Answers
Answer:
a) sin x
b) cos² x
c) sin²x
Step-by-step explanation:
Step(i):-
Given that the trigonometric equation
[tex]tan(\frac{x}{2} ) + cos x tan (\frac{x}{2} ) = sin x[/tex]
we have to use trigonometric formulas
[tex]1-cosx = 2sin^{2} (\frac{x}{2} )[/tex]
[tex]sin x = 2 sin \frac{x}{2} cos\frac{x}{2}[/tex]
now
[tex]tan\frac{x}{2} = \frac{sin\frac{x}{2} }{cos\frac{x}{2} }[/tex]
= [tex]\frac{2sin(\frac{x}{2} ) sin\frac{x}{2} )}{2sin\frac{x}{2} cos\frac{x}{2} }[/tex]
= [tex]\frac{2sin^{2} (\frac{x}{2} ) )}{sinx }[/tex]
= [tex]\frac{1-cosx}{sinx}[/tex]
Step(ii):-
[tex]tan(\frac{x}{2} ) + cos x tan (\frac{x}{2} ) = \frac{1-cosx}{sinx} +cosx \frac{1-cosx}{sinx}[/tex]
= [tex]\frac{1-cosx +cosx(1-cosx)}{sinx}[/tex]
= [tex]\frac{1-cosx+cosx-cos^{2} x}{sinx}[/tex]
= [tex]\frac{1-cos^{2} x}{sinx}[/tex]
= [tex]\frac{sin^{2}x }{sinx}[/tex]
= sinx
Related Questions
6y + 12x + 4y - 9x - 3x
Combining like terms
I need some help!
Answers
Answer:
10y
Step-by-step explanation:
Which is the equation for the line that passes through (5,-3) and has a slope of 6?
Answers
So ummm. I kind of got this wrong, and I had to delete my answer, I swear, I am SOOOO sorry. If there is a way I can give your points back I will do so.
So um yeah, just ignore this.
someone help pls thank u
Answers
Express the limit as a definite integral on the given interval. lim n→[infinity] n xi ln(1 + xi2) Δx, [2, 7] i = 1
Answers
Answer:
Step-by-step explanation:
[tex]Consider \ the \ following \ series[/tex]
[tex]\lim_{n \to \infty} \sum \limits ^n_{i=1} x_i \ In ( 1+ x_i^2) \Delta x , [2,7][/tex]
[tex]Let's \ recall \ the \ explanation \ of[/tex] d[tex]efinite[/tex] [tex]\ integral \ in \ terms \ of \ Riemann \ sum[/tex]
[tex]\int^b_a \ f(x) \ dx = \lim_{n \to \infty} \sum \limits ^n_{i=1} \ f(x_i) \Delta x , \ where \ \Delta x = \dfrac{b-a}{n}[/tex]
[tex]By \ efinition, \ the \ limit \ is \ then \ expressed \ as \ integral[/tex]
[tex]\lim_{n \to \infty} \sum ^a_{i=1} \ x_i \ In (1+x_i^2) \Delta x = \int^7_2 xIn (1+x^2) \ dx[/tex]
Determine which relation is a function.
Answers
Based on this triangle, which one of the following statements is true? (Note: the triangle is not drawn to scale)
[PLEASE LEAVE A SMALL EXPLANATION ILL MARK BRAINLIEST]
Answers
Answer:
A
Step-by-step explanation:
All triangles angles add up to 180°
25 pts will award brainliest
Question 14 (5 points)
(05.02 LC)
What is the value of x in the solution to the following system of equations? (5 points)
x − 2y = 2
3x + y = 6
Answers
Answer:
x = 2 and y = 0
Step-by-step explanation:
x - 2y = 2
3x + y = 6
using the substitution method, we solve the first equation for 'x' to get
x = 2y + 2
plug that into 'x' in the second equation
3(2y + 2) + y = 6
6y + 6 + y = 6
7y = 0
y = 0
find 'x':
3x + 0 = 6
x = 6/3
x = 2
Answer:
x=2
Step-by-step explanation:
PLZ help: The theoretical probability that a pop song plays on your MP3 player is 0.45. There are 80 songs on your MP3 player. How many of the songs are pop songs?
Answers
Answer:
36
Step-by-step explanation:
80 * .45 = 36
Answer:There are 36 pop songs on your playlist
Step-by-step explanation:
what is the slope for (-11,7),(15,-3)
Answers
Formula: Y2-Y1/X2-X1
Answer:
m=-5/13
Explanation
Solve for X
1q - 2 x = 7
Help!
Answers
Hope this helps :)
please find the Equations PLEASE
Answers
Answer:
9) y = -x
10) y = -3/2x + 12
11) y = 3/4x - 5
12) y = -2/3x
What is the value of 5k+m when k=-3 and m= -9
Answers
Answer: -24
Step-by-step explanation:
Substitute k and m with -3 and -9 then solve.
Which expression is equivalent to √96
Answers
Answer:
√96 = 4√6
Step-by-step explanation:
Factor the radicand. Take the square root of the factors.
The expression that should be equivalent to [tex]\sqrt{96}[/tex] is considered to be the [tex]= 4\sqrt 6[/tex]. The calculation is given below,
Calculation of an expression:Since the expression is [tex]\sqrt{96}[/tex]
So, we can solve by breaking it
[tex]= \sqrt{2^5\times 3} \\\\= \sqrt{2^4 \times 2 \times 3} \\\\= \sqrt 2^4 \times \sqrt 6\\\\= 4\sqrt 6[/tex]
Hence, we can conclude that The expression that should be equivalent to [tex]\sqrt{96}[/tex] is considered to be the [tex]= 4\sqrt 6[/tex].
Learn more about an expression here: https://brainly.com/question/1673286
What is the diameter of this circle? A) 2 cm B) 3.14 cm C) 4 cm D) 8 cm
Answers
Answer:
The answer is c
Step-by-step explanation:
Well, since the Circle is 8cm you can divide the circle by two to get 4
Which points are solutions to the system of inequalities? Select ALL that apply.
(-2, 4)
(2, -1)
(3, 1)
(0, 0)
(0, -1)
Answers
Answer:
0,0
2,-1
-2,4
Step-by-step explanation:
What is the surface area of this shape?
1 cm
5 cm
4 cm
2 cm
6 cm
3 cm
Answers
Answer: 6 cm
Step-by-step explanation:
The surface area of the given shape is 80 cm².
From the given figure, the dimensions of large cuboid is length= 5 cm, width= 3 cm and height= 2 cm.
What is surface area of a cuboid?The surface area of a cuboid is the total space occupied by it. A cuboid is a six-faced three-dimensional shape in which each face is in the shape of a rectangle.
Formula to find the total surface area of a cuboid is 2(lw+wh+lh)
Surface area of a large cuboid
= 2(5×3+3×2+5×2)
= 2(15+6+10)
= 2×31
= 62 cm²
The dimensions of smaller cuboid is length= 1 cm, width= 1 cm and height= 4 cm
Surface area of a smaller cuboid
= 2(1×1+1×4+1×4)
= 2(1+4+4)
= 2×9
= 18 cm²
Total surface area = 62+18
= 80 cm²
Therefore, the surface area of the given shape is 80 cm².
Learn more about the surface area of a cuboid here:
https://brainly.com/question/26403859.
#SPJ2
To begin a bacteria study, a petri dish had 2300 bacteria cells. Each hour since, the number of cells has
increased by 7.2%.
Lett be the number of hours since the start of the study. Let y be the number of bacteria cells.
Write an exponential function showing the relationship between y and t.
PLEASE HELP :)
Answers
Answer: [tex]y= 2300(1.072)^t[/tex]
Step-by-step explanation:
The exponential growth equation : [tex]y=A(1+r)^t[/tex] , where A=initial value, r= rate of growth , t= time.
Given: A = 2300, r= 7.2% = 0.072
Let t be the number of hours since the start of the study. Let y be the number of bacteria cells.
then, the exponential function showing the relationship between y and t will be:
[tex]y= 2300(1+0.072)^t\\\\\Rightarrow\ y= 2300(1.072)^t[/tex]
Guys.. I’m going to get held back, I. Need. Help.
Answers
Good night!!
Answer:
1). -12
2). -6
Hope this helps<3
You will drop the bottle/water mass so that it hits the lever at different speeds. Since an object in free fall is accelerated by gravity, you need to determine the heights necessary to drop the bottle to achieve the speeds of 2 m/s, 3 m/s, 4 m/s, 5 m/s, and 6 m/s. Use the equation Ht = v squared over 2 g. to calculate the height, where Ht is the height, v is the speed (velocity), and g is the gravitational acceleration of 9.8 m/s2. Record these heights in Table B. To achieve a speed of 2 m/s, the bottle must be dropped at m. To achieve a speed of 3 m/s, the bottle must be dropped at m. To achieve a speed of 4 m/s, the bottle must be dropped at m. To achieve a speed of 5 m/s, the bottle must be dropped at m. To achieve a speed of 6 m/s, the bottle must be dropped at m
Answers
Answer:2,3,4,5,6
Step-by-step explanation:
Answer:
0.20
0.46
0.82
1.28
1.84
Step-by-step explanation:
HELP PLZ 20 POINTSSSS
Answers
Answer:
cube................
Answer:
A)
Step-by-step explanations:
Please help me ASP please
Answers
lxw so 3/4 x 4/5 then get ur answer
Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions
that a randomly chosen student answered correctly. Here is the probability distribution of X along with
summary statistics:
0
1
2
2.
3
X = # correct
P(X)
0.05
0.20
0.50
0.25
Mean: Hex = 1.95
Standard deviation: Ox 0.8
Mr. Gupta decides to score the tests by giving 10 points for each correct question. He also plans to give
every student 5 additional bonus points. Let Y represent a random student's score.
What are the mean and standard deviation of Y?
Hy =
points
Oy
points
Answers
Answer:
24.5 points
8 points
Step-by-step explanation:
khan academy
The mean is 1.95 and the standard deviation is 2.41 for the given distribution.
What is the standard deviation?A standard deviation (σ) is a measure of the distribution of the data in reference to the mean.
The given data as :
Correct question (x) Probability
0 0.05
1 0.20
2 0.50
3 0.25
In this scenario, we must calculate the mean, which is the product of the correct question and the probability. The mean will then be subtracted from the correct question. multiply the difference between the correct question and the mean by probability. This indicates the pay variance. off's The standard deviation of the distribution is given by taking the square root of the variance of the correct question.
Mean = 0 × 0.05 + 1 × 0.20 + 2 × 0.50 + 3 × 0.25
Mean = 1.95
Variance = (0 - 1.95)² + (1 - 1.95)² + (2 - 1.95)² + (3 - 1.95)²
Variance = 3.8025 + 0.9025 + 0.0025 + 1.1025
Variance = 5.81
Standard deviation = √(Variance)
Standard deviation = √(5.81)
Standard deviation = 2.41
Thus, the mean is 1.95 and the standard deviation is 2.41 for the given distribution.
Learn more about the standard deviation here:
brainly.com/question/16555520
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Which triangles are congruent by SAS?
Answers
Answer: VTU and HGF
Step-by-step explanation:
Bob is 17 years older than john. In 5 years, the sum of their ages will be 51. Find their current age
Answers
Simplify the ratio 4:26
Answers
Answer:
The simplest form of 426 is 213.
Answer:
2:13
Step-by-step explanation:
To simplify the ratio 4:26, we find the greatest common divisor of 4 and 26, and then we divide 4 and 26 by the greatest common divisor.
The greatest common divisor that you can use to simplify 4:26 is 2. Which means the answer to ratio 4:26 simplified is 2:13.
If you would help it would be life-saving
Answers
Answer:
waiting for the wishing well, put they hands put they hands to the wishing well still no ns but oh well they pain and they wishes in the wishing well.
Step-by-step explanation:
Answer:
Step-by-step explanation:
y = [tex]\frac{3}{2}x[/tex]
2) [tex]y=\frac{3}{2}*64\\[/tex]
y = 3 * 32 = 96
[tex]3) x = \frac{2}{3}y\\\\x =\frac{2}{3}*39=2*13=26[/tex]
[tex]4)y=\frac{3}{2}x\\\\y=\frac{3}{2}*1=\frac{3}{2}[/tex]
URGENT PLEASE HELP GIVE RIGHT ANSWER.
Answers
Answer:
its negative 8
Step-by-step explanation:
you can see it there
what is 30% as a fraction in simplest form and as a decimal to the nearest hundredtgh
Answers
Answer:
fraction-3/10
decimal-.3
Answer:
Step-by-step explanation:
There are a few ways you could look at this, but this is the way that I prefer:
A percent is essentially already a fraction out of 100. 100% = 1. Therefore, 30% = [tex]\frac{30}{100}[/tex].
To simplify this, divide the top and the bottom by 10. This equals [tex]\frac{3}{10}[/tex]. Because 3 is a prime number and 10 is not divisible by 3, this is completely simplified.
To find the percent of any fraction, the easiest way is to simply divide the top by the bottom.
3/10 = 0.3
This is your final answer, as there is no number in the hundredth place or beyond to concern yourself with.
* HELP QUICK I WILL MARK BRANLIEST* If the circumference of a circle is 10x inches, what is the area, in square inches, of
the circle?
1) 10 sq. in
2) 254 sq. in.
3) 50. sq. in.
4) 100 sq. in.
Answers
Answer:
100 Sq in.
Step-by-step explanation:
A group of young adults reported their average number of hours of exercise per week and measured their resting heart rates. An approximate least-squares regression line was used to predict the resting heart rate from a given number of hours of exercise per week.
Answers
Answer: this young adults resting heart rate was 6 more beats per minute than predicted based on the number of hours of exercise
Step-by-step explanation: y’all welcome