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].
Josh used 3 packages of spaghetti to make dinner for 19 guests. How much did
each guest have?
Answer:
6.3
Step-by-step explanation:
19/3=6.3 repeating so i just shortened it to 6.3.
final answer: 6.3
Luigi ha 2 figli di 15 e 11 anni. Fra 18 anni la sua età sarà uguale alla somma delle età che avranno i figli. Quanti anni ha oggi Luigi?
Answer:
please if you need help, type in English, thanks :)
Which of these is a simplified form of the equation 7x + 4 = 5 + 3x + 1x?
1. 3x = 9
2. 3x = 1
3. 11x = 9
4. 11x = 1
Answer:
Step-by-step explanation:
hhhhhhhhhhhhhhhhhhhhhhhhhhhhh
What are the Missing sides?
Answer:
i think the answer is A ,if I'm wrong plz tell me
Anybody Know? It’s just a SOLVE FOR X
Answer:
Hello! answer: 10
Step-by-step explanation:
x = 10 because...
10 × 3 = 30 30 + 5 = 35 35 + 55 + 90 = 180 therefore x = 10 hope that helps!
9x−4=−1 how do i show my work for this?
Answer:
x = 1/3
Step-by-step explanation:
9x - 4 = -1
9x = -1 + 4
9x = 3
Find a,b,c and d?..........
9514 1404 393
Answer:
a = 6, b = 12, c = 6, d = 6√3
Step-by-step explanation:
The two triangles are the "special" triangles.
The 45-45-90 triangle has side lengths in the ratios 1 : 1 : √2.
The 30-60-90 triangle has side lengths in the ratios 1 : √3 : 2.
Then ...
c : a : 6√2 = 1 : 1 : √2 ⇒ c = a = 6
and ...
a : d : b = 1 : √3 : 2 ⇒ d = 6√3 and b = 12 . . . (since a=6)
The lengths are ...
a = 6, b = 12, c = 6, d = 6√3
PLEASE HELP!!!!!!!!!!
Answer:
second
Step-by-step explanation:
[tex]\frac{2x}{5} +\frac{1x}{5} +\frac{5}{8} -\frac{2}{8} = \frac{3x}{5} +\frac{3}{8}[/tex]
Answer:
3/5 x + 3/8
remove parentheses:
2/5x + 5/8 + 1/5x - 1/4
simplify terms:
3/5x + 5/8 - 1/4
make 1/4 have a common denominator to 15/8 by multiplying 2/2.
3/5x + 5-2/8 =
3/5x + 3/8
HELPPP HELPPP HELPPP!!!!
Answer:
Step-by-step explanation:
area =8*4 cm
=32 cm^2
Answer:
area of the figure=8×4
=32 cm²
A personnel psychologist studying adjustment to the job of new employees found a correlation of .3 between amount of education and rating by job supervisors 2 months later. The psychologist now plans to use the amount of education to predict supervisors’ later ratings. Indicate the independent/predictor variable, dependent/criterion variable, and beta. Write the Z-score prediction model; give the predicted Z-scores for supervisor ratings for employees with the amount of education Z-score of -1.5, -1, -.5
Answer:
the predictor variable is: amount of education
the criterion variable is: the Supervisors' rating
the beta is: .3
the Zy scores are -0.45, -0.3, 0.15
Step-by-step explanation:
r=beta which is the same; hence correlation equals regression
use this formula for the Z-scores
Zy= (beta) (Zx)
zy=(.3) (-1.5) = -0.45
(E) -1.5;
Zy=-0.45
(F)-1,
Zy=-0.3
(G)-.5.
Zy=-0.15
Find the value of x for which ABCD Is a parallelogram:
Please help :,)
Rewrite the following logarithmic expression as an exponential expression
Answer:
it should be the same answer....?
Step-by-step explanation:
if x is directly proportional to y and x= 4.5 when y = 3 find y when x = 24.
A) 63 B) 85 C) 16
x=4.5 - - -> y=3
x=24 - - - -> y= n
4.5n= 72
n= 72/4.5
n= 16
the answer is C) 16
Question about decimals
I have a math problem
205.17/713.95
I worked it out all by hand and eventually got to 34.79797241 as the calculator stated. This problem was very time consuming as it took a lot of work to complete. I was wondering if there was a simpler way of cutting my answer short that would also be correct?. I am unable to determine if this number is terminal or repeating as the decimal answer looks repeating with the 7979 but then appears to be terminal with the 241 part. Im assuming this number is terminal? Do I just need to suck it up and do the math or Is there a certain part of the decimal place value it would be appropriate to just stop at?
One more question unrelated to my previous questions.
I originally tried to solve this problem out of (A.) 713.95the divisor /by 205.17 the dividend as I know I am ALWAYS supposed to put the bigger number in the dividend section, but I am curious on how I would go about solving this question the opposite way (B.) with 205.17 as the divisor /by 713.95 as the dividend. I know this is possible as the calculator states
(A.) 713.95/205.17 =3.479797241
(B.) 0.2873730653 (I'm guessing this overwhelmingly long decimal is also terminal?)
Answer:
Both are terminating decimalsStep-by-step explanation:
Answer to your questions:
First of all, both A and B are correct and both quotients are terminating decimals.To find out if the decimal is terminating or not, multiply the quotient by divisor. If you get exactly the same number as dividend, then it is terminating otherwise it is non-terminating.The fraction may have greater numerator than denominator, in this case the quotient will be greater than one.Now regarding simplification. You would be asked to give an answer rounded to some extend. One decimal place, two decimal places, 3 significant numbers etc. For the first operation you would get 34.8 (rounded to nearest tenth). Or you may be asked to have a best estimated result. In this case you would round the initial numbers and find results. 205/714 ≈ 0.29The perimeter of the
rectangle is 14 m and
the area is 12 m2.
Calculate the length
of the rectangle
diagonal
Answer:
5
Step-by-step explanation:
area of rectangle = l(ength)×w(idth)
perimeter = 2×l + 2×w
diagonal = sqrt(l² + w²) (Pythagoras)
l×w = 12. => l = 12/w
2×l + 2×w = 14
2×12/w + 2×w =14
12/w + w = 7
12 + w² = 7w
w² - 7w + 12 = 0
=> (after a little thinking and trying : what 2 numbers multiply to 12 and add to -7 ? -3 and -4
=> (w-3)×(w-4) = 0
so, we get 2 solutions for w : 3 and 4
that gives us 2 solutions for l : 4 and 3
so, one is 3 and the other 4. it does not matter which is which. length 4 and width 3 produce the same diagonal as length 3 and width 4.
diagonal = sqrt(l² + w²) = sqrt(16 +9) = sqrt(25) = 5
20/5 as a whole number
Answer:
4 is the answer
Step-by-step explanation:
Please help!!! Here’s a picture of my question
Answer:
option no. D
Step-by-step explanation:
i+34j+14k
hope it helps
Ive been stuck on this problem for an hour, help pleaseee.
The graph of the function is given below. Give all y-intercepts and x-intercepts shown.
Answer:
y intercept: [tex]y = 1[/tex]
x intercept: [tex]x = -1[/tex] and [tex]x = -3[/tex]
Step-by-step explanation:
Given
The attached graph
Solving (a): The y intercepts
This is the point where [tex]x = 0[/tex]
From the attached graph, [tex]x = 0[/tex] when
[tex]y = 1[/tex]
Hence, the y intercept is 1
Solving (b): The x intercepts
This is the point where [tex]y = 0[/tex]
From the attached graph, [tex]y = 0[/tex] when
[tex]x = -1[/tex] and [tex]x = -3[/tex]
Hence, the x intercept are -1 and -3
what is the area of this figure
Answer:
A=162.56in^2
Step-by-step explanation:
make sure u separate the different shapes
what are some ways customers could get in financial trouble with credit cards? write in sentence or paragraph form
Answer:
the ways customers could get in financial trouble with thier credit cards are:
The Allure of Excessive Spending Interst Makes Paying Off the Balance Difficult. There's a chance you'll end up in debt.
You run the risk of damaging your credit score.
Minimum payments can give the impression of safety.
Credit Card Terms Can Be Confusing.
It's more difficult to keep track of spending, especially
when using multiple credit cards.
Step-by-step explanation:
-
The following rule is used to work out the total cost, in cunos, ofhings
Total cost - 9 euros for each hour plus 20 euro
Paolo hires the room for 5 hours.
(a) Work out the total cost.
Answer:
65
Step-by-step explanation:
9+9+9+9+9
or
9×5 both = 45
45+20 euros = 65
45 euros per 5 hours , + bonus the 20 euros = 65 in total.
If f(x) = 3x - 1 and f(x) = 3f(x) = 3, find x.
Answer:
x = 4/3
Step-by-step explanation:
f(x) = 3x - 1
f(x) = 3
set equal
3x - 1 = 3
add 1 to both sides
3x = 4
Divide both sides by 3
x = 4/3
Answer:
x=4/3
Step-by-step explanation:
[tex]\tt f(x)=3x-1[/tex] [tex][\tt f(x)=3][/tex]
[tex]\tt 3=3x-1[/tex]
[tex]\tt 3+1=3x[/tex]
[tex]\tt 4=3x[/tex]
[tex]\tt x=\cfrac{4}{3}[/tex]
A person of interest was identified by the police. Using three different telecommunication towers,
the police were able to gather the following information about the person's cell phone location.
• The person is 7 miles away from A(4,4.6).
• The person is 5 miles away from B(-3.5, - 3.8).
• The person is 6 miles away from C(-6, 5.5).
Use the information from towers A, B, and C to find the approximate location of the person of
interest.
Answer:
Well since he tracked the person through the communication towers he was able to gather information, with this information we can solve and find out how far this person is.
Step-by-step explanation: read above and trust
Stephan can type 2700 words in 90 mins Jim can type 2450 in 70 mins gavin can type 1600 words in 40 mins who can type the fastest rate of words per minute
Answer:
Gavin with 40 words per minute
Step-by-step explanation:
Stephan speed- 2700 words/90 minutes = 30 words per minute
Jim speed- 2450 words/70 minutes= 35 words per minute
Gavin 1600 words / 40 minutes= 40 words per minute
Write the numbers in order from least to greatest. *
1 point
Captionless Image
1/4; 0.4; 0.55; 3/5
0.4; 1/4; 0.55; 3/5
1/4; 3/5; 0.4; 0.55
3/5; 0.4; 1/4; 0.55
Answer:
1/4; 0.4; 0.55; 3/5
0.25, 0.40, 0.55, 0.60
Already in order.
0.4; 1/4; 0.55; 3/5
0.40, 0.25, 0.55, 0.60
1/4; 0.4; 0.55; 3/5
1/4; 3/5; 0.4; 0.55
0.25, 0.60, 0.40, 0.55
1/4; 0.4; 0.55; 3/5
3/5; 0.4; 1/4; 0.55
0.60, 0.40, 0.25, 0.55
1/4; 0.4; 0.55; 3/5
What is the value of x in the equation 25x = 16?
O A + 4
5
OB.
+4
oc. + 1
OD
NIH
clos
Reset
Answer:
C. ±4/5
Step-by-step explanation:
25x² = 16
25x² - 16 = 16 - 16
25x² - 16 = 0
25x² + 20x - 20x - 16 = 0
(25x² + 20x) + (- 20x - 16) = 0
5x(5x + 4) - 4(5x + 4) = 0
(5x - 4)(5x + 4) = 0
5x - 4 =0
5x + 4 = 0
[tex]x=-\frac{4}{5}[/tex]
[tex]x=\frac{4}{5}[/tex]
± is a symbol which represents addition and subtraction.
Determine the equation of the circle graphed below.
Step-by-step explanation:
radius= √(2+2)²+(0+3)²=√4²+3²=√16+9
=√25=5
the equation is
(x+2)²+(y+3)²=25
or
x²+y²+4x+6y-12 = 0
work out the area of this circle. take pi to be 3.142 and give your answer to be 2 decimal places. 11,2 cm
Answer:
11.2 i think so but you will write 11.2
In a dark room, the pupil of a human eye grows to a diameter of about 3.2 x 10 inches. It
bright light, the pupil shrinks to a diameter of about 8 x 10 inches. How much greater is
the pupil's diameter in a dark room than in bright light?
Answer: the answer is 48 inches
Step-by-step explanation:
A right triangle (90) has a one angle that measures 35 degrees. What is the measure of the third angle?
A. 90 degrees
B. 145 degrees
C. 55 degrees
D. 180 degrees
Answer:
55°
Step-by-step explanation:
triangle= 180°
third angle= 180-90-35
= 55°