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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Armando and Mikayla have a new grandson. How much money should they invest now so that he
will have $80,000 for his college education in 18 years? The money is invested at 8% compounded
annually
9514 1404 393
Answer:
$20,020
Step-by-step explanation:
The future value formula is helpful.
FV = P(1 +r)^t
$80,000 = P(1.08^18) = 3.9960195P
P = $80,000/3.9960195 = $20,019.92
They should invest about $20,020 now.
Rewrite 3^-7 using a positive exponent.
Answer: 1/3^7
Step-by-step explanation:
Round 24,837,618 to the ten thousands place. I’m on math college so I need help on this problem!
Answer:
24,840,000
Step-by-step explanation:
Round up of numbers includes rounding them up to a given place value.
We are asked to round 24,837,618 to the ten thousands place.
The ten thousands place is the place where the number 3 in the number is located.
The number after 3 = 7 is a number above 5. Hence, we add 1 to 3, making it 4
Therefore, 24,837,618 to the ten thousands place is 24,840,000
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:
Which equation expresses d in terms of t and a?
Answer:
Option D
Step-by-step explanation:
I got it right
9. What is the likelihood that a randomly selected couple's relationship survived between 90 and 150 days
Answer:
0.5818
Step-by-step explanation:
Suppose the average teenage romantic relationship is normally distributed with a mean number of 100 days with a standard deviation of 30 days.
Answer:
The z score is used to determine how many standard deviations that the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and if it is negative then it is below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}\\ \\where\ \mu=mean,\sigma=standard\ deviation, x=raw\ score[/tex]
Given that:
[tex]\mu=100\ days,\sigma=30\ days\\\\For\ x=90\\\\z=\frac{90-100}{30} =-0.33\\\\For\ x=150\\\\z=\frac{150-100}{30} =1.67[/tex]
Therefore, from the normal distribution table, P(90 < x < 150) = P(-0.33 < z < 1.67) = P(z < 1.67) - P(z < -0.33) = 0.9525 - 0.3707 = 0.5818
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
I need help with Number 7 please!!!
Answer:
8.06 ft or [tex]\sqrt{65}[/tex] ft
Step-by-step explanation:
Since Rebecca bought a square table and squares have equal sides, you can take the square root of the area of the table, which gives you [tex]\sqrt{65}[/tex] ft per side. This can be approximated to 8.06 ft.
Can any one help me?
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]
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.
Find out more information about radioactive decay here:
https://brainly.com/question/1236735
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:
what is /4 of 3/4 =
What is 1/4 of 3/4
Answer:
3/16
Step-by-step explanation:
1/4 of 3/4 is just another way of saying (1/4)*(3/4). When multiplying fractions, you must multiply the numerators and denominators to get the product so the numerator of the products is 1*3 and the denominator is 4*4 to get:
3/16
Answer:
3/16
Step-by-step explanation:
1/4 of 3/4
= 1/4 × 3/4
you multipy the numerators together and then multiply both denominators
ie. 1×3 divided by 4×4
= 3/16
Kai is making a chessboard using pieces of wood that measure 1 square inch.
When he finishes, the chessboard will have an area of 64 square inches.
How many pieces of wood should he put along each side?
A cube has a volume of 125 cubic inches. What is the length of each edge?
Answer:
The correct option will be: c. 8 pieces of wood.Step-by-step
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
look at picture
look at picture
Answer:
point ??????? I think not sure
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
Use rounding to estimate the product of 5,555 and 4,444 round both numbers to the nearest thousand to find answer
Step-by-step explanation:
Given that the first number is
5,555 and
the second number is 4,444
the product of 5,555 and4,444= 24686420
to the nearest thousand 5,555= 6000
to the nearest thousand 4,444= 5000
Therefore the product of 6000 and 5000 is
=6000x5000
=30000000
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
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.
To learn more about the rational number visit:
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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
HELP PLEASEEEE! suppose the average wait time for a sandwich at a local deli is 5 min with a standard deviation of 3 min. Is it unusual to get a sandwich in only 12 minutes?
A. Yes because 12 min is more than two standard deviations below the mean.
B. No, because 12 min is less than two standard deviations above the mean.
C. No, because 12 min is more then two standard deviations above the mean.
D. Yes because 12 min is more than two standard deviations above the mean.
Answer:
D
Step-by-step explanation:
Here, we want to state if it is unusual or not get a sandwich in 12 minutes given the mean time and the standard deviation.
The answer here is that it is unusual.
The reason why it is unusual is because, two standard deviations above the mean in this case will be 5 + 3 + 3 = 11
Looking at the value given which is 12, we can see that this value is actually greater than the value which is 2 standard deviations above the mean.
What we are saying here is that 12 is greater than two standard deviation above the mean which is valued at 11
Geometric Sequence♡
5, -2, 4/5
the common ratio was 2/5
find the 10th term
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.
Y-intercept:(??,??)
X-intercept: (??,??)
Answer:
the y-intercept is 2.5 or 2 and 1/2
the x-intercept is 3.5 or 3 and 1/5
Step-by-step explanation:
hope this helps :3
if it did pls mark brainliest
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
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.
175 miles at a speed of 25 miles per hour?
Answer:
That would take you 7 hours to get to your location.
How many 1-inch cubes fill one row of the carton?
Answer: 5 because it has 5 space left
Answer:
5
Step-by-step explanation:
i did this on i-ready and got it right Good luck!