Which of these expressions is the simplified form of the expression (StartFraction sine (x) Over 1 minus cosine squared (x) EndFraction) tangent (StartFraction x Over 2 EndFraction) ?
Answer:
[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2}) = \frac{1}{1+cosx}[/tex]
Step-by-step explanation:
Given
[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2})[/tex]
Required
Simplify
[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2})[/tex]
---------------------------------------------------------------------------------------------------
Considering the denominator of the first bracket
[tex]1 - cos^2x[/tex]
This can be rewritten using different of two squares as follows:
[tex](1 - cosx)(1 + cosx)[/tex]
So, [tex]1 - cos^2x[/tex] can be replaced with [tex](1 - cosx)(1 + cosx)[/tex] in the given expression.
Also, from trigonometry identity
[tex]tan\frac{x}{2} = \frac{1 - cos x}{sin x}[/tex]
So, [tex]tan\frac{x}{2}[/tex] can be replaced with [tex]\frac{1 - cos x}{sin x}[/tex] in the given expression
---------------------------------------------------------------------------------------------------
[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2})[/tex] becomes
[tex](\frac{sinx}{(1-cosx)(1+cosx)}) * \frac{1 - cos x}{sin x}[/tex]
[tex](\frac{sinx * (1 - cos x)}{(1-cosx)(1+cosx) * sin x})[/tex]
Cancel out similar expressions
[tex]\frac{1}{1+cosx}[/tex]
The expression cannot be further simplified.
Hence:
[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2}) = \frac{1}{1+cosx}[/tex]
The simplified form of the expression :
[tex]\frac{sinx}{1-cos^{2} x} .tan\frac{x}{2} =\frac{1}{1+cosx}[/tex]
We have some trigonometric formula as:
[tex]sin2x=2sinx= cosx\\2cos^{2} x=1+cos2x[/tex]
We have the expression
[tex]\frac{sinx}{1-cos^{2} x} .tan\frac{x}{2} \\=\frac{sinx}{sin^{2} x} .tan\frac{x}{2} \\=\frac{1}{sin x} .tan\frac{x}{2}\\=\frac{1}{2sin \frac{x}{2} cos\frac{x}{2}} .tan\frac{x}{2}\\=\frac{1}{2sin \frac{x}{2} cos\frac{x}{2}} .\frac{sin\frac{x}{2}}{cos\frac{x}{2}} \\=\frac{1}{2cos^{2} \frac{x}{2}}\\=\frac{1}{1+cos{x} }[/tex]
Therefore, the simplified form of the expression is:
[tex]\frac{sinx}{1-cos^{2} x} .tan\frac{x}{2} =\frac{1}{1+cosx}[/tex]
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A family is purchasing 17 tickets for a downtown walking tour. Adult tickets are $10, child tickets are $7, and senior tickets are $8.50. The total
cost of the tickets is $141.50, and they are purchasing 2 more senior tickets than adult tickets.
Create and solve a system of linear equations to represent this situation. Then select the true statement.
А. The solution to this system is nonviable because it results in a fractional number of tickets.
B. The solution to this system is no viable because it results in a negative number of tickets.
C. The solution to this system is viable.
D. The solution to this system is nonviable because it results in a fractional amount of money.
Answer:
А. The solution to this system is nonviable because it results in a fractional number of tickets.
Step-by-step explanation:
Let x represent the number of adult tickets, y represent the number of child ticket and z represent the number of senior ticket.
Since the number of purchased ticket is 17, hence:
x + y + z = 17 (1)
The total cost of tickets is $141.50, hence:
10x + 7y + 8.5z = 141.5 (2)
they are purchasing 2 more senior tickets than adult tickets, therefore:
x = z + 2 (3)
Solving equation 1 2 and 3 simultaneously gives:
x =17/3, y = 23/3, z = 11/3
Therefore the solution to this system is nonviable because it results in a fractional number of tickets.
Answer:
А.The solution to this system is nonviable because it results in a fractional number of tickets
Step-by-step explanation:
took the test on edmentum and got it correct
Can any one help me?
find two numbers that equal 11,000 when added together, but also equal 3,000 when subtracted from each other
Answer:
4000 and 7000
Step-by-step explanation:
Find the value of (27) to the - 2/3
Answer: Yes. For example: (27)^2/3 would be 3^2 which = 9.
Step-by-step explanation: Hopefully this help :D ask for more help if you need!
Given g(x) = -3x + 1, find g(2).
Answer:
- 5
Step-by-step explanation:
Step 1:
g ( x ) = - 3x + 1 Function
Step 2:
g ( x ) = - 3 ( 2 ) + 1 Input x
Step 3:
g ( x ) = - 6 + 1 Multiply
Answer:
g ( x ) = - 5 Add
Hope This Helps :)
600 feet per hour. What is his
speed miles
in
per hour?
Answer:hi
Step-by-step explanation:
A survey of 800 school employees yielded the following information: 430 were instructors, 589 were full-time faculty, and 340 of the instructors were full-time faculty. How many school employees were full-time faculty but were not instructors
Answer:
249Step-by-step explanation:
let n(U) be the total number of school employees = 800
Let n(I) be amount of instructors = 430
Let (F) be full-time faculty = 589
Let n(InF) be the instructors who were full-time faculty = 340
The number of employees who were full-time faculty but were not instructors is expressed as:
n(FnI') = n(F) - n(InF)
n(FnI') = 589 - 340
n(FnI') = 249
Hence the number of school employees who were full-time faculty but were not instructors are 249
Kyle plans to estimate the area of the figure below by identifying the full and partial squares that make up the figure.
If Kyle uses the strategy, which statement best describes the figure?
O 20 full squares and 8 partial squares
0 24 full squares and 12 partial squares
0 36 full squares and 12 partial squares
O 40 full squares and 8 partial squares
Answer:
The answer is one hundred percent D
Step-by-step explanation:
Hi
Answer:
D
Step-by-step explanation:
t/8 = -4 find the value of t please :)
Answer:
t = -32
Step-by-step explanation:
I multiplied -4 to 8
Have a wonderful day <33
7th grade math help me plzzz
Answer:
-7 minus 9 = -16
-3-(-10) =7
8-12=-4
4-(-5)=9
Step-by-step explanation:
im in 7th grade on edginuity got it all right
Jason delivers newspapers on Saturdays and Sundays only. Each newspaper weighs about 1 pound 5 ounces. If he delivers 15 newspapers each day, how much do the two days' worth of newspapers weigh in pounds and ounces?
Answer:
39pounds 6oz
Step-by-step explanation:
15x2=30
1x30=30pounds
5x30=150oz
30p+150oz=39.37500
37500p=6oz
39pounds and 6 oz
how do you solve for x
-3x-6y=0
Answer:
x = 2y
Step-by-step explanation:
Simplifying
3x + -6y = 0
Solving
3x + -6y = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '6y' to each side of the equation.
3x + -6y + 6y = 0 + 6y
Combine like terms: -6y + 6y = 0
3x + 0 = 0 + 6y
3x = 0 + 6y
Remove the zero:
3x = 6y
Divide each side by '3'.
x = 2y
Simplifying
x = 2y
look at picture
look at picture
Answer:
point ??????? I think not sure
Which two options describe the standard deviation?
The variance square
The extreme distance from the mean expected from the data points
The square root of the variance.
The average distance from the mean expected of the data.
Answer:
The square root of the variance.
The average distance from the mean expected of the data.
Step-by-step explanation:
Standard deviation is a measure of dispersal. It determines the average distance from the mean expected of the data.
Variance is also related to the standard deviationIt is the square root of the variance. The dispersion or variation of a set of values away from the mean is the standard deviation.
Standard deviation = [tex]\sqrt{variance}[/tex]
Help please!!!!!! I can’t figure it out.
Answer:
A.) parallel
Step-by-step explanation:
they are on opposite sides, and will never touch.
Hope I helped!! :)
A line which has an undefined slope is _____.
A. zero
B. horizontal
C. vertical
D. undefined
Answer:
c, vertical
Step-by-step explanation:
blablablablablanlabla
Please Answer ASAP!!
Answer:
0.17
Step-by-step explanation:
hope i helped
1.5d + 9.25 = 4 + 2.25d
what is d?
.
Answer:
d = 7
Step-by-step explanation:
1.5d + 9.25 = 4 + 2.25d
Combine the constants and the variables.
5.25 = 0.75d
Divide.
d = 7
Archaeologists used pieces of burned wood, or charcoal, found at the site to date prehistoric paintings and drawings on walls and ceilings of a cave in Lascaux, France. Use the information in Example 3 of Section 3.1 to determine the appropriate age of a piece of burned wood, if it was found that 88% of the C-14 found in living trees of the same type had decayed. (Round your answer to the nearest hundred years.) years
Answer:
The age of the wood is [tex] t = 17527.5 \ years [/tex]
Step-by-step explanation:
From the question we are told that 88% of of the C-14 found in living trees of the same type had decayed , this means that the proportion of C-14 that is remaining is mathematically evaluated as
[tex] 1 - 0.88 = 0.12[/tex]
Hence
[tex] N = 0.12N_o[/tex]
Here N represents the remaining C-14 while [tex]N_o[/tex] is the original amount of C-14
Generally the half life of C-14 is [tex]h = 5730 \ years[/tex]
Generally from the formula of radioactive decay
[tex]N = N_o * 2^{-\frac{t}{h} }[/tex]
=> [tex]0.12N_o = N_o * 2^{-\frac{t}{5730} }[/tex]
=> [tex]0.12 = 2^{-\frac{t}{5730} }[/tex]
taking the natural log of both sides
=> [tex] ln [0.12] = ln[ 2^{-\frac{t}{5730} }][/tex]
=> [tex] ln [0.12] = -\frac{t}{5730}ln(2) [/tex]
=> [tex] t = 17527.5 \ years [/tex]
The appropriate age of burned wood will be "17527.5 years".
Radioactive decayAccording to the question,
The proportion of C-14 = 1 - 0.88
= 0.12
then,
N = 0.12 N₀
Now,
The half-life of C-14 will be:
h = 5730 years
By using Radioactive decay formula, we get
→ N = N₀ × [tex](2)^{-\frac{t}{h} }[/tex]
By substituting the values,
0.12N₀ = N₀ × [tex](2)^{-\frac{t}{5730} }[/tex]
0.12 = [tex]2^{-\frac{t}{5730} }[/tex]
By taking "log" both sides,
ln[0.12] = ln[[tex]2^{-\frac{t}{5730} }[/tex]]
ln[0.12] = -[tex]\frac{t}{5730 \ ln(2)}[/tex]
hence,
The age will be:
t = 17527.5 years
Thus the above response is correct.
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2. Use prime factorization to find the
LCM of 30 and 75.
Answer:
150 is the LCM for 30 and 75
How many pounds are in 80 kilograms?
Answer:
176.37 pounds are in 80 kilograms
Step-by-step explanation:
The kilogram, or kilogramme, is the base unit of weight in the Metric system. It is the approximate weight of a cube of water 10 centimeters on a side.
A pound is a unit of weight commonly used in the United States and the British commonwealths. A pound is defined as exactly 0.45359237 kilograms.
the list price of a fan is Rupees 1500 If the shopkeeper allows 20% is ground how much to the customer pay for it with a 10% vat
Answer:
450
Step-by-step explanation:
First we have to find the discount
20% of 1500 = 300
if you search up 20 x 1500/100, it would say 300
you can do that same equation in your maths book, and also by canceling out
10% vat tax
so 10% of 1500 = 150
since it is tax, we have to add it to our discount
300 + 150 = 450
450 is the answer
What is the answer for number five
Answer:
Can you write it down i could help but i cant see the link
Step-by-step explanation:
Answer:
FULL SEND imma say A but I honestly have no idea lol
Step-by-step explanation:
A coin is tossed and -sided die numbered 1 through is rolled. Find the probability of tossing a and then rolling a number greater than .
Complete question :
A coin is tossed and a die is rolled. Find the probability of tossing a tail and then rolling a number greater than 2.
Answer : 1/3
Step-by-step explanation:
For a coin :
Sample space = (T, H)
Probability = required outcome / Total possible outcomes
Probability of tail, p(T) = 1 / 2 = 0.5
For a fair die:
Sample space = (1, 2, 3, 4, 5, 6)
Required outcome = number greater than 2 = (3, 4, 5, 6) = 4
P(number greater than 2) = 4/6 = 2/ 3
Hence, probability of a tail, then a number greater than 2 :
(1/2 * 2/3) = 2 /6 = 1/3
Geometric Sequence♡
5, -2, 4/5
the common ratio was 2/5
find the 10th term
HELPPPP PLS ASAPPPPP EASY
Answer:
on what
Step-by-step explanation:
??????
Answer:
What do you need help with?
Step-by-step explanation:
Upload a picture
In terms of the entire bill, which rational number represents the net change to Callie’s bank account? What does the sign on the number mean?
Answer:
Callie has 4 months to pay off the bill. The rational number is +4. The sign is positive because it represents a quantity of something, in this case, months.
Step-by-step explanation:
this is correct...
trust me :)
The sign is positive because it represents a quantity of something, in this case, months.
Callie has 4 months to pay off the bill.
The rational number is +4.
What is the rational number?
A number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.
The sign is positive because it represents a quantity of something, in this case, months.
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Morgan born is paid $11.20 an hour for a 40-hour week.Her estimated benefits are 33% of her wages.What is value of her total yearly employee benefits?
Answer:
Как ты это делаешь
Step-by-step explanation:
For a certain product we obtained a regression line equation Y = 10 - 0.8 X, where X is price (in $) and Y is sales (in $1,000). The slope of the line (- 0.8) represents:___---.
A. If the price were $10, expected sales would be $8,000.B. If the price were zero, expected sales would $800.C. If the price increases by $1, sales will decrease by $800, on average.D. Sales are maximized when the price is $0.8.
E. None of the other answers are correct.
Answer:
C. If the price increases by $1, sales will decrease by $800, on average
Step-by-step explanation:
Slope of regression equation represents the increase/decrease in dependent variable Y due to unit change in independent variable X. Here, independent variable is X is price and dependent variable Y is sales. The slope negative sign represent decrease in dependent variable due to unit increase in independent variable. Sales is given in ($1000) So, (0.8*1000)=800. It means that due to unit dollar increase in price the sales will decrease by $800. Thus, If the price increases by $1, sales will decrease by $800, on average is the correct interpretation.