             [tex]\boldsymbol{Replaces \ u=\dfrac{x-2}{3} \longmapsto \dfrac{du}{dx}=\dfrac{1}{3} \longmapsto \ dx=3 \ du }[/tex]

                                               [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=\int\limits \frac{3}{Sin^2(u) }du } \end{gathered}$}[/tex]

                                                    [tex]\boldsymbol{\sf{Simplify }}[/tex]

                                              [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=3\int\limits csc^2(u)du } \end{gathered}$}[/tex]

                                                    [tex]\boldsymbol{\sf{Solving \ now }}[/tex]

                                                    [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\int\limits csc^2(u)du } \end{gathered}$}[/tex]

                                            [tex]\boldsymbol{\sf{This\:is\:a\:standard\:integral. }}[/tex]

                                                     [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=-cot(u)} \end{gathered}$}[/tex]

                                       [tex]\boldsymbol{\sf{We\:replace\:the\:integrals\:already\:solved. }}[/tex]

                                                   [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=\int\limits \frac{3}{Sin^2(u) }du } \end{gathered}$}[/tex]

                                                      [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=-cot(u)} \end{gathered}$}[/tex]

                                      [tex]\boldsymbol{The\:substitution\:is\:undone\: u=\dfrac{x-2}{3} ;}[/tex]

                                                      [tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{=-3cot\left(\frac{x-2}{3}\right) } \end{gathered}$}[/tex]

       [tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf Answer \longmapsto \bf{\int\limits \dfrac{1}{sin^2\left(\dfrac{x-2}{3}\right) }dx }=\boldsymbol{ -3cot\left(\frac{x-2}{3}\right)+C } \end{gathered}$}}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \underline{\bf{\green{I\:hope \ it \ helps \ you..... Regards }}} \end{gathered}$}[/tex]

The times taken to assemble a clock at a factory are approximately normally distributed with a given mean Mu = 3 hr and standard deviation Sigma = 0.5 hr. What percentage of the times are between 2 hr and 4 hr?
34%
47.5%
68%
95%

At Mr. Donald's farm, there are 35 chickens and 50 cows. What is the ratio of the number of cows to the number of chickens at Mr. Donald's farm?

Help will give thanks to the first to answer

Anny is not a very good driver, so she drives really slow. She normally drives at a speed of 50 miles per hour if it is not raining, and 30 miles per hour if it is raining. Today she drove in the sun in the morning and in the rain in the afternoon, for a total of 120 miles in 180 minutes. How many minutes did she drive in the rain?

The low temperature was 35°F. This was 13°F lower than the dayt high temperature. Write an equation to determine whether the high temperature was 48°F or 42°F.​

Find the value of x.

whats the difference between-2/3 and-1/4=​

A number cube has side lenghts of 1 1/4 inches. What is the volume, in cubic inches, of the number cube?

A company makes electronic components for TV's. 0% pass final inspection. 110 components are inspected in one day. What is the expected value of the number that fails inspection in one day?



a.
0

b.
110

c.
100%

d.
11


Please can you help me please don’t send for me link !

Round to the nearest ten 3465 695​

Convert (87.1352) 10 to base 8
​

Mr. Rodriguez is assembling supply kits for his students. He has 24 pencils and 32 erasers. All the kits must have the same number of each item, and all items must be used.
Check your work on Zearn.
1. What is the largest number of kits Mr. Rodriguez can make?
The largest number of kits Mr. Rodriguez can make is
kits.

2. How many pencils and erasers will be in each kit?
pencils and
erasers will be in each kit.

Solve for x. Round to the nearest tenth, if necessary.
U
67
T
x
142°
y

Henry stores the arrowheads he has found in a box the shape of a rectangular prism. The box is 14 inches long, 12 inches wide, and 2 inches high. He plans to paint the exterior of the box. How many square inches does he have to paint?



Pls help it would be very helpful

An above-ground garden is in the shape of a rectangular prism measuring 6 feet by 13 feet by 4 feet. The soil costs $1.70 per cubic foot. How much will it cost to fill the above -ground garden fully?

Which of the following logarithmic equations is equivalent to the exponential
equation below?
e^x = 15.29

if there are nine students in the class and the three students decided to work together what portion of the wall would they use all together​

can anyone help me find x, please?​

Sarah is demonstraing the idea that polynomials are closed under addition. Her work and explanation are shown.
Select an equation and phrases to complete the statement.
Part A:
Add 30° +63 7 to
Equation A 223 - (2x)2 + 42-1
Equation B (2x)? +4. 4. - 9
Equation C (-8x)2 – (3x)3 +7
Part B:
This is closed because
of the sum are
and the sum is a polynomial.

a class has five students what is the probability that four of the students were born on a weekday

The seasonal demand for a particular product is given below: Period 1 2 3 4 5 6 Demand 300 450 100 450 450 100 The fixed parameters are: Fixed Cost $8 Unit Production Cost $1 Holding Cost $ 1.3 Calculate total ordering cost using following three methods: i) Lot-for-Lot ii) Wagner-Whitin algorithm iii) Fixed order quantity​

If a phone company charges $0.45 for the first minute and $0.35 for each additional minute for a long distance call , how much will a 20 minute long distance call cost ?

The volume of a rectangular prism is 200 cubic inches. If the area of the base is 20 square inches, what is the height of the prism?

Is {(1,3),(2,4),(3,7),(4,13 )} a function?

Which of the following types of reproduction involve the cell cycle

Budding

Binary fission

Spore Formation

Venessa has a piggy bank that contains a collection of nickels, pennies, dimes and quarters. She randomly draws a coin out of the
Egy bank, records the result, and then replaces the coin. The results of her draws are shown below.

Based on the results above, predict the number of times a dime would be drawn if Venessa draws a coin 336 times.

A. 58

B. 36


C. 64

D. 38

Based only on the information given in the diagram, it is guaranteed that
ARST - AUVW
5
067
R
Л
w
A. True
B. False

What is the probability of getting a head with the flip of a coin?What is the probability of getting a head with the flip of a coin?

Carolyn lives near two parks. Centennial Park is 2 km away and Canatara Park is 2,548 meters away. Canatara Park is located closer to Carolyn. Is this true or false?

True
False

Mary knits scarves and sweaters to sell. Scarves take 2 hours to knit and sweaters
take 10 hours. Mary would like to spend no more than 40 hours per week knitting
and knit at least 5 items per week.


What are two possible solutions she could knit based on this word problem?

(Select the 2 correct options.)

A. 3 scarves and 4 sweaters

B. 6 scarves and 3 sweaters

C. 10 scarves and 1 sweater

D. 2 scarves and 2 sweaters