The equation of a rational function that has been translated left 2 units and shifted up 1 unit is: f(x) = (a(x - 2) + b + 1) / (c(x - 2) + d)
What is a function?A relation is a function if it has only One y-value for each x-value.
A general form of a rational function is:
f(x) = (ax + b) / (cx + d)
To translate this function left 2 units, we need to replace x with x + 2. This gives us:
f(x + 2) = (a(x + 2) + b) / (c(x + 2) + d)
To shift this function up 1 unit, we need to add 1 to the numerator. This gives us:
f(x + 2) = (a(x + 2) + b + 1) / (c(x + 2) + d)
Therefore, the equation of a rational function that has been translated left 2 units and shifted up 1 unit is: f(x) = (a(x - 2) + b + 1) / (c(x - 2) + d)
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A sample of 80 high school drama club and art club students were surveyed to choose a favorite free-time activity: playing computer games, listening to music, or watching movies/TV. 50% of the sample is art club students. From the sample, it is found that 18.75% were art club students who prefer playing computer games and 16.25% were art club students who prefer watching movies/TV. 5% were drama club students who prefer playing computer games, while 20% were drama club students who prefer watching movies/TV. 36.25% of the students surveyed chose watching movies/TV. Which of the following is a correct two-way relative frequency table for the data?
Correct two-way relative frequency table for the data is option A.
Describe Frequency table?A frequency table is a way to organize and display data in a table format by showing the number of times a certain data point or category appears in a given dataset. It is used in statistics and data analysis to quickly and easily understand the distribution of a set of data.
A frequency table typically consists of two columns: the first column lists the categories or data points, and the second column lists the frequency or count of each category. The categories can be anything from numbers to words, but they should be mutually exclusive and exhaustive, meaning that each data point should fit into one and only one category, and all possible data points should be included in the table.
Frequency tables are commonly used to represent categorical data, such as survey responses, demographic data, and results of experiments. They are also useful for visualizing patterns and trends in the data, such as the most common or rare categories, and can be used to calculate various statistical measures, such as percentages, proportions, and averages.
The correct answer is:
Playing Listening Watching Row Totals
Computer to Music Movies/TV
Games
Drama Club Students 5% 25% 20% 50%
Art Club Students 18.75% 15% 16.25% 50%
Column Totals 23.75% 40% 36.25% 100%
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The complete question is:
A density curve showing the fuel efficiency of cars is shown.
Which values are the possible measures of center for this density curve? Check all that apply.
answer:
u=30 mpg
median=28 mpg
The possible values of the density curves is mean μ = 30 mpg and the median = 28 mpg
What is the probability distribution?A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.
The mean of probability distribution is also known as expected value. It is denoted by E ( X ). E(X), or mean μ of a discrete random variable X is calculated by multiplying each value of the random variable by its probability and taking the sum of the values.
Given data ,
Let the probability distribution be represented as P
Now , the value of P from the figure is
The balancing point at which a density curve would be in equilibrium if it were formed of solid material is represented by the curve's mean.
A symmetric density curve has the same median and mean.
So , the mean of the probability density curve is μ = 30 mpg
And , the median of the probability density curve lies between 25 and 30
where median = 28 mpg
Hence , the mean and median of the density curve is solved
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The complete question is attached below.
A density curve showing the fuel efficiency of cars is shown.
Which values are the possible measures of center for this density curve? Check all that apply.
Answer:
A and D
Step-by-step explanation:
e2020
The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. What percentage of tires will have a life of 34,000 to 46,000 miles?.
Answer:
Step-by-step explanation:
We know that the life expectancy of the tires is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. Let X be the life expectancy of the tire. Then X ~ N(40,000, 5,000^2).
To find the percentage of tires that will have a life of 34,000 to 46,000 miles, we need to calculate the z-scores for both values using the formula:
z = (X - μ) / σ
where X is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.
For X = 34,000:
z = (34,000 - 40,000) / 5,000 = -1.2
For X = 46,000:
z = (46,000 - 40,000) / 5,000 = 1.2
Now, we need to find the area under the standard normal distribution curve between these two z-scores. We can use a table of standard normal probabilities or a calculator to find this area.
Using a standard normal table or a calculator, we find that the area to the left of z = -1.2 is 0.1151, and the area to the left of z = 1.2 is 0.8849. Therefore, the area between these two z-scores is:
0.8849 - 0.1151 = 0.7698
So, approximately 76.98% of the tires will have a life of 34,000 to 46,000 miles.
Write and solve an inequality for x
.
The figure shows triangle A B C. Point D lies on line A C. Segment B D is perpendicular to line A C. The length of segment B D is x minus 4 units. The length of segment B C is 6 units.
A. x − 4 < 6; x < 10
B. x − 4 < 6; x < 2
C. x − 4 > 6; x < −2
D. x − 4 > 6; x < −10
100 points pls help!!!
The inequality for this problem, along with it's solution, is given as follows:
A. x − 4 < 6; x < 10
What is the segment addition postulate?The segment addition postulate is a geometry axiom that states that when a line segment is divided into a number of smaller segments, the total length is given by the sum of the lengths of each of the smaller segments.
For this problem, we have that BD is a smaller segment of segment BC, hence the inequality is given as follows:
BD < BC.
Replacing with x, the solution is obtained as follows:
x - 4 < 6
x < 6 + 4
x < 10.
Meaning that option a is the correct option.
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PLEASE HELP !! ASAP THANKS :)
Answer:
The graph will shift 3 units down
Which of the following explains why 23(x+3)=23(x−6) has no solution?
Answer:
Step-by-step explanation:
We can expand and simplify the equation as follows:
23(x+3) = 23(x-6)
23x + 69 = 23x - 138
69 = -138
The last equation is clearly false, which means there is no value of x that can satisfy the original equation.
This is an example of a contradiction, where the equation leads to an impossible statement. Therefore, the equation has no solution.
Sam baked for the same amount of time each day for 6 days. He baked cakes and bread. Each day he baked bread for 3 hours. He baked for a total of 72 hours. Use the following information to create an equation that shows the number of hours, x, Sam spent baking cakes each day
Step-by-step explanation:
72 hours total baking during 6 days.
that means 72/6 = 12 hours of baking every day.
3 hours of these 12 hours he used to bake bread.
that leaves 12 - 3 = 9 hours every day for baking cakes.
so, to summarize all this in an arithmetic expression :
x = 72/6 - 3 = 9
what is the length of ab
Answer:
Step-by-step explanation:
[tex]6x-10=2x+18[/tex] (opposite sides of parallelogram are equal)
[tex]4x-10=18[/tex] (subtracted [tex]2x[/tex] from both sides)
[tex]4x=28[/tex] (added 10 to both sides)
[tex]x=7[/tex] (divided both sides by 4)
Substitute [tex]x=7[/tex] to find length AB:
[tex]AB=6x-10[/tex]
[tex]=6[/tex]×[tex]7-10[/tex]
[tex]=32[/tex]
George has opened a new store and he is monitoring its success closely. He has found that this store’s revenue each month can be modeled by r(x)=x2+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x)=x2−4x+5 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r−c)(5) mean about George's new store?
Answer:
(r - c)(5) is the amount of profit generated by the George's store 5 months after it has been open.The total amount of profit 5 months after the store has been open is $5,400.Step-by-step explanation:
Given functions:
[tex]r(x)=x^2+5x+14[/tex]
[tex]c(x)=x^2-4x+5[/tex]
where:
r(x) is the store's revenue each month (in hundreds of dollars).c(x) is the store's expenses each month (in hundreds of dollars).x is the number of months since the store has been open.Profit is calculated by subtracting expenses from revenue.
Therefore, the composite function for profit is:
r(x) - c(x) = (r - c)(x)Since x represents the number of months the store has been open:
(r - c)(5) is the amount of profit generated by the George's store 5 months after it has been open.
To calculate the total amount of profit in the first 5 months, substitute x = 5 into the composite function:
[tex]\begin{aligned}\implies (r-c)(5)&=r(5)-c(5)\\&=(5^2+5(5)+14)-(5^2-4(5)+5)\\&=(25+25+14)-(25-20+5)\\&=(50+14)-(5+5)\\&=64-10\\&=54\end{aligned}[/tex]
Since the revenue and expenses functions are measured in hundred of dollars, so too is the profit function. Therefore, the amount of profit generated in 5 months is $5,400.
the telephone line transfers 5760 KB data in 240 seconds what is the transfer rate per second
The data transfer rate per second is found as: 24 KB / sec.
Explain about the rate of change?Slope is also known as constant rate of change. Divide the change in y-values by both the change in x-values to determine that average rate of change. Identifying changes in measurable parameters like maximum pace or average velocity calls for the knowledge of the average fluctuation rate.Data transfer: 5760 KB
Time : 240 seconds
Rate per second = Data transfer / Time
Rate per second = 5760/ 240
Rate per second = 24
Thus, the data transfer rate per second is found as: 24 KB / sec.
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Explain why y−7x−5=2/6.
Answer:
the expression
y -7/x-5 = 1/3 or 2/6
Step-by-step explanation:
Cross multiplying both sides:
3(y-7) = x - 5
3y - 21 = x - 5
3y - x = 21 - 5
3y - x = 16
The simplified equation is 3y-x=16.
Consider the following piece wise function:
Evaluate the expression: 3f(5) - f(-12)= {fill in the blank)
The answer to the expression is 24.
What is expression?Expression is an action or a way of speaking that shows a feeling, opinion, or attitude. It can be done through words, body language, facial expressions, tone of voice, and other forms of communication. Expression is used to communicate ideas, thoughts, emotions, and feelings. It is a fundamental way of connecting with others and conveying meaning.
To evaluate the expression, we need to first calculate the values of f(5) and f(-12). For f(5), the function is defined as
f(x) = 2x + 3. Thus, f(5) = 2(5) + 3 = 13. For f(-12), the function is f(x) = -x + 7. Thus, f(-12) = -(-12) + 7 = 19. We can now calculate 3f(5) - f(-12) = 3(13) - 19 = 24.
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Pamela is 15 years younger than Jiri. The sum of their ages is 81. What is Jiri's age?
Answer:
Jiri is 48 years old
Step-by-step explanation:
STEP 1
Let Jill's age be equal to: x
Let Pamela's age be equal to :Jiri's age(x) - 15
STEP 2
Total sumof Jiri and Pamela's age= 81
Sum= Pamela's age + Jiri's age
81 = (x-15) + x
81 =x -15 + x
81 = x+x -15
81= 2x -15
Collect like terms
81 + 15= 2x ( recall - changes to + when crossing the =)
96=2x
Divide both sides by 2
96/2 =2x/2
48 = x
Recall Jiri's age is equal to x
Hence Jiri's age is equal to 48
The two figures at right are similar. Give the scale factor, and x and y.
The scale factor is 1.5. And the value of the variables 'x' and 'y' will be 9 and 10, respectively.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
The ratio of the corresponding sides will be constant. Then the scale factor is given as,
SF = 12 / 8
SF = 1.5
The equation is given as,
x / 6 = 12 / 8 = 15 / y
From the first two terms, then we have
x / 6 = 12 / 8
x = 9
From the last two terms, then we have
12 / 8 = 15 / y
y = 10
The scale factor is 1.5. And the value of the variables 'x' and 'y' will be 9 and 10, respectively.
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Mackenzie has $46. 13 less than Taylor. How would you show how
much money Mackenzie has?
Please solve ASAP PLEASE
Answer:
Step-by-step explanation:
46+13 = 59
Answer:
Let Mackenzie have x
and Taylor have y
Then, since Mackenzie has 46.13 less than Taylor,
x = y - 46.13
Therefore, to show how much money Mackenzie has we will use the equation
x = y - 46.13
remember Makenzie has $x.
Taylor has $y
Makenzie money is less than Taylor's money by 46.13
so we take away 46.13 from Taylor's money to get that of Makenzie
Makenzie's money x = Taylor's money y - 46.13
x = y - 46.13
Step-by-step explanation:
Write the equation of a rational function that has been reflected, shifted down 6, right 8, and stretched by a factor of 4.
To write the equation of a rational function that has been reflected, shifted 6 down, 8 to the right and stretched by a factor of 4, we have to start with the basic rational function which is:
f(x)= 1/xThe reflected function we multiply it by -1 resulting in: g(x)= -1/xHow to shift a function?To shift it down by 6, we must subtract 6 from the function, so we have:
h(x) = -1/x-6To shift the function to the right by 8, we substitute x for (x-8), finding this result:
i(x)= -1/(x-8)-6To stretch the function by a factor of 4, we have to multiply the denominator by 4, which will result in:
j(x)= -1/4(x-8))-6Therefore, the equation of the rational function will be:
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A restaurant offers a 13% discount on all of its food. What is the new total after the discount has
been applied to a bill of £39?
Give your answer in pounds and include the £ sign.
Answer:
£33.93
Step-by-step explanation:
A 13% discount means that the new price will be 87% of the original, as 100 - 13 = 87.
This can be calculated by converting the percentage into a decimal, then multiplying by the decimal:
87 / 100 = 0.87
39 * 0.87 = 33.93
The lengths of three line segments are 4 centimeters, 5 centimeters, and 9 centimeters.
Based on the information, we can infer that it is FALSE because it's not possible to construct a triangle with the measures of 4cm, 5cm and 9cm in length on its sides.
How to know if the statement is false or true?To find out if the statement is false or true, we must analyze the information on the lengths of the sides of the triangle and review the construction rules of a triangle to find out if its lengths have any condition.
In accordance with the above, we find that no triangle can be built with these lengths on its sides because, according to the Triangle Inequality Theorem, the sum of two of the sides of the triangle must be greater than the length of the third side. Therefore, if the sum of 4 + 5 results in 9, it is false that we can build a triangle with these measurements.
Note: This question is incomplete. Here is the complete information:
True or false.
Using this information, triangles can be constructed.
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A parking garage opens at 8am Some cars are parked parked in the garage overnight T he graph shows the total number of cars in the garage. What is the slope for this graph?
A. 1
B. 2
C. 3
D. 5
The answer to 3 v12 x V5, given in its simplest form, is avb, where a and b are integers.
Calculate the values of a and b.
The simplest form of the given expression 3√12 × √5 is 6√15.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The given expression is as follows:
3√12 × √5
To solve this problem, we can simplify the expression first:
3√12 × √5 = 3√(12 × 5) = 3√60
To further simplify the expression, we can factor 60 into its prime factors:
60 = 2² × 3 × 5
Here, we can rewrite the expression as:
3√60 = 3√(2² × 3 × 5) = 3 × 2√15
Thus, the values of a and b are a = 6 and b = 15.
Therefore, the simplest form of the given expression is 6√15.
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The correct question is as follows:
The answer to 3 √12 × √5, given in its simplest form, is a√b, where a and b are integers.
Calculate the values of a and b.
2x + 2 = 5x -8 simplify
Many mortgage lenders offer a way to lower your interest rate by paying some of the interest up front. This prepaid interest is known in the industry as points. Each point corresponds to 1% of the amount borrowed. In short, you're paying a fee to lower your interest rate. A lender offers you a 10 year fixed mortgage of 100,000 at 2.7% interest when you buy 1 point Find the monthly payment. Do not round intermediate calculations. Round your answer to the nearest cent.
We have the fοllοwing respοnse after answering the given questiοn: The equatiοn mοnthly payment, rοunded tο the next penny, is $959.49.
What is the equatiοn?In a mathematical equatiοn, the equals sign (=), which cοnnects twο claims and denοtes equality, is utilized. In algebra, an equatiοn is a mathematical statement that prοves the equality οf twο mathematical expressiοns.
Fοr instance, in equatiοn 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressiοns can be used tο describe the relatiοnship between the twο sentences οn either side οf a letter. The lοgο and the particular piece οf sοftware frequently cοrrespοnd. like, fοr instance, 2x - 4 = 2.
[tex]P = \frac{rP}{(1 - (1 + r)^{-n}}[/tex]
where P is the regular mοnthly payment, r is the interest rate each mοnth, n is the number οf payments, and P is the amοunt οf interest that has already been paid in dοllars.
r = 0.027 / 12 = 0.00225
The number οf payments must then be determined. There are 120 mοnthly payments fοr a 10-year mοrtgage.
n = 120
P = 1% * $100,000 = $1,000
Nοw that the data have been entered, we can cοmpute the monthly payment:
[tex]P = (0.00225 \times $99,000 / (1 - (1 + 0.00225)^{(-120)})) + $8.33[/tex]
where $8.33 represents the mοnthly charge fοr the prepaid interest and $99,000 represents the tοtal amοunt bοrrοwed after subtracting the prepaid interest.
If we cοndense this phrase, we get:
P = $959.49
Hence, The mοnthly payment, rοunded tο the next penny, is $959.49.
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a. Substitute 0 for x and, without using a calculator, find the country's population in
The population of the country in 2024, as predicted by this function, is 1,847 million. The population of the country in 2051, as predicted by this function, is 2,927 million.
What are exponential function?An exponential function is a mathematical function that increases or decreases at a rate proportional to its current value. Exponential functions are used in a variety of sciences and everyday applications. For example, population growth is an exponential function of time because the population increases by a fixed percentage each year.
The exponential function f(x) = 565(1.026)ˣ models the population of a country, f(x), in millions, x years after 1970. Substituting 0 for x, the population of the country in 1970 was 565 million. Substituting 27 for x, the population of the country in 1997 was 1,118 million. The population of the country in 2024, as predicted by this function, is 1,847 million. The population of the country in 2051, as predicted by this function, is 2,927 million.
It appears that the population of the country is growing by a factor of 3 every 27 years. This is evident from the fact that the population in 1997 is 3 times the population in 1970, and the population in 2024 is 3 times the population in 1997. This pattern is expected to continue with the population in 2051 being 3 times the population in 2024.
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What is the radius of a sphere that has a surface area of 2903.33 in2?
7.6 in
15.2 in
13.5 in
8.6 in
Answer:
B. 15.2 inches.
You make party favors for an event. You tie 9 inches of ribbon around each party favor. Write an expression for the number of inches of ribbon needed for n party favors.
The ribbon costs $3 for each yard. Write an expression for the total cost (in dollars) of the ribbon.
As a result, the price of the ribbons is proportional to the number of party favours, with each Favour costing (3/4) dollars.
What are quantity and example?A measurable quality such as weight, length, time, volume, or pressure is referred to as quantity. A unit is a unit of measurement that is used to measure other quantities (for example, a gramme, a second, a liter, or a pascal are unit of the above quantities). Chemists employ a wide range of measurements.
The amount of ribbon required for n party favours is calculated as follows:
19n inches (since each party Favour requires 9 inches of ribbon)
As the price is stated in dollars per yard, we must first convert the amount of inches to yards before we can determine the ribbon's total cost. Since there are 36 inches in every yard, we can calculate the number of yards by dividing the total amount of inches by 36:
Total yards of ribbon = (9n) / 36 = (n) / 4
Thus, the following phrase represents the ribbon's overall cost:
3 × (n/4) = (3n) / 4 dollars
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Come someone explain/help me how to do this? really appreciate it!
The monthly periodic rate is 1.25%, the finance charge is $6.99 and John's new balance is $566.24.
How to determine the monthly periodic rateThis monthly periodic rate calculated as
Monthly periodic rate = Annual percentage rate / 12
So, we have
Monthly periodic rate = 15% / 12
Monthly periodic rate = 1.25%
The finance chargeThis is the interest charged for the month.
So, we start by calculating the average daily balance using:
Average daily balance = ((Previous month's balance + Current month's purchases and cash advances) - Current month's payments and credits) / Number of days in the month
Substitute the known values in the above equation, so, we have the following representation
Average daily balance = (428.10 + 281.15) - 150.00) / 31
Average daily balance = $18.04
So, we have
Finance charge = Average daily balance x Monthly periodic rate x Number of days in the month
Finance charge = $18.04 x 1.25% x 31
Finance charge = $6.99
The value of John's new balanceThe new balance is calculated as
New balance = Previous month's balance + Current month's purchases and cash advances + Finance charge - Current month's payments and credits
Substitute the known values in the above equation, so, we have the following representation
New balance = $428.10 + $281.15 + $6.99 - $150.00
New balance = $566.24
Hence, the new balance is $566.24
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find the perimeter of P and area of A of triangle JKL J(-5,-7),K(2,3),L(-1,-7)
Answer: To find the perimeter of triangle JKL, we need to find the length of each side and add them up. We can use the distance formula to find the length of each side:
Side JK = sqrt[(2 - (-5))^2 + (3 - (-7))^2] = sqrt[7^2 + 10^2] = sqrt[149]
Side KL = sqrt[(-1 - 2)^2 + (-7 - 3)^2] = sqrt[(-3)^2 + (-10)^2] = sqrt[109]
Side LJ = sqrt[(-1 - (-5))^2 + (-7 - (-7))^2] = sqrt[4^2] = 4
Therefore, the perimeter of triangle JKL is:
P = JK + KL + LJ = sqrt[149] + sqrt[109] + 4
To find the area of triangle JKL, we can use the formula:
A = 1/2 * base * height
We can choose any side as the base, and the corresponding height will be the perpendicular distance from the opposite vertex to the base. Let's choose side KL as the base. The height from vertex J to side KL is the perpendicular distance between J and the line containing KL. We can find this distance using the formula for the distance between a point and a line:
Area = 1/2 * KL * h
where h = |(2 - (-1))( -7 - 3) - (-5 - 2)(-1 - 3)| / sqrt[(-1 - 2)^2 + (-7 - 3)^2]
Simplifying the above expression, we get:
h = 24 / sqrt[109]
Therefore, the area of triangle JKL is:
A = 1/2 * KL * h = 1/2 * sqrt[109] * 24 / sqrt[109] = 12
So, the perimeter of triangle JKL is sqrt[149] + sqrt[109] + 4, and the area of triangle JKL is 12.
Step-by-step explanation:
Can someone please help me with this math problem?
Determine if the relation is a function. If it is not, What are the two ordered pairs as proof?
Using the vertical line test we can see that this is not a function.
Is the relation a function?When we have a graph of a relation, one thing we can do to check if this is a function is do the vertical line test.
If you can draw a vertical line that intercepts the graph more than once, then it is not a function.
Here we can see a circle, multiple lines intercept the graph twice,so this is not a function.
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Give the following angle as a bearing. 54
Answer:
Step-by-step explanation:
20 degees
Please help!!
Complete the identity
cos^2 θ/2=?
According to algebraic identities ,
[tex] \cos( \frac{ \theta}{2} ) = \sqrt{ \frac{1 + \cos(\theta) }{2} } \\ [/tex]
Therefore ,
[tex]\boxed{ { \cos}^{2} (\frac{\theta}{2} ) = \frac{1 + \cos(\theta) }{2} } \\ [/tex]
hope helpful! :)
Answer:
Using the half-angle formula for cosine, we can express cos(θ/2) in terms of the values of cos θ and sin θ:
cos(θ/2) = ±√[(1 + cos θ)/2]
The sign of the square root depends on the quadrant in which θ/2 lies.
Since we are given cos^2 θ/2, we need to eliminate the square root in the expression for cos(θ/2). To do this, we can use the fact that:
sin^2 θ/2 = 1 - cos^2 θ/2
Substituting the expression for cos^2 θ/2 from the previous identity, we get:
sin^2 θ/2 = 1 - cos^2 θ/2 = 1 - cos^2 (θ/2)
Solving for cos(θ/2) in terms of sin(θ/2), we get:
cos(θ/2) = ±√[1 - sin^2 θ/2]
Substituting the expression for sin^2 θ/2 from above, we get:
cos(θ/2) = ±√[cos^2 θ/2]
The sign of the square root depends on the quadrant in which θ/2 lies. Therefore, the completed identity for cos^2 θ/2 is:
cos(θ/2) = ±cos θ/2
Step-by-step explanation: