Given f(x)=4(x−2)^3+2, classify each statement about f^−1(x) as true or false.
Choose the answers which are correct or false.
1. The point of symmetry on f^−1(x) is (2,2).
2. The domain of f^−1(x) is (−∞,4).
3. The graphs of f^−1(x) and f(x) are reflections across the line y = x
4. f^−1(x) is not a function.
Answers
Answer:
1. True
2. False
3. True
4. False
Step-by-step explanation:
Given function:
[tex]f(x)=4(x-2)^3+2[/tex]
1. Point of SymmetryThe point-of-symmetry of a cubic graph is its point of inflection.
To find the x-value of the point of inflection of a cubic function, differentiate the function twice:
[tex]f'(x)=12(x-2)^2[/tex]
[tex]f''(x)=24(x-2)[/tex]
Set the second differentiated function to zero and solve for x:
[tex]\implies 24(x-2)=0[/tex]
[tex]\implies x-2=0[/tex]
[tex]\implies x=2[/tex]
Substitute the found value of x into the original function to find the y-value of the point of inflection:
[tex]\implies y=4(2-2)^3+2[/tex]
[tex]\implies y=4(0)^3+2[/tex]
[tex]\implies y=0+2[/tex]
[tex]\implies y=2[/tex]
Therefore, the point of symmetry of the cubic function is (2, 2).
The inverse of a cubic function its reflection in the line y = x.
As the point of symmetry is (2, 2), then its reflection in the line y = x is also (2, 2).
So the point of symmetry on f⁻¹(x) is (2, 2).
2. DomainThe given function has an unrestricted domain and range.
Domain of f(x): (-∞, ∞) → all real numbersRange of f(x): (-∞, ∞) → all real numbersThe domain of the inverse function is the range of the function.
The range of the inverse function is the domain of the function.
Therefore, as the domain and the range of the original function are unrestricted, so are the domain and range of the inverse function.
Domain of f⁻¹(x): (-∞, ∞) → all real numbersRange of f⁻¹(x): (-∞, ∞) → all real numbers3. Reflection across the line y = xThe inverse of a cubic function with an unrestricted domain is its reflection across the line y = x.
Therefore, the graphs of f⁻¹(x) and f(x) are reflections across the line y = x.
4. Inverse functionTo find the inverse of the given function, swap x and y:
[tex]\implies x=4(y-2)^3+2[/tex]
Rearrange to make y the subject:
[tex]\implies x-2=4(y-2)^3[/tex]
[tex]\implies \dfrac{x-2}{4}=(y-2)^3[/tex]
[tex]\implies \sqrt[3]{\dfrac{x-2}{4}}=y-2[/tex]
[tex]\implies y=\sqrt[3]{\dfrac{x-2}{4}}+2[/tex]
Replace y with f⁻¹(x):
[tex]\implies f^{-1}(x)=\sqrt[3]{\dfrac{x-2}{4}}+2[/tex]
As we have already established, the domain and range of the inverse function are unrestricted. As each x-value has only one y-value associated with it, f⁻¹(x) is a function.
Related Questions
Helpp
can you tell me how???
Answers
2 a) The letter A represents the value 0/3 on the number line.
2 b) The letter B represents the value 1/3 on the number line.
What is a number line?
A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.
The number line is given.
The letter A represents the value of 0.
Find the value of 0/3.
Zero divided by anything yields the value 0.
Therefore, the value 0/3 is represented by letter A = 0.
Find the value of 1/3.
The decimal notation of fraction 1/3 is 0.33.
The value of 1/2 is 0.5.
This number should lie between 0 and 0.5.
Therefore, the value 1/3 is represented by letter B.
To learn more about number line from the given link
https://brainly.com/question/25230781
#SPJ1
2a) Which letter represents the better 0/3?
2b) Which letter represents the better 1/3?
Kimberley's car can go 290 km on 21 L of gas. How far will her car go on 31 L of gas?
Answers
Answer:
428km
Step-by-step explanation:
21 L=290km
1 L=290/21
31 L=290/21×31=428km (to 3 s.f.)
3. There were 340,000 cattle placed on feed.
Write an equivalent ratio that could be
used to find how many of these cattle were
between 700 and 799 pounds. How many
of the 340,000 cattle placed on feed were
between 700 and 799 pounds?
Answers
The number of cattle would be 136,000 and the comparable ratio would be 4/10.
What is the equivalent ratio?When we compare two ratios, they are said to be equivalent.
To determine whether two or more ratios are equivalent, they can be compared to one another.
For instance, ratios 1:2 and 2:4 are equivalent.
Equivalent ratios are two ratios with the same value.
By multiplying or dividing the two amounts by the same number, you may determine the corresponding ratio.
Finding equivalent fractions follows the same procedure.
So, an equivalent ratio is required by the question.
This refers to a fraction that is equal to 2/5 of the fraction between 700 and 799.
We multiply the numerator and denominator by the same amount to produce an equivalent fraction.
When we divide both by 2, we get:
(2*2)/(5*2) = 4/10
While working with thousands, tenths are helpful since subtracting a zero when taking a tenth makes it usable.
As a result, 1/10 would equal 34000, and 4/10 would equal four times that: 4(34000) = 136000.
Therefore, the number of cattle would be 136,000 and the comparable ratio would be 4/10.
Know more about equivalent ratios here:
https://brainly.com/question/2328454
#SPJ1
Complete question:
There were about 340,000 cattle placed on feed. Write an equivalent ratio that could be used to find how many of these cattle were between 700- 799 pounds. How many of the 340,000 cattle placed on feed were between 700-799 pounds?
Weight Group. Fraction of total cattle
less than 600. 1\5
pounds.
600-699. 11/50
700-799. 2\5
800. 9\20
two of the six-membered rings are represented in chair conformations. the connection between these two rings is analogous to
Answers
When two of the six membered rings are represented in chair conformations, the connection between these two rings is analogous to cyclohexane bridge.
A "cyclohexane bridge," where the two six-membered rings are connected by two carbon atoms, which act as a bridge between them. The conformation of this bridge can vary, and it is often depicted as a zigzag line in organic chemistry diagrams.
The exact conformation of the bridge and the two chair conformations of the rings will depend on the specific molecule being discussed.
To know more about cyclohexane bridge here
https://brainly.com/question/17019157
#SPJ4
-- The given question is incomplete, the complete question is
"When two of the six membered rings are represented in chair conformations, the connection between these two rings is analogous to _______" --
what is the midsegment of a triangle? the triangle midsegment is a segment joining the of two sides of a trinagle. what is the triangle midsegment theorem? if a segment joins the of two sides of a triangle, then the segment is to the third side and as long.
Answers
The triangle midsegment is a very important concept in geometry, and the triangle midsegment theorem states that the midsegment of a triangle is parallel to the third side and has a length equal to half of the length of the third side
The triangle midsegment theorem states that the midsegment of a triangle is parallel to the third side of the triangle and has a length that is equal to half of the length of the third side.
In this explanation, we will define the midsegment of a triangle and explain the triangle midsegment theorem in more detail.
To begin, let's consider a triangle ABC with midpoints D and E on sides AB and AC respectively. The segment DE is the midsegment of triangle ABC.
According to the triangle midsegment theorem, the length of DE is equal to half the length of the third side of the triangle, BC. Mathematically, this can be represented as follows:
DE = BC/2
In addition to the length, the midsegment of a triangle is also parallel to the third side. This means that if we extend the midsegment, it will eventually intersect the third side of the triangle.
The triangle midsegment theorem states that the midsegment of a triangle is parallel to the third side and also has the same length as half of the third side.
To know more about triangle here.
https://brainly.com/question/8587906
#SPJ4
rewrite this question without any fractions or decimals, ill give points if u help thx
Answers
Answer:
14x + 36 = 15
Step-by-step explanation:
To remove the fractions, multiply the entire equation by the LCM of 9 and 6.
LCM of 9 and 6 = 18
Multiply the entire equation by 18,
[tex]18*\dfrac{7}{9}x+*18*2=18*\dfrac{5}{6}[/tex]
2*7x + 36 = 3 *5
14x + 36 = 15
Let's consider what the question asks for:
--> equation without fractions:
To get rid of fractions, we must multiply a common multiple of 9 and 6 to get rid of the bottom denominator:
--> common multiple of 9 and 6: 54
Let's multiple:
[tex]\dfrac{7}{9}x+2=\dfrac{5}{6} \\\\54*(\dfrac{7}{9}x+2} )=54*\dfrac{5}{6} \\\\6*7x+108=9*5\\\\42x+108=45[/tex]
Answer: 42x + 108 = 45
Mr. Wilson's height is at least 6 inches more than twice his daughter's height. If he is 76 inches tall, what is the tallest that his daughter can be?
Answers
The tallest that his daughter can be is 35inches.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given;
Mr. Wilson's height is at least 6 inches more than twice his daughter's height.
He is 76 inches tall.
Now, let the height of daughter be x
So, 2x+6=76
x+3=38
x=35
Therefore, by the equation the height of daughter will be 35inches.
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ1
For organisms which need a partner for reproduction but rely on a chance encounter for meeting a mate, the birth rate is proportional to the square of the population. Thus, the population of such a type of organism satisfies a differential equation of the formdP/dt=aP2−bPwith a,b>0.Sketch a graph of dP/dt against P. Note when dP/dt is positive and negative.
Answers
The graph of dP/dt against P is a parabola, with the equation of the form [tex]y = ax^2 - bx[/tex] where a and b are positive parameters.
The graph has a vertex at [tex](b/2a, -b^2/4a)[/tex].
When P is less than b/2a, dP/dt will be positive, meaning the population is increasing. As P increases, dP/dt will reach a maximum at (b/2a, -b^2/4a) and then decrease, meaning the population is decreasing. When P is greater than [tex]b/2a, dP/dt[/tex] will be negative.
For example, if a = 4 and b = 1, the graph of dP/dt against P is [tex]y = 4x^2 - x[/tex], with the vertex at (0.5, -0.125). When P is less than 0.5, dP/dt will be positive, and when P is greater than 0.5, dP/dt will be negative.
Learn more about vertex here:
https://brainly.com/question/12563262
#SPJ4
Jake paints 13 birdhouses red. He wants 7 yellow. How many more does he paint red than yellow? Use the strategy Make 10 to subtract
Answers
As per unitary method, Jake painted 6 more birdhouses red than yellow.
The Unitary Method is a strategy used to simplify mathematical calculations. The idea is to make the calculation easier by breaking down the numbers into smaller parts and then recombining them to find the final answer.
In this problem, we want to find out how many more birdhouses Jake painted red than yellow. To do this, we'll use the Unitary Method to subtract 7 from 13.
Starting with the larger number, we'll break down 13 into 10 and 3. We can then subtract 7 from 10 and find that there is a difference of 3.
This means that we have 3 left over from the larger number, which we can add to the smaller number (3) to find the final answer.
Therefore, the final answer is 3 + 3 = 6.
To know more about unitary method here,
https://brainly.com/question/28276953
#SPJ4
Find the geometric mean of √7 and √343.
Answers
Answer: 7 √7
Step-by-step explanation: If you find the greatest common factor of 343, you get 49 and 7 and 49 breaks down to 7 and 7. you now have 3 7's. You now group two of those sevens and bring it out of the radical, leaving one 7 under the radical. This gives you 7 √7.
Russell and Valerie start to walk away from the Cafeteria to their classes.
Russell walks 10 yards due West, then turns 40° toward South and walks 5 yards.
Valerie walks 10 yards due East, then turns 60° toward North and walks 5 yards.
Which student is farther from the cafeteria? Explain how you know using a diagram and words.
Answers
The person that is farther from the cafeteria would be Valerie.
How is Valerie farther from the Cafeteria?To determine which student is farther from the cafeteria, we need to calculate the distance each student has traveled from the cafeteria.
For Russell, his total displacement can be calculated using vector addition:
10 yards (due West) + 5 yards (South of West) = 10.87 yards at an angle of 305° from due West.
For Valerie, her total displacement can be calculated using vector addition:
10 yards (due East) + 5 yards (North of East) = 12.5 yards at an angle of 75° from due East.
Since the magnitude of the vector representing Valerie's displacement is larger, she is farther from the cafeteria.
Read more on distance here:https://brainly.com/question/2854969
#SPJ1
given the scores 41, 44, 99, 46, 39, 47, 38, 46, what measure of central tendency should you compute?
Answers
A measure of central tendency is a single data that represents the center spot of a dataset. This data can also be known as “the central location” of a dataset.
In statistics, there are mainly three common measures of central tendency:
1. The mean is: (41 + 44 + 99 + 46 + 39 + 47 + 38 + 46) / 8 = 46
2. The median is:
38, 39, 41, 44, 46, 46, 47, 99
Middle values: 44 and 46
Average of middle values: (44 + 46) / 2 = 45
The median of this data set is 45.
3. In this case, the mode is 46, as it appears twice in the data set.
All of these measures find the central location of a dataset using various methods. Depending on the type of data you are analyzing, one of these three measures may be better to use than the other two.
To know more about Central Tendency:
https://brainly.com/question/30218735
#SPJ4
I need help the question is Becca hit 7 more home runs than Beverly hit? which equation and solution represents this scenario
Answers
Becca hit 21 + 7 = 28 home runs.
The addition is the method of adding two or more entities together. In math, addition is the procedure of calculating the sum of two or more numbers.
It is a preliminary arithmetic operation that is typically used in our day-to-day life. One of the most common uses of addition is when we deal with money, calculate our bills, or calculate time.
The addition is an operation used to sum up, numbers. The result that is received after addition is known as the sum of the given numbers.
For example, if we wish to calculate the Becca hit, we would add the Beverly hit and 7.
To know more about arithmetic operation, here
https://brainly.com/question/25834626
#SPJ4
--The given question is incomplete; the complete question is
"Becca hit 7 more home runs than Beverly. Beverly hit 21 home runs. How many runs did Becca hit?"--
Maliyah buys a bus ticket to New Orleans, her favorite city in America. The original price of $120 . She uses a coupon code to get a 20% discount off of the original price . She is then charged a 6% tax on the discounted price . What is the final cost for Maliyah's bus ticket
Answers
As per unitary method, Maliyah's bus ticket to New Orleans will cost $101.76 after using a coupon code and paying the tax.
The Unitary Method is a problem-solving strategy that is used to break down complex problems into smaller, more manageable parts.
To determine the final cost of Maliyah's bus ticket to New Orleans, we will use the unitary method of problem solving. This method involves breaking down the problem into smaller parts and solving each part separately to find the final answer.
The first step is to find the discounted price of the ticket. To do this, we multiply the original price of $120 by the discount percentage of 20%.
$120 * 0.20 = $24
Next, we subtract this amount from the original price to get the discounted price.
$120 - $24 = $96
Next, we find the amount of tax charged on the discounted price by multiplying the discounted price by the tax rate of 6%.
$96 * 0.06 = $5.76
Finally, we add this amount to the discounted price to get the final cost of the ticket.
$96 + $5.76 = $101.76
To know more about unitary method here.
https://brainly.com/question/28276953
#SPJ4
a lawn can be mowed by 8 people in 6 hours. if 3 people take the day off and do not help mow the grass, how many hours will it take to mow the lawn?
Answers
If 8 people can mow the lawn in 6 hours, then the rate at which a single person mows the lawn is 1/6 of the total area. When 3 people take the day off, the number of people mowing the lawn becomes 8 - 3 = 5.
Therefore, the rate at which the 5 remaining people mow the lawn is 5 * 1/6 = 5/6 of the total area.
The time it takes to mow the lawn is inversely proportional to the rate at which the people mow the lawn.
So, to find the time it takes to mow the lawn with 5 people, we can divide the original time of 6 hours by the new rate of 5/6:
6 hours / (5/6)
= 6 * (6/5) hours
= 7.2 hours
So, it will take 7.2 hours to mow the lawn with 5 people.
For such more question on total area
https://brainly.com/question/27950508
#SPJ4
Which fraction is equivalent to 0.23?
OA /
О в.
O C.
O D.
231
990
23
99
23
100
OE. /
Answers
Answer:
23/100
Step-by-step explanation:
HELP I WILL GIVE BRAINLEST!!! Solve for the value of r
Answers
13r-2=180
13r=182
Solution
R=14
5r-5+8r+3=180
Next, combine like terms.
13r-2=180
Then get r by itself
13r=182
r=14
Hope that helped!
This is so difficult
Answers
The relation that represents a function is the last one:
x: 1, 2, 3, 4
y: 1, 1, 1, 1,
What relation representes y as a function of x?A function is a relation where each one of the inputs is mapped into a single one output.
For example the first option has the input x = 1 mapped into 3 different outputs, then it is not a function.
The only one that is a function is the last one:
x: 1, 2, 3, 4
y: 1, 1, 1, 1,
Where none of the inputs appears more than one time.
Learn more about functions at:
https://brainly.com/question/2328150
#SPJ1
Question
Explain why a linear function that is continuous has an infinite number of solutions. Then determine which of the following representations show all the solutions of the function: a table, a graph, or an equation.
Answers
There are infinitely many possible solutions to a continuous linear function graph or equation.
What is an example of a linear function?A constant rate of change here in the coordinate plane describes a straight line. As an illustration, the equation y = 3x – 2 depicts a linear function since it is a straight line in the coordinate plane. This function may be expressed as f(x) = 3x - 2 since y can be substituted with f(x).
An unlimited number of solutions exist for a linear function. Therefore, we may replace the domain with an endless amount of values.
A table lists all of the possible solutions.
All of the solutions are represented by an equation or graph.
To know more about Linear function visit:
https://brainly.com/question/29205018
#SPJ1
What is the difference between qualitative forecasting techniques and quantitative forecasting techniques?
Answers
The difference between qualitative forecasting techniques and quantitative forecasting techniques is:
Quantitative projections frequently rely on historical information, like past sales and income numbers, production and financial reports, and website visitor statistics. You may use seasonal sales data, for instance, to estimate the production and labour requirements for the upcoming year based on the monthly or quarterly results from the previous year. Additionally, statistical modelling, trend analysis, or other information from authoritative sources like governmental organisations, professional groups, and academic institutions are used in quantitative forecasting.
Techniques for qualitative forecasting are derived from the knowledge and intuition of seasoned business professionals. These forecasting methods involve data interpretation together with the expert knowledge you've gained through years of work experience, so they go beyond simple guesswork. For instance, if you require qualitative data to predict sales for the year, you may calculate the influence of a new advertising campaign or promotion your business is preparing, consider the implications of emerging technology for customer behaviour, and consider current social fads and trends.
Learn more about forecasting techniques:
https://brainly.com/question/28494130
#SPJ4
AP Calculus...
May I have a little help...
Answers
You posted way too many questions. The rule is one question at a time.
I'll answer question 14 to get you started.
We are told that
f(4) = -1f(6) = 1The values -1 and 1 don't really matter. All we care about is the sign change from negative to positive or vice versa. This sign change tells us that f(x) must be zero at least once in the interval [4, 6]. Refer to the intermediate value theorem for more information. Therefore, we have at least one root in the interval [4, 6].
Visually you can think of it like being in United States (below the x axis; negative territory) and then moving to Canada (above the x axis; positive territory). Since f(x) is a continuous function, the curve must cross the border at least once. The border represents the x axis. The term "root" is another way of saying "x intercept".
The previous paragraphs all help point to the fact that statement I is valid. Unfortunately, we don't have enough information to determine if statement II is valid or not. The function f(x) may have an absolute max on this interval, or it may not. We would need info about its derivative.
----------------
Answer to problem 14 is "I only" which is choice B.
A boat is heading towards a lighthouse, whose beacon-light is 141 feet above the water. From point A, the boat's crew measures the angle of elevation to the beacon, 7 , before they draw closer. They measure the angle of elevation a second time from point B at some later time to be 14°. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Answers
The distance that exists from point A to B is 583 feet
How to solve for the distanceThe distance is given as Xa - Xb
WE have to solve for Xa
Tan 7 = 141 / Xa
Xa = 141 / Tan 7
Xa = 1148.4
Next we have to solve for xB
At B the vertical change remains 141 we are to find XB using the angle 14 degrees
Tan 14 = 141 / Xb
Xb = 141 / tan 14
Xb = 565.52
Then the distance = 1148.4 - 565.52
= 582.88
≈ 583 feet
Read more on distance here:https://brainly.com/question/2854969
#SPJ1
Law of cosines: a2=b2+c2-2bccos(A)
What is the measure of angle N to the nearest whole degree
Answers
The measure of the angle N will be 82.8 degrees.
What is the law of cosines?The square of the length of any one side of a triangle is equal, by the cosine rule, to the sum of the squares of the lengths of the other two sides, multiplied by the cosine of the angle they are a part of.
Given that the formula form cosine law is,
a²=b²+c²- 2.bc.cos(A)
Let us assume the values a = 6, b = 5, and c = 4. The angle N will be calculated as:-
a²=b²+c²- 2.bc.cos(A)
6² = 5² + 4² - 2 x 5 x 4 cos(A)
36 = 25 + 16 - 40cos(A)
-5 = - 40cosA
cosA = 1 / 8
A = cos⁻¹( 1 / 8 )
A = 82.81°
Therefore, the value of angle N is 82.81°
To know more about the law of cosines follow
https://brainly.com/question/4372174
#SPJ1
The table shows the cost per pound of various vegetables at a farmers’ market.
Two people purchase 2 1/2 pounds of pinto beans, 1 1/3 pounds of brussels sprouts, and 2 pounds of olives. If the people split the total cost evenly, enter the cost per person of the purchased vegetables in the space provided.
Answers
The required cost per person of the purchased vegetables is given as $7.62.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
The total cost of vegetables for 2 1/2 pounds of pinto beans, 1 1/3 pounds of brussels sprouts, and 2 pounds of olives is given as,
= 5/2× 1.24 + 4/3 ×2.82 + 2 × 4.19
= $15.24
This, amount of the bill is split between two people,
= 15.24 / 2
= $7.62
Thus, the required cost per person of the purchased vegetables is given as $7.62.
Learn more about arithmetic here:
https://brainly.com/question/11424589
#SPJ5
I need help this can anybody help me
Answers
By transitive property, proved RQ is parallel to SU.
What are parallel lines?Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.
Given that,
RS║VT
∠6≅∠3
To prove: RQ║SU
RS║VT (Given)
∠6≅∠3 (Given)
∠5≅∠3 (Alternate interior angles between the parallels RS and VT)
Now, ∠6≅∠5 (Transitive property)
Since, ∠6 is congruent to ∠5, then they are alternate angles between RQ and SU.
Then, RQ║SU
Hence, proved RQ is parallel to SU.
To learn more about parallel lines visit:
https://brainly.com/question/16701300.
#SPJ1
pls help me dont understand
Answers
Answer: -3/5
Step-by-step explanation:Where is says f(3/5), plug the value of 3/5 wherever you see x. In this case it would be after the negative 5 and positive 2. Solve the rest using basic addition,subtraction, and multiplication rules. The answer should turn out to be -3/5/
would you expect the data sets described below to possess relative frequency distributions that are symmetric, skewed to the right, or skewed to the left? explain
Answers
the correct choice is tilted to the right.
What is frequency distribution?
The gathered data is arranged in tables based on frequency distribution. The information could consist of test results, local weather information, volleyball match results, student grades, etc. Data must be presented meaningfully for understanding after data gathering. A frequency distribution graph is a different approach to displaying data that has been represented graphically.
The given statement is "The salary of everyone employed by a large university."
The distribution is skewed to the right because the starting pay for all employees at a large university is modest and there may be select positions with significant payouts.
Therefore, the correct choice is tilted to the right.
Learn more about frequency distribution, by the following link
https://brainly.com/question/16698786
#SPJ4
[tex] log_{a}(15) = m \: and \: log_{a}(5) = n \\ then \: what \: is \: \\ log_{a}( \sqrt{3} ) [/tex]
options =
1)
[tex] \frac{1}{2}n - m [/tex]
2)
[tex] \frac{1}{2} (n - m)[/tex]
3)
[tex]n \times m[/tex]
4)
[tex]n \div m[/tex]
Answers
Answer:
m-n/2
Step-by-step explanation:
we are here given that,
[tex]\longrightarrow \log_{a}(15)=m [/tex] and ,
[tex]\longrightarrow \log_{a}(5) = n [/tex]
Taking the first given equation, we have;
[tex]\longrightarrow \log_{a}15=m \\ [/tex]
[tex]\longrightarrow \log_{a}(5\times 3) = m\\[/tex]
[tex]\longrightarrow \log_a 5 + \log_a 3 = m [/tex]
now substitute the value from second equation,
[tex]\longrightarrow n + \log_a 3 = m \\ [/tex]
[tex]\longrightarrow \log_a(\sqrt3)^2 = m - n \\ [/tex]
[tex]\longrightarrow 2 log_a \sqrt3 = m - n \\ [/tex]
[tex]\longrightarrow \underline{\underline{ \log_a \sqrt3 = \dfrac{m-n}{2}}} [/tex]
And we are done!
Please help!! Urgent!
Answers
The values x = -1 and x = 7 are the real solutions of the given graph.
Finding the roots of a cubic graphical equationA cubic formula incorporating the nth roots, the four fundamental operations of arithmetic, and the four coefficients (radicals).
The required real roots for the function f(x) = 0 are the points where the given curve intersects the x-axis on the graph.
From the given graph, we can see that the real solution of the given graph are x = -1 and x = 7.
Learn more on cubic graph here: https://brainly.com/question/20333781
#SPJ1
Graph one period of: y = -8 cos 5x
Answers
The graph of one period of: y = -8 cos 5x is graph (a)
How to determine the graphFrom the question, we have the following parameters that can be used in our computation:
y = -8 cos 5x
Tto graph one period of y = -8 cos 5x, we use the following
Determine the amplitude and period of the function. In this case, the amplitude is 8 and the period is 2π/5.Plot the maximum and minimum values of the function over one period. These occur when cos 5x is equal to 1 and -1, respectively.Connect the maximum and minimum points with a smooth curve to form one period of the function.
In this case, the graph is (a)
Read more about trigonometry at
https://brainly.com/question/24349828
#SPJ1