Mathematics High School

Hello ! Here's a calculus question!

Find that value of

[tex]\\ \rm\Rrightarrow {\displaystyle{\int\limits_{\pi}^{2\pi}}}\dfrac{sin^6x+cos^6x}{sin^3xcos^3x}[/tex]


Note:-

Answer must include all steps properly .

Kindly don't waste time here if you don't know the answer .

All the best !​

Answers

Answer 1

Answer:

Undefined.

Formula's used:

[tex]\longrightarrow \bold{sec(x) = \dfrac{1}{cos(x)} }[/tex]

[tex]\longrightarrow \bold{cosec(x) = \dfrac{1}{sin(x)} }[/tex]

[tex]\longrightarrow \bold{cot(x) = \dfrac{1}{tan(x)} }[/tex]

[tex]\longrightarrow \bold{tan(x) = \dfrac{sinx}{cos(x)} }[/tex]

[tex]\longrightarrow \bold{sin^2x + cos^2 x = 1 }[/tex]

[tex]\longrightarrow \sf \bold{Sum \ Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx}[/tex]

[tex]\longrightarrow \bold{ \int \:{sec^2(ax+b) = \dfrac{1}{a}tan(ax+b)+c }}[/tex]

[tex]\longrightarrow \bold{\int \:\dfrac{1}{ax+b} =\dfrac{1}{a} ln|ax+b|+c}[/tex]

Explanation:

[tex]\sf \Longrightarrow \int _{\pi }^{2\pi }\:\dfrac{sin^6(x)+cos^6(x)}{sin^3(x) \ * \ cos^3\left(x)}[/tex]

[tex]\sf \Longrightarrow \sf \int _{\pi }^{2\pi }\:\dfrac{sin^6\left(x\right)}{sin^3\left(x\right)\cdot \:cos^3\left(x\right)} +\dfrac{cos^6\left(x\right)}{sin^3\left(x\right)\cdot \:cos^3\left(x\right)}[/tex]

[tex]\Longrightarrow \sf \int _{\pi }^{2\pi }\:\dfrac{sin^3\left(x\right)}{\:cos^3\left(x\right)} +\dfrac{cos^3\left(x\right)}{sin^3\left(x\right)}[/tex]

                                                               

[tex]\Longrightarrow \sf \int _{\pi }^{2\pi }\ tan^3(x)+ cot^3(x)[/tex]

[tex]\sf \Longrightarrow \sf \int _{\pi }^{2\pi } \tan ^3(x)dx+\int _{\pi }^{2\pi } \cot ^3 (x)dx[/tex]

[tex]\Longrightarrow \sf \bold{ [ }-\ln |\sec \left(x\right) |+\dfrac{\sec ^2(x)}{2}-\dfrac{\cot ^2 (x)}{2}-\ln |\sin(x)| \bold{ ] }^{2\pi }_\pi[/tex]

apply limits

[tex]\sf \Longrightarrow \sf -\ln \left|\sec \left(2\pi \right)\right|+\dfrac{\sec ^2\left(2\pi\right)}{2}-\dfrac{\cot ^2\left(2\pi\right)}{2}-\ln \left|\sin \left(2\pi\right)\right|-(-\ln \left|\sec \left(\pi \right)\right|+\dfrac{\sec ^2\left(\pi\right)}{2}-\dfrac{\cot ^2\left(\pi\right)}{2}-\ln \left|\sin \left(\pi\right)\right|)[/tex]

simplify using trigonometric basic functions

[tex]\Longrightarrow \sf -\ln \left|\dfrac{1}{\cos \left(2\pi \right)}\right|+\dfrac{\left(\dfrac{1}{\cos \left(2\pi \right)}\right)^2}{2}-\dfrac{\cot ^2\left(2\pi \right)}{2}-\ln \left|\sin \left(2\pi \right)\right|- ( -\ln \left|\dfrac{1}{\cos \left(\pi \right)}\right|+\dfrac{\left(\frac{1}{\cos \left(\pi \right)}\right)^2}{2}-\dfrac{\cot ^2\left(\pi \right)}{2}-\ln \left|\sin \left(\pi \right)\right|)[/tex]

The value of cot(2π) is not defined. [ cot(2π) = ∞ ]

⇒  Undefined

Answer 2

Answer:

[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \boxed{\text{un} \text{de} \text{f}}[/tex]

General Formulas and Concepts:
Calculus

Differentiation

DerivativesDerivative Notation

Integration

Integrals

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Integration Methods: U-Substitution + U-Solve

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx[/tex]

Step 2: Integrate Pt. 1

[Integrand] Rewrite:
[tex]\displaystyle \frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x} = \frac{\sin^6 x}{\sin^3 x \cos^3 x} + \frac{\cos^6 x}{\sin^3 x \cos^3 x}[/tex][Integrand] Simplify:
[tex]\displaystyle \frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x} = \tan^3 x + \cot^3 x[/tex][Integrand] Rewrite:
[tex]\displaystyle \frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x} = \tan x (\sec^2 x - 1) + \cot x (\csc^2 x - 1)[/tex]


Step 3: Integrate Pt. 2

[Integral] Rewrite:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \int\limits^{2 \pi}_{\pi} {\tan x (\sec^2 x - 1) + \cot x (\csc^2 x - 1)} \, dx[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \int\limits^{2 \pi}_{\pi} {\tan x (\sec^2 x - 1)} \, dx + \int\limits^{2 \pi}_{\pi} {\cot x (\csc^2 x - 1)} \, dx[/tex]

Step 4: Integrate Pt. 3

Identify variables for u-solve.

1st Integral

Set u:
[tex]\displaystyle u = \sec x[/tex][u] Apply Trigonometric Differentiation:
[tex]\displaystyle du = \sec x \tan x \, dx[/tex][du] Rewrite:
[tex]\displaystyle dx = \frac{1}{\sec x \tan x} \, du[/tex]

2nd Integral

Set v:
[tex]\displaystyle v = \csc x[/tex][v] Apply Trigonometric Differentiation:
[tex]\displaystyle dv = - \cot x \csc x \, dx[/tex][dv] Rewrite:
[tex]\displaystyle dx = \frac{-1}{\cot x \csc x} \, dv[/tex]

Step 5: Integrate Pt. 4

[Integrals] Apply Integration Method [U-Solve]:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \int\limits^{x = 2 \pi}_{x = \pi} {\frac{\tan x (\sec^2 x - 1)}{\sec x \tan x}} \, du + \int\limits^{x = 2 \pi}_{x = \pi} {\frac{- \cot x (\csc^2 x - 1)}{\cot x \csc x}} \, dv[/tex][Integrals] Simplify:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \int\limits^{x = 2 \pi}_{x = \pi} {\frac{u^2 - 1}{u}} \, du - \int\limits^{x = 2 \pi}_{x = \pi} {\frac{v^2 - 1}{v}} \, dv[/tex][Integrals] Apply Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \frac{u^2}{2} \bigg| \limits^{x = 2 \pi}_{x = \pi} - \int\limits^{x = 2 \pi}_{x = \pi} {\frac{1}{u}} \, du - \Bigg( \frac{v^2}{2} \bigg| \limits^{x = 2 \pi}_{x = \pi} - \int\limits^{x = 2 \pi}_{x = \pi} {\frac{1}{v}} \, dv \Bigg)[/tex][Integrals] Apply Logarithmic Integration:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \frac{u^2}{2} \bigg| \limits^{x = 2 \pi}_{x = \pi} - \ln | u | \bigg| \limits^{x = 2 \pi}_{x = \pi} - \Bigg( \frac{v^2}{2} \bigg| \limits^{x = 2 \pi}_{x = \pi} - \ln | v | \bigg| \limits^{x = 2 \pi}_{x = \pi} \Bigg)[/tex]Back-Substitute variables u and v:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \frac{\sec^2 x}{2} \bigg| \limits^{2 \pi}_{\pi} - \ln | \sec x | \bigg| \limits^{2 \pi}_{\pi} - \Bigg( \frac{\csc^2 x}{2} \bigg| \limits^{2 \pi}_{\pi} - \ln | \csc x | \bigg| \limits^{2 \pi}_{\pi} \Bigg)[/tex]Simplify:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \bigg( \ln | \csc x | - \ln | \sec x | + \frac{\sec^2 x - \csc^2 x}{2} \bigg) \bigg| \limits^{2 \pi}_{\pi}[/tex]Apply Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^{2 \pi}_{\pi} {\frac{\sin^6 x + \cos^6 x}{\sin^3 x \cos^3 x}} \, dx = \boxed{\text{un} \text{de} \text{f}}[/tex]

∴ we have found the value of the given integral.

---

Learn more about integration: https://brainly.com/question/14413972

Learn more about calculus: https://brainly.com/question/20197752

---

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Related Questions

PLEASE SOMEONE HELP!!

Answers

Take the lowest point (0,-3) and move it left 3 and up 6 to get it to (-3,3) and just sketch an approximate shaped u to match the original graph. It doesn’t have to be accurate because the question says so.

If x = 5, then 3x + 4x - 15 equals:
A. 20
B. 15.
c. 40
D. 50
E 10

Answers

Answer:

20

Step-by-step explanation:

Given:

x = 5

Substitute the value of x into the expression:

⇒ 3x + 4x - 15

⇒ 3(5) + 4(5) - 15

Simplify the expression:

⇒ 15 + 20 - 15

⇒ 15 + 5

⇒ 20 (Option A)

Answer:

A. 20

given function:

3(x) + 4(x) - 15

put x = 5

3(5) + 4(5) - 15

simplify

15 + 20 - 15

answer

20

100 POINTS What is the IQR for the data set?

{31, 76, 34, 35, 39, 49, 55}

Drag and drop the correct answer into the box.

IQR

Answers

set : {31, 76, 34, 35, 39, 49, 55}

arrange ascending to descending:

{ 31, 34, 35, 39, 49, 55, 76 }

given,

first quartile: 34third quartile: 55

I.Q.R:

interquartile range : third quartile - first quartile 55 - 3421

Answer:

21

Step-by-step explanation:

Place the numbers in order from smallest to largest:

31, 34, 35, 39, 49, 55, 76

The median (Q2) is the middle value = 39

Q1 is the middle value of the numbers smaller than the median = 34

Q3 is the middle value of the numbers larger than the median = 55

IQR = Q3 - Q1

      = 55 - 34

      = 21

I need help please with this 1 problem

Answers

Answer:

See below, please

Step-by-step explanation:

We know

[tex]f(x) = {x}^{2} + 3x - 7[/tex]

[tex]g(x) = 3x + 5[/tex]

[tex]h(x) = 2 {x}^{2} - 4[/tex]

Hence

[tex]f(g(x))[/tex]

[tex] = {(3x + 5)}^{2} + 3 \times (3x + 5) - 7[/tex]

[tex] = (9 {x}^{2} + 30x + 25) + (9x + 15) - 7[/tex]

[tex] = 9 {x}^{2} + 39x + 33[/tex]

[tex]h(g(x))[/tex]

[tex] = 2 \times {(3x + 5)}^{2} - 4[/tex]

[tex]2 \times (9 {x}^{2} + 30x + 25) - 4[/tex]

[tex] = 18 {x}^{2} + 60x + 50 - 4[/tex]

[tex] = 18 {x}^{2} + 60x + 46[/tex]

[tex](h - f)(x)[/tex]

[tex] = h(x) - f(x)[/tex]

[tex] = (2 {x}^{2} - 4) - ( {x}^{2} + 3x - 7)[/tex]

[tex] = {x}^{2} - 3x + 3[/tex]

[tex](f + g)(x)[/tex]

[tex] = f(x) + g(x)[/tex]

[tex] = ( {x}^{2} + 3x - 7) + (3x + 5)[/tex]

[tex] = {x}^{2} + 6x - 2[/tex]

Find the surface area of this figure.

Answers

Answer:

57 inches^2 is the answer buddy

Step-by-step explanation:

BxH divided by 2

how to copy and paste

Answers

Answer:

control + C then Control + V

Step-by-step explanation:

Answer:

If you have a PC, press Windows, Print Screen.

Step-by-step explanation:

Hope this helps..


I need helpppppppppppp

Answers

The answer to question 3 is D. 15(4a+3). And the answer to question 4 is A. 90. Have a great day

Help my sister she doesn’t understand this and I got to go

Answers

Answer:

1/2

1/4

2/4

1/4

2/4

1/4

Question is in the picture below, please help.

Answers

Answer:

A)6 cm B)32 inch

Step-by-step explanation:

A)1 cm:8 inch

(1×6)cm:(8×6)inch

Thus, if the height is 48 inch, the scale in cm is 6 cm

B)Normal linear form

The length=4cm

(1×4) cm:(8×4) inch

Thus, if the scale length is 4 cm, the real painting length will be 32 inch

The base of a triangular door wedge has an area of 55 square centimeters. The height of the wedge is 5 centimeters. Find the volume of the door wedge.

Answers

Answer:

the answer ios yes

Step-by-step explanation:

55-243 equals the sum of 11

Which of the following lines is perpendicular to the line with this equation ?
y =4/5X – 12

a. y= -4/5x +9
b. y=5/4x +4
c. y= -5/4x -15
d.y= 4/5x -5

Answers

Answer:

soln,

a

y=5/4×-15

Answer:

C: y = -5/4x - 15

Step-by-step explanation:

A perpendicular line is always the negative reciprocal of the slope. In this case, the slope is 4/5. Therefore, the negative reciprocal is -5/4. Only look at the numbers connected to X for the slope, do not look at the constant.

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answers

Answer:

76 in²

Step-by-step explanation:

Area of the figure

Area (top rectangle) + 2 x Area (bottom rectangle)12 x (7 - 2) + 2 x 2 x 412 x 5 + 1660 + 1676 in²

Given f(x)= 2x^3+kx-1, and x+1 is a factor of f(x), then what is the value of k?

Answers

Answer:

put x=-1, and the rest will be easy

If x + 1 divides f(x), this means x = -1 is a root of f(x), i.e. f(-1) = 0. Plugging in x = -1 gives

f(-1) = 2 (-1)³ + k (-1) - 1 = -3 - k = 0

Solve for k; you end up with k = -3.

To solve the equation x ^2 - 2x = 3 by the technique of completing the square, you would add 4 to each side of the equation as one of the steps to reaching the solution.

Answers

Answer:

x = -1

x = 3

Step-by-step explanation:

[tex]\sf x^2 - 2x = 3[/tex]

Add 1 to both sides:

[tex]\sf \implies x^2 - 2x+1 = 3+1[/tex]

Factor the left side:

[tex]\sf \implies (x-1)^2 = 4[/tex]

Square root both sides:

[tex]\sf \implies x-1 = \pm2[/tex]

Therefore:

[tex]\sf \implies x-1=-2 \implies x=-1[/tex]

[tex]\sf \implies x-1=2 \implies x=3[/tex]

Find the number that makes the ratio equivalent to 36:81.
4:

Answers

Answer:

9

Step-by-step explanation:

9*4 = 36

9*9 = 81

divide both by 9 and you get 4:9

The units are equal to 0.2 mile

Valeria will Need to travel from information to Security frequently.

•She can ride a golf cart along the solid lines from one to other at 12 miles per hour.

•She can walk along the dashed line at 4 miles per hour.

She wants to use the faster method. How should she travel

Answers

Answer:

Take the golf cart for the fastest time, and bragging rights.

Step-by-step explanation:

See attachment

The golf cart will make the trip in 0.383 hours, while walking would require 0.85 hours.

What was the average temperature change per hour?

Answers

Where is the picture mf?

Answer: So, the average temperature dropping is 2 degrees per hour.

Step-by-step explanation:

Select the correct answer.
Sophia has unsharpened pencils that are 20 centimeters long. What is the approximate surface area of a pencil?

Answers

The surface area of the pencil is the amount of space it covers

The surface area of the pencil is 61 square centimeters

How to determine the surface area?

The given parameters are:

H = 20 cm

L = 0.5 cm

The surface area (SA) is then calculated as:

SA = 6LH + 3[tex]\sqrt 3[/tex]L^2

This gives

SA = 6 * 0.5 * 20 + 3[tex]\sqrt 3[/tex] * 0.5^2

Evaluate the sum

SA = 61

Hence, the surface area of the pencil is 61 square centimeters

Read more about surface area at:

https://brainly.com/question/6613758

Evaluate the following expression. Round your answer to two decimal places.
logz 11

2.18?
2.40?
0.46?
0.84?

Answers

The correct answer would be- A: 2.18

Select all the systems of equations that have exactly one solution.
Option 1. y = 4x - 1 and y = -4x + 7 Option 2. y = 3x + 1 and y = 2x + 1

Option 3. y = x + 2 and y = x + 7 Option 4. 2x + 2y = 20 and 3x + 3y = 30

Option 5. x + y = 40 and x + y = 90

Answers

Answer:

Option one and option 2

Step-by-step explanation:

Only ones that have 1 solution, option 3 and 5 have no solution, option 4 has infinetly many.

i need help with this i will give 100 pt

Answers

Answer:

1. Where you shop at

2. The tax in the state you live in.

Hope this helps!

Answer:

1. Where you shop at2. The tax in the state you live in.

Step-by-step explanation:

Solve for w.
W/4 = 4 What does W equal?

Answers

Answer:

16

Step-by-step explanation:

sooo all you have to do is make W alone. to do that you multiply 4 to both sides of the equation

W = 4(4)

w = 16

What is the answer to this question?

Answers

Answer:

A = 16.5 cm²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between bases and b₁, b₂ the bases

here h = 3, b₁ = 7 , b₂ = 4 , then

A = [tex]\frac{1}{2}[/tex] × 3 × (7 + 4) = 1.5 × 11 = 16.5 cm²

What is the perimeter of 4ft and 8ft

Answers

Answer:

24

Step-by-step explanation:

4+4+8+8

8 + `16 = 24

How many solutions are there? 100pts

Answers

Answer:

infinite many solutions

Step-by-step explanation:

5(2(b)+1) = 10(b) + 510(b) + 5 = 10(b) + 5

As L.H.S = R.H.S, there are infinite many solutions

[tex]\\ \rm\Rrightarrow 5(2b+1)=10b+5[/tex]

[tex]\\ \rm\Rrightarrow 10b+5=10b+5[/tex]

[tex]\\ \rm\Rrightarrow 0=0[/tex]

Infinite solutions

express the following rational algebraic expression to its simple form.show your solution​
5. ײ+5×-14/ײ-4​

Answers

Answer

[tex] \frac{ \times -+7}{×+2} [/tex]

Which angles are not supplementary

Answers

Answer: Choice c)

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

Explanation:

Choice a) can be ruled out because angles A and D are supplementary. Supplementary angles add to 180 degrees by definition. They form a straight line or straight angle.

Choice b) and choice d) are eliminated for similar reasoning as choice a).

Choice c) is the only thing left. It turns out that angles B and D are not supplementary, but rather they are vertical angles. They are opposite one another in this X shape. Vertical angles are always congruent.

Note: Angles B and D are supplementary if and only if the angles are 90 degrees each.

express 1.284 in form of p/q

Answers

Step-by-step explanation:

1.284=1284/1000

divide both by 4

=321/250

A sollid piece of iron in the form of a cuboid of dimensions 49cm × 33 cm× 24 cm , is moulded to form a solid sphere. find the radius of the sphere ​

Answers

Answer:

Radius of sphere is 21 cm

Step-by-step explanation:

Given:

A sollid piece of iron in the form of a cuboid of dimensions 49cm × 33 cm× 24 cm , is moulded to form a solid sphere.

To Find:

Radius of the sphere

Solution:

Volume of sphere = Volume of cubiod

↠ 4/3 πr³ = LBH

↠ 4/3 × 22/7 × r³ = 49 × 33 × 24

↠ 4/3 × 22/7 × r³ = 38808

↠ 4 × 22/7 × r³ = 38808/3

↠ r³ = 38808 × 3 × 7/4 × 22

↠ r³ = 441 × 21

↠ r³ = 9261

↠ r = 21 cm

Hence,

Radius of sphere is 21 cm

Answer:

21.00 cm to the nearest hundredth.

Step-by-step explanation:

The volume of the sphere will  be equal to the volume of the cuboid.

So 4/3 π r^3 =  49*33*24     where r = radius of the sphere.

r^3 = (49*33*24 ) / 4/3 π

r^3 = 38808 / 4.18879

      =  9264.728

r = ∛9264.728

  = 21.0028  cm.

There were 15 birds in the park. Some (n) of them flew away. Which expression could be
used to figure out how many birds are still remaining in the park?

Answers

Answer:

15-n

Step-by-step explanation:

subtract the number that flew away from the total number of birds that were there

Other Questions
Help me please !!!!!! There are 357 basketball fans who plan to go to a game. How many buses will be needed, given that each bus can hold 45 fans? Regarding intimate relationships, _______ tend to emphasize personal and relationship privacy issues while _______ tend to emphasize family and ingroup network connection issues. Use the bar graph below to answer the following question.Which girl is the shortest? What is BC?Enter your answer in the box. l i k e i s a i d 8th grade math I need help on this question I dont get what its asking what so ever If IN = 2x + 10 and AT = 26, find x. Group of answer choices 10 8 12 6 How did the First Industrial Revolution change labor in America?a. It caused the need for more raw materials and slave labor.O b. It enabled labor to go from hands-on to machine-powered.O c. It caused laborers to form unions.8/12 AABC is equilateral.AB = 11x and AC = 3x + 64.=PLEASE HELP Differentiate betweenOperating system andlanguage translator Can somebody help me with this? PROJECT: HISTORICAL EVENTS AND POPULATION GROWTHOBJECTIVESAnalyze the impact of population growth in India.Understand the meaning, implication, and impact of historical events.Use appropriate formatting, graphics, and media to introduce and organize a topic.Use precise language and vocabulary to convey a style appropriate to the discipline.pls help its due tonight This is used so that important parts of the song stay with the listener.variationthemebridgerepetition "The United States is one of only two countries that allow direct consumer advertisements for prescription medications. These advertisements lie to patients."The writer wants to revise the sentence below to qualify the claim and express it in less absolute terms.These advertisements lie to patients.Which of the following choices best revises the sentence to meet the goal?A. These advertisements misinform patients, intentionally or not.B. These advertisements are examples of misinformation and should be banned. C. Each of these advertisements represents a lie to patients.D. All of these advertisements provide misinformation to patients. How can impeachment preserve democracy? Long-billed curlews eat many different kinds of insects, including grasshoppers, as a source of food. It has been shown that pesticide use kills many of these insects. How would you expect an increase in pesticide use to affect to the population of long-billed curlews in the same area Lies den Text und setze die fehlenden Wrter richtig ein. Consider the following reaction: 2 Bi(s) + 3 Cl2(g) 2 BiCl3(s)How many grams of chlorine gas are required to produce 3.32 grams of bismuth chloride isproduced? Use correct significant digits and units, for example 1.234 g. Solve, using the correct order ofoperations, when x = 8 and y = 6.2x - (4 + y)