Find the integration of (1-cos2x)/(1+cos2x)
Given:
The expression is:
[tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex]
To find:
The integration of the given expression.
Solution:
We need to find the integration of [tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex].
Let us consider,
[tex]I=\int \dfrac{1-\cos 2x}{1+\cos 2x}dx[/tex]
[tex]I=\int \dfrac{2\sin^2x}{2\cos^2x}dx[/tex] [tex][\because 1+\cos 2x=2\cos^2x,1-\cos 2x=2\sin^2x][/tex]
[tex]I=\int \dfrac{\sin^2x}{\cos^2x}dx[/tex]
[tex]I=\int \tan^2xdx[/tex] [tex]\left[\because \tan \theta =\dfrac{\sin \theta}{\cos \theta}\right][/tex]
It can be written as:
[tex]I=\int (\sec^2x-1)dx[/tex] [tex][\because 1+\tan^2 \theta =\sec^2 \theta][/tex]
[tex]I=\int \sec^2xdx-\int 1dx[/tex]
[tex]I=\tan x-x+C[/tex]
Therefore, the integration of [tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex] is [tex]I=\tan x-x+C[/tex].
If p is directly proportional to q, and p = 40 when q = 15, find q when p = 64
tessa burned 357 calories in 42 minutes on the elliptical. ashley only spent 0 minutes on the elliptical and burned 267 calories. who burned calories at a faster rate
Answer:
ashley
Step-by-step explanation:
because she didnt spend any time
help with this question
9514 1404 393
Answer:
A = 49π/36 or 59π/36
Step-by-step explanation:
The given angle is coterminal with the same angle modulo 2π.
(563/36)π = 14π +(59/36)π
so the coterminal angle is 59π/36 ≈ 1.6389π, a 4th-quadrant angle. The 3rd-quadrant angle with the same sine value is found by subtracting this angle from 3π:
A = 3π -(59π/36) = 49π/36
The two values of A that satisfy the equation are ...
A = 59π/36A = 49π/36_____
In degrees, the two angles are 245° and 295°.
What is the equation of the curve that best fits the data? Round to the nearest hundredths, when appropriate. picture*
Answer:
.....
Step-by-step explanation:
Up and down
An expression is shown. Which one of the expressions below is equivalent?
Answer:
C
Step-by-step explanation:
An engine runs for 3.2 hours. How many seconds did it run?
Answer:
11520 seconds
Step-by-step explanation:
3.2 x 60= 192 minutes
192 x 60= 11520 seconds
If f(x) = 3x + 2 and g(x) = 2x - 2, what is (f - g)(x)?
A. x + 4
B. X-2
O c.
Х
OD.
5x-2
O E.
X-4
Answer:
option A
Step-by-step explanation:
f(x) = 3x + 2
g(x) = 2x - 2
(f - g)(x) = f(x) - g(x)
= (3x + 2) - (2x - 2)
=3x + 2 - 2x + 2
= x + 4
The value of function (f - g)(x) is,
⇒ (f - g)(x) = x + 4
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Function are,
f(x) = 3x + 2 and g(x) = 2x - 2
Hence, The value of function (f - g)(x) is,
⇒ (f - g)(x) = (3x + 2) - (2x - 2)
⇒ (f - g)(x) = 3x + 2 - 2x + 2
⇒ (f - g)(x) = x + 4
Thus, The value of function (f - g)(x) is,
⇒ (f - g)(x) = x + 4
Learn more about the function visit:
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the equation s=2√5x can be used to estimate the speed ,s,of a car in milles per hour, given the length in feet ,x, of the tire marks it leaves on the ground .A card travelling 90 miles per hour came to a sudden stop according to the equation ,how long would the tire marks be for this car A 355 feet B 380 feet C 405 feet D 430 feet
Answer:
405 feet
Step-by-step explanation:
s = 2 * (√5) * 90
s = 2 * 201.246117975
s = 402.49223595
Closest estimate
405 feet
Answer:
Since The equation that depicts the motion of the Car is given.
The speed in terms of the tire marks...
s= 2√5x
where x is the tire marks(in feet.)
s is the speed(miles per hr)
We can't use the speed in Miles per hr when the tire mark is feet.
1mile = 5280ft
90miles x 5280ft/1mile = 475,200ft/hr
Making x the subject
x= s/2√5
x= 475/200/(2√5 )
=106,257ft
I still can't see what I'm missing or You sure you didn't forget to add something else to the question?
Identify the unlike terms in the expression:
3a + 11b + 30 + 4a + 3b
Answer: 7a+14b+30
How to: Combine like terms
Have a great day and stay safe ! sorry if im wrong
Juan drank 3 quarts of water. Alfred drank 8 quarts. How many cups of water did they drink altogether?(no links will get brainliest)
Answer: 44 Us Cups
Step-by-step explanation:
Complete the comparison 5+4. A.9+1. B.10+0.C.5-4.D.15-4
Answer:
A.5+4<9+1
B. 5+4<10+0
C. 5+4>5-4
D. 5+4=15-4
Step-by-step explanation:
A. 9<10
B. 9<10
C. 9>1
D9=9
Answer:
A=10>5+4
B=10>5+4
C=1<5+4
D=11>5+4
Step-by-step explanation:
Helaine graphed the equation 12x−4y=3. What was the slope of Helaine’s line?
Answer:
The slope is 3
Step-by-step explanation:
12x−4y=3
Solve for y
Subtract 12x from each side
-12x +12x−4y=-12x+3
-4y = 12x+3
Divide each side by -4
-4y/-4 = -12x / -4 +3/-4
y = 3x -3/4
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 3
Answer:
The slope is 3
Step-by-step explanation:
12x−4y=3
Solve for y
Subtract 12x from each side
-12x +12x−4y=-12x+3
-4y = 12x+3
Divide each side by -4
-4y/-4 = -12x / -4 +3/-4
y = 3x -3/4
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 3
.....................
Answer:
Final volume, V2 = 8.57 liters
Step-by-step explanation:
Given the following data;
Initial volume, V1 = 7.7 liters
Initial pressure, P1 = 6.9 atm
Final pressure, P2 = 6.2 atm
To find the new volume V2, we would use Boyles' law.
Boyles states that when the temperature of an ideal gas is kept constant, the pressure of the gas is inversely proportional to the volume occupied by the gas.
Mathematically, Boyles law is given by;
[tex] PV = K[/tex]
[tex] P_{1}V_{1} = P_{2}V_{2} [/tex]
Substituting into the equation, we have;
[tex] 6.9 * 7.7 = 6.2*V_{2} [/tex]
[tex] 53.13 = 6.2V_{2} [/tex]
[tex] V_{2} = \frac {53.13}{6.2}[/tex]
[tex] V_{2} = 8.57 [/tex]
Final volume, V2 = 8.57 liters
Therefore, the new volume is 8.57 liters.
Answer:
just greeting so that the other one can get a brainliest (would be kind if the favor would be returned :D )
150 round 2 decimal places
Answer:
[tex]150 = 150.00[/tex]
The annual per capita consumption of bottled water was 32.6 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 32.6 and a standard deviation of 12 gallons. The probability that someone consumed more than 33 gallons of bottled water is?
Answer:
0.4867
Step-by-step explanation:
Given an approximately normal distribution:
Z = (x - mean) / standard deviation
Mean = 32.6 ; Standard deviation = 12
For :
P(x > 33)
Z = (33 - 32.6) / 12
Z = 0.4 / 12
Z = 0.0333
Hence, using the Z distribution table :
P(Z > 0.0333) = 1 - P(Z < 0.333)
P(Z > 0.0333) = 1 - 0.51328
P(Z > 0.0333) = 0.48672
Plz help me well mark brainliest if correct.......????
Answer:
D
Step-by-step explanation:
shows change over time
(Click on the picture to see question) please help me!
Hi there! Using one of the logarithmic property below:
[tex] \large \boxed{ log_{a}(b) = n \longrightarrow {a}^{n} = b}[/tex]
From the equation:
[tex] \large{ log_{2}(y) = x + 7}[/tex]
Therefore,
[tex] \large{ {2}^{x + 7} = y} \\ \large{y = {2}^{x + 7} }[/tex]
Answer
y = 2^(x+7) the second choice.ABCD angles add up to 300⁰, what is the angle of B?
Answer:
I don't know im sorry I wish I could help
Answer:
75
Step-by-step explanation:
You know hat there is 4 angles. You want to divide 300 by 4 since that's the tal out of all 4 ofangles.When u divide, you 75.
This is what I would
Help pls this is 5th grade math
Answer:
2 is scalene
3 is right
4 is right
5 is equalatirel
6 is scalene
7 is isocoles
8 is equalatirel
9 is right
Step-by-step explanation:
Answer:
2: scalene
3: right
4: right
5: equilateral
6: scalene
7: isosceles
8: equilateral
9: right
Step-by-step explanation:
2: A scalene triangle has no congruent sides
3: A right triangle has a 90 degree angle
4: A right triangle has a 90 degree angle
5: An equilateral triangle has 3 congruent sides
6: A scalene triangle has no congruent sides
7: An isosceles triangle has 2 congruent sides
8: An equilateral triangle has 3 congruent sides
9: A right triangle has a 90 degree angle
29x-7y=-17 solve for x
Answer:
[tex]x= -\frac{17}{29} +\frac{7y}{29}[/tex]
Step-by-step explanation:
[tex]29x-7y=-17[/tex]
[tex]x= -7y/29 + -17/29[/tex] Divide every number by x except
Evaluate the following
6!
Answer:
Mind showing a picture?
Thank you!
What is the value of -(-9)?
Explain your reasoning.
Answer:
-(-9) is 9
Step-by-step explanation:
-(-9)
(when there are two negatives multiplyed with eachother, the product will be postive)
+ 9
+ 9 = 9
- ( - 9 ) =
( - 1 ) × ( - 1 × 9 ) =
( - 1 ) × ( - 1 ) × ( 9 ) =
( + 1 ) × 9 =
1 × 9 =
9
Part A: Students from 4 towns attend a conference. Each town is assigned a number from 1 to 4. Drag yes or no next to the first sentence.
Yes or No
A number is drawn and replaced 6 times. Is this a fair way to pick 6 members to give each town representation? __________
Part B: What is the probability that Town 1 will have at least 1 representative after 6 number draws, to the nearest percent?
probability = __________ %
Answer:
Part A - No
Part B - 100 %
Step-by-step explanation:
Part A.
This is because, a fair chance requires that each member has the same probability of being picked.
Since there are 4 towns, a fair chance would be 1/4.That is, 1 out of every town.
Part B
The probability of at least 1 representative after 6 number draws is P(at least 1) = 1 - P(none from Town 1)
P(none from town 1) = 0
P(at least 1) = 1 - P(none from Town 1)
P(at least 1) = 1 - 0 = 1
In percentage 1 × 100 % = 100 %
Grandma Marlene and Grandpa Gary are putting holiday lights on the gutters of their house. Grandma Marlene leans a 16-foot ladder up against the house, which makes the base of the ladder 9 feet from the house. How far up the house is the ladder?
Answer: 48
Step-by-step explanation: if i did the math correct 1/3 times the base (9) times 16 is 48. the formula is 1/3 x Bh
maths question is here
9+92*12312
Answer:
it would be 101 i believe
Answer:
1,132,713
Step-by-step explanation:
9+ 92 * 12312
= 9 + 1,132,704
= 1,132,713
What is the perimeter of the triangle
Answer:
56 units
Step-by-step explanation:
add each side, you can get the hypotenuse using the formula a^2+b^2=c^2
Jerome solved the equation below using the steps shown. Step 1: 3x + 6 = 18 step 2: 3x = 12 step 3: x = 4 what operation did her perform to get from step 2 to step 3
Answer:
divided both sides of the equation by 3
Step-by-step explanation:
The number of residents in a city is 57,000 people. The population is increasing each
year by 1.2%. Write an equation to model this situation.
What is the area of the following picture ( HELP PLEASE )
Answer:
area=l*b
10*8
80#
Step-by-step explanation:
hope you like it