Which product is less than 5/8? 4/3×5/8, 3/2×5/8, 7/10×5/8, 9/7×5/8
Answers
Related Questions
math project : I need an interesting project idea for mathematics that can relate 3 different topics, I should write a full research paper related on the topic this are some examples related to the project
You must state a question that you would like to answer. This must be a specific question within your topic and should be explored thoroughly to create a complete paper.
Examples:
(i) How can we use Mathematical/Calculus-based tools to study the spread of COVID-19?
(ii) Designing a new Mathematical/Calculus-based model to analyze the spread of COVID-19
(iii) How many entrances should there be at Expo to accommodate all visitors?
(iv) How much water does the UAE need in order to sustain its ever changing population? (i.e. comparing water usage vs. water production)
Literature review:
You must show using multiple references and sources of the current literature on your given topic. This does NOT imply that information is simply copied from the internet but rather you must present a comprehensive review and summary of the latest research on your topic. It is suggested that you chose a specific aspect of your topic in order to include all required elements.
Examples:
(i) Review of the existing Mathematical/Calculus-based models used to analyze the spread of COVID-19
(ii) Review of existing Mathematical/Calculus-based models and calculations regarding risk insurance.
Answers
A mathematics topic that van be looked into is how linear algebra, graph theory and optimization can be used on the airline industry.
How to explain the informationIn this case, to solve the scheduling issues faced by airlines such as planning flights, assigning planes and crews to routes - mathematical techniques can be employed.
By leveraging Linear Algebra, operators can simulate the flow of aircrafts and passengers while Graph Theory can help model flight schedules and aircraft routes.
Simultaneously using Optimization techniques in the problem-solving process can work to streamline various operations resulting in reduced costs and improved efficiency which can increase profit margins.
Learn more about mathematics on:
https://brainly.com/question/929808
#SPJ1
Translate the phrase into an algebraic expression.3 more than b
Answers
3 more than b means b plus 3.
Translating into an algebraic expression, we have:
\(b+3\)Answer: b + 3.
how do i do this ? find the domain + range of a graph ?
Answers
Answer:
its 4 i know it
Step-by-step explanation:
Find m and c for this line
Y+3x=1
Answers
Answer:
m = -3 ; c = 1
Step-by-step explanation:
y = -3x + 1
y = mx + c
m = -3
c = 1
Evaluate |x - y| + 4 if x = -1, y = 3, and z = -4.
Answers
Answer:
8
Step-by-step explanation:
Substitute the values in the expression, we have:
\(\displaystyle{|-1-3|+4}\)
Evaluate:
\(\displaystyle{|-4|+4}\)
Any real numbers in the absolute sign will always be evaluated as positive values. Thus:
\(\displaystyle{|-4|+4 = 4+4}\\\\\displaystyle{=8}\)
Hence, the answer is 8. A quick note that z-value is not used due to lack of z-term in the expression.
1. At her new job Mary earns $100 more than twice the salary she earned as a college intern.
If she now earns $2100, how much did she earn as an intern?
Answers
Answer:
$1000
Step-by-step explanation:
Inverse operation
2100-100=2000
2000/2=1000
Sorry if its wrong but hope this helpssss
Graph the system of equations on your graph paper to answer the question.
{y=x−4y=−x+6
What is the solution for this system of equations?
Answers
Answer: (5 , 1)
Step-by-Step explanation:
hihi your problem is a system of question y = x-4 and y = -x+6 okay so graph them both normally and then find the point where they intersect which is gonna be a coordinate point, and that's your solution !!
y = x-4
the y intersect is going to be 4
the slope is a positive 1 , going up to the right, through the positive quadrant, line is facing to the right
y = -x+6
the y intersect is going to be -6
the slope is going to be a -1 , following up the opposite way the line is going to face the left
once you graph them both you'll see the point of intersection, the solution
make sure you drew your lines very clearly !!!!
the solution is x = 5 and y = 1 which is also (5 , 1)
hopefully this was helpful !
x=a\(a-3\sqrt{x^{3} -8a+3\)
Answers
Using long division;
\(\frac{a^3-3a+3}{a-3}=a^2+3a+1+\frac{6}{a-3}\)The time t(in minutes) required to empty a tank of wastewater varies
inversely with the rate r (in gallons per minute) of pumping. The constant of
variation is 56. Find the time it will take to empty the tank when the rate is 4
gal/min
O A. 14 minutes
O B. 52 minutes
O .
C. 224 minutes
O D. 0.07 minutes
Answers
Answer:
A.
Step-by-step explanation:
answer A. 14 minutes is your answer
pls help me!! thank you!!
Answers
Full working out shown from step 1 to last.
follow it and you get 24 square feet as final answer. Good luck in other questions!!!
what is an equation of a parabola with a with the given vertex and focus vertex: (-2, 5) focus: (-2, 6)
Answers
Answer:Equation of parabola is
4y=x2+4x+24
Step-by-step explanation: Hope This helps!
which table does not show y as a function of x?
Answers
Answer:
I am confident the answer is H.
9.949 round to the nearest tenth and hundredth
Answers
9.9 and 9.95 are the result of rounding off 9.949 to the nearest tenth and hundredth.
What is Rounding off?When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For whole numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done. An integer with one or more "0"s at the end in a specific base is said to be round. In this way, 590 is more rounded than 592 but less rounded than 600. A round number is frequently understood to stand for a value or values close to the nominal value expressed in both formal and informal language.So, rounding off:
9.949 (nearest tenth) = 9.99.949 (nearest hundredth) = 9.95Therefore, rounding off of 9.949 to the nearest tenth and hundredth is 9.9 and 9.95.
Know more about Rounding off here:
https://brainly.com/question/28128444
#SPJ9
In a survey of 259 professional athletes, it was found that 110 of them owned a convertible, 91 of
them owned a giant screen TV, and 120 owned a sporting goods store. 15 owned a convertible and a
store, 43 owned a TV and a store, and 44 owned a covertible and a TV. 9 owned all three items.
1. How many athletes did not own any of the three items?
2. How many owned a covertible and a TV, but not a store?
3. How many athletes owned a convertible or a TV?
4. How many athletes owned exactly one type of item in the survey?
5. How many athletes owned at least one type of item in the survey?
6. How many owned a TV or a store, but not a convertible?
Answers
1. Number of athletes did not own any of the three items = 259 - 228
= 31.
2. Number of athletes own a convertible and a TV but not a store = 44 - 9
= 35.
3. Number of athletes own a convertible or a TV = 110 + 91 - 44
= 157.
4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.
5. Number of athletes owned at least one type of item = 259 - 31
= 228
6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71
= 118.
The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.
Total number of athletes surveyed = 259
Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228
Number of athletes who did not own any of the three items = 259 - 228 = 31.
The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.
Number of athletes who own a convertible and a TV = 44
Number of athletes who own all three items = 9
Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35
The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.
Number of athletes who own a convertible or a TV = 110 + 91 - 44
= 157.
The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.
Number of athletes own a convertible only = 110 - 15 - 9 = 86
Number of athletes own a TV only = 91 - 44 - 9 = 38
Number of athletes own a store only = 120 - 15 - 43 - 9 = 53
Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.
The number of athletes who owned at least one type of item can use the result from part (1).
Number of athletes who owned at least one type of item = 259 - 31
= 228
The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.
Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159
Number of athletes own a TV or a store not a convertible = 13 + 34 +71
= 118.
For similar questions on athletes
https://brainly.com/question/25631156
#SPJ11
How do I Solve this equation
Answers
Hey there!
Solve for f :
Answer :f = 27.9 ✅
Explanation:> Given expression :
\( \displaystyle \frac{f}{9} = 3.1 \\ \\ \)
> Multiply both sides by 9 :
\( \displaystyle \frac{f}{9} \times \red{9} = 3.1 \times \red{9} \\ \\ \Longrightarrow \boxed{ \green{f = 27.9}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \)
Therefore, our answer is f = 27.9
▪️Learn more about first-degree equations:
↣https://brainly.com/question/27399223
↣https://brainly.com/question/26728137
1. A random sample of 25 customers for lunch at a local restaruant stayed an average of 45 minutes with a standard deviation of 10 minutes. Another random sample of 30 customers for dinners at this restaurant stayed an average of 55 minutes with a standard deviation of 15 minutes. Determine a 95% confidence interval for the difference of the mean time that the customers stayed for lunch and for dinner.
a. (3.35, 16.65) b. (3, 17) c. (3.06, 16.94) d. (-3.35, 16.62) e. (-3, 17)
Answers
A 95% confidence interval for the difference of the meantime that the customers stayed for lunch and for dinner the correct option is option a (3.35, 16.65).
Given:
The number of random customers n1 = 25
The number of random customers n2 = 30
x1 = 45, x2 = 55
σx1 = 10, σx2 = 15
Zα12 = Z0.025 = 1.96
95% confidence interval,
= {(x2-x1) ± Zα12 [(σx1)^2/n1 + (σx2)^2/n2]^0.5}
= {(55-45) ± 1.96 [\(10^{2}\)/25 + \(15^{2}\)/30]^0.5}
= {10 ± 1.96(4 + 7.5)^0.5}
= {10 ± 1.96(11.5^0.5)}
= {10 ± 1.96(3.3911)}
= {10 ± 6.6466}
=> (10-6.6466, 10 + 6.6466)
=> (3.35, 16.65)
So, the correct option is a (3.35, 16.65) for the difference of the meantime.
To learn more about the confidence interval visit: https://brainly.com/question/24131141
#SPJ4
Write the equation of the exponential function, base 2.
Answers
Answer:
y=4(12)x
Step-by-step explanation:
An exponential function is in the general form
y=a(b)
Part BSince the equations for both triangles have a2 + b2, you can think of the two equations for cand n as a system of equations. Substitute what a? +b2 equals in the first equation for o? + b2 in the second equation. After you substitute, what equation do you get?Part CNow, take the square root of both sides of the equation from part B and write the resulting equation Part D Is there any way for this equation to be true?How?Part EWhat does this show about the relationship between the two triangles?Part FDoes this mean that triangle 1? Why or why not?Sorry if its a lot of questions but I really need this to be answer
Answers
Part B
We know,
\(\begin{gathered} a^2+b^2=c^2 \\ a^2+b^2=n^2 \end{gathered}\)Now, we substitute a^2+b^2=c^2 in the second equation
\(\begin{gathered} a^2+b^2=n^2 \\ c^2=n^2 \end{gathered}\)So, the new equation is c^2 = n^2
Part C
Now, taking the square root of both sides of the equation from part B, we get
\(\begin{gathered} \sqrt[]{c^2}=\sqrt[]{n^2} \\ c=n \end{gathered}\)Part D
The equation obtained is true thanks to the Pythagorean theorem, because the corresponding legs in both triangles are of equal measure, we will obtain that their hypotenuse is also equal.
You can see that the 90° angles is conformed by 2 sides, these sides are the legs and the last side is the hypotenuse.
Part E
This means that the 2 triangles are equal, they have 3 sides equals.
The triangles also meet the criterion that explains that if two sides and the angle opposite the longest side are equal, the triangles are equal.
Part F
Yes, the triangle 1 is a rigth triangle because this has a right angle, that is, a 90 degree angle
a new social media sit is increasing its user base by approximately 4% per month. If the site currently has 35.930 users, what will the approximate user base be 10 months from now?
Answers
Answer:
The approximate user base of the social media site 10 months from now would be approximately 52,374.
Step-by-step explanation:
To calculate the approximate user base of the social media site 10 months from now, considering a 4% increase per month, we can use the following steps:
1. Calculate the monthly growth factor: 1 + (4% / 100) = 1 + 0.04 = 1.04
2. Apply the growth factor to the current user base for each month:
Month 1: 35,930 * 1.04 = 37,387.2 (approx.)
Month 2: 37,387.2 * 1.04 = 38,868.49 (approx.)
...
Month 10: Previous Month * 1.04
By repeating this calculation for each month, we can determine the approximate user base 10 months from now.
Month 1: 37,387.2
Month 2: 38,868.49
Month 3: 40,391.33
Month 4: 41,957.61
Month 5: 43,569.34
Month 6: 45,228.24
Month 7: 46,936.32
Month 8: 48,695.44
Month 9: 50,507.45
Month 10: 52,374.40 (approx.)
Therefore, the approximate user base of the social media site 10 months from now would be approximately 52,374.
To draw graph of 4x + 5y = 19, Find y when x = 1
Answers
4 + 5y = 19
5y = 19 - 4
5y = 15
y = 15/5
y = 3
Please help ill mark brainliest!
Answers
A marketing specialist at a large bank analyzes global commercial and residential real estate property indexes.
What inference can be drawn from these graphics?
A person who moved from Spain to Australia in 2010 would probably be alarmed by the high prices of homes in Australia.
The majority of individuals who purchased commercial real estate in the UK in 2004 and sold it in 2008 most likely suffered a huge loss.
If the trends shown in the graphics continued to the present day, a couple from the US who moves to France should expect to pay more for a similar home there.
Based on the trends shown, it is probable that since 2010 commercial real estate prices have increased in all countries except the UK, US, and Australia.
Answers
According to the graphs, the most accurate conclusion is that a person who moved from Spain to Australia in 2010 would probably be alarmed by the high prices of homes in Australia (option A).
How to select a suitable conclusion to the graphics?To select an appropriate conclusion that matches the information in the graphs we must carefully analyze the information in the graphs. Additionally, we can read each of the options and check them with the trends shown in the graphs.
In accordance with the above procedure, we can infer that the most accurate conclusion is that a person who moved from Spain to Australia in 2010 would probably be alarmed by the high prices of homes in Australia because the Residential real estate graph shows that In 2010 housing was more expensive in Australia than in Spain.
Learn more about conclusions in: https://brainly.com/question/78686
#SPJ1
what the dog doing ?
Answers
The dog is playing with his chew toy!
Answer:
Explanation
Step-by-step explanation:
In general, dogs can run 15-20 mph
humans can run 6-8 mph
You are significantly slower than the dog,
the fastest human is around 27 miles per hour, unfortunately, even if you were this fast
the fastest dog can run 40 miles per hour as an estimate
even house cats can run at 30 mph maximum if they really wanted,
You have no chance of outrunning this dog, and barely a chance of outsmarting it if that option was available, in conclusion, the dog is chasing you at a speed of around 30 mph about 6-7x more than your own speed with no chance of outrunning it(the dog).
Katrina has the option of an 8-year nonsubsidized student loan of $29,000 at an annual interest rate of 2.5% or an 8-year subsidized loan of $29,000 at an annual interest rate of 4.5%. Determine for which loan Katrina will pay less interest over the term of the loan if she starts making payments 2 years after obtaining the loan. (Assume Katrina makes monthly payments for each loan. Round your answers to the nearest cent, as appropriate.) The total interest paid on the nonsubsidized loan is $
Answers
Katrina would pay less amount of interest on the nonsubsidized student loan
The total interest paid on the nonsubsidized loan is $3,860.80
What is monthly compounding?
Monthly compounding means that the interest is computed and added to existing outstanding loan balance at the end of each month.
In this case, the loan would be repaid monthly but the first monthly payment would occur after 2 years of taking out the loans.
In other words, for the first 2 years, the interest would increase the balances with no corresponding reductions by a way of loan repayment, note that interest to be added monthly, as a result, we can compute outstanding balance 2 years for both loans using the future value formula of a single cash flow shown below:
FV=PV*(1+r/n)^(n*t)
FV=balance after 2 years=unknown
PV=loan amount
r=annual interest rate
n=number of times interest is compounded annually=12
t=number of years before repayments commence=2
Non-subsidized loan:
FV=$29,000*(1+2.5%/12)^(12*2)
FV=$30,485.28
Subsidized loan:
FV=$29,000*(1+4.5%/12)^(12*2)
FV=$31,725.71
Having determined the loan balances after 2 years, we can now compute the monthly payments that would be made in the remaining 6 years using the present value formula of an ordinary annuity because monthly payments would occur at the end of each month:
PV=PMT*(1-(1+r)^-N/r
PV=balance of loan after 2 years
PMT=monthly payment=unknown
r=monthly interest rate=annual interest rate/12
N=number of monthly payments in 6 years=12*6=72
Non-subsidized loan:
$30,485.28=PMT*(1-(1+2.5%/12)^-72/(2.5%/12)
PMT=$456.40
total monthly payments=$456.40*72
total monthly payments=$32,860.80
Interest= total monthly payments-loan
interest=$32,860.80-$29,000
interest=$3,860.80
Subsidized loan:
$31,725.71 =PMT*(1-(1+4.5%/12)^-72/(4.5%/12)
PMT=$503.61
total monthly payments=$503.61 *72
total monthly payments=$36,259.92
Interest= total monthly payments-loan
interest=$36,259.92 -$29,000
interest=$7,259.92
Find out more on student loan on:https://brainly.com/question/24980832
#SPJ1
A rancher has 200 feet of fencing to enclose two adjacent rectangular corrals. What dimensions should
be used so that the enclosed area will be a maximum?
Answers
Length is 33.33 feet and width is 25 feet are dimensions should
be used so that the enclosed area will be a maximum.
What is Area of Rectangle?The area of Rectangle is length times of width
Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.
Here, the dimensions of the rectangles are the same.
The width of the two rectangles is W=2W+2W=4W
The length of the two rectangles is L=L+L+L=3L
Because the adjacent side has a common length.
3L+4W=200
3L=200-4W
Divide both sides by 3
L=(200-4W)/3
Let us form an equation using the area of rectangle formula:
A=2LW
=2(200-4W)/3.W
A=400-8W²/3
Let us differentiate to get the area to be maximized dA/dW=0
1/3×(400-8W²)=0
1/3(400-16W)=0
400-16W=0
400=16W
Divide both sides by 16
W=25
The width is 25 feet.
Substitute W value in equation to get L value:
L=200-4×25/3
=200-100/3
=100/3
=33.33
The length is 33.33 feet.
Now let us find the maximum area
A=2LW
=2×33.33×25
=1666.66
Hence, length is 33.33 feet and width is 25 feet are dimensions should
be used so that the enclosed area will be a maximum.
To learn more on Rectangle click:
https://brainly.com/question/20693059
#SPJ1
The square and circle below are tangent at one point and meet at four other points, as shown. If the side of the square is 8 units long, what’s the radius of the circle?
Answers
Thus, the radius of circle is for the given combined figure of circle and square is found as: 5 units.
Explain about the tangent on circle:A straight line that only touches the circumference of a circle once is said to be the tangent to that circle. The point of tangency or contact point is the location where the tangent contacts a circle.
ABCD is a square having each side 8 units.
A center O of circle with radius r is passing through A and D such that it forms tangent to BC at E.
Joining OD, OA, OE and OF.
AD is the chord, having mid point F. Line OF meets at center of circle to point F.
Thus, OF ⟘ AD.
In the right angle ODF,
OD=r
OF= 8—r
DF = FA = 4
OD² = OF² +FD²
r² = (8-r)² + 4²
Simplifying,
r² = 64 + r² - 16r + 16
16r = 80
r = 5
Thus, the radius of circle is for the given combined figure of circle and square is found as: 5 units.
Know more about the tangent
https://brainly.com/question/4470346
#SPJ1
A car travels 60 kilometers in one hour before a piston breaks, then travels at 30 kilometers per hour for the remaining 60 kilometers to its destination. What is its average speed in kilometers per hour for the entire trip?
Answers
Answer:
Total Distance : 1*60 +60=120
Total time taken = 1+ 60/30= 1+2=3
Hence average speed for the trip = 120/3= 40 kmph
Hence Answer is 40
Step-by-step explanation:
The average speed is 40 km/h.
What is Average speed?The average speed of a body is equal to the total distance covered, divided by the total time taken. The formula for average speed is given as:
Average Speed Formula:Average Speed = Total distance covered ÷ Total time taken
Example:
sing the average speed formula, find the average speed of Sam, who covers the first 200 kilometers in 4 hours and the next 160 kilometers in another 4 hours.
Solution:
To find the average speed we need the total distance and the total time.
Total distance covered by Sam = 200Km + 160 km = 360 km
Total time taken by Sam = 4 hour + 4 hour = 8 hour
Average Speed = Total distance covered ÷ Total time taken
Average Speed = 360 ÷ 8 = 45km/hr
Given:
d1= 60 km
d2= 30
d3 = 60
Total Distance : 1*60 +60=120
Total time taken = 1+ 60/30= 1+2=3
Now,
average speed = total distance/ total time taken
= 120/3
= 40 kmph
Learn more about average speed here;
https://brainly.com/question/12322912
#SPJ2
necesito ayuda con estas consignas
Answers
Yo no hablo espanol
Yo no ayudo tu. :(
You roll two fair dice, a green one and a red one.
Required:
a. What is the probability of getting a sum of 8? (Enter your answer as a fraction.)
b. What is the probability of getting a sum of 4?
c. What is the probability of getting a sum of 8 or 4?
d. Are these outcomes mutually exclusive?
Answers
Answer:
\(a.\ \frac{5}{36}\\b.\ \frac{1}{12}\\c.\ \frac{2}{9}\\d.\ $Not mutually exclusive$\)
Step-by-step explanation:
Given two fair dice are rolled, one green and one red.
To find:
a. Probability of getting a sum of 8.
b. Probability of getting a sum of 4.
c. Probability of getting a sum of 8 or 4.
d. Are these outcomes mutually exclusive?
Solution:
First of all, let us have a look at the output of roll of two dice.
There are a total of 36 outcomes.
{(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)}
a. Getting a sum equal to 8, we have following outcomes:
{(2, 6), (3,5), (4, 4), (5,3), (6, 2)}
5 possible outcomes for this event.
Formula for probability of an event E can be observed as:
\(P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}\)
\(P($Getting 8$) = \dfrac{5}{36}\)
b. Getting a sum equal to 4, we have following outcomes:
{(1, 3), (2,2), (3, 1)}
3 possible outcomes for this event.
Formula for probability of an event E can be observed as:
\(P($Getting 4$) = \dfrac{3}{36} = \dfrac{1}{12}\)
c. Probability of getting a sum of 8 or 4?
Following possible outcomes are there:
{(2, 6), (3,5), (4, 4), (5,3), (6, 2), (1, 3), (2,2), (3, 1)}
Total 8 possible outcomes:
\(P($Getting 8 or 4$) = \dfrac{8}{36} = \dfrac{2}{9}\)
d. Are these outcomes mutually exclusive?
These events are not mutually exclusive because they contain the similar outcome from both of the dice.
i.e. (4, 4) and (2, 2)
4. Find the average value of the given function on the given interval. Then find all points c whose existence is guaranteed by the Mean Value Theorem for Integrals. (a) f(x) = x2 – 8x + 10 on (2, 5] (b) f(x) = Vx on [1, 16]
Answers
The average value of the given function on the given interval is = 7/2 and 6.25 respectively
What is Average?
The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
(a) f(x) = x2 – 8x + 10
f = 1/b-a \(\int\limits^b_a {f(n)} \, dx\)
f = 1/5-2 \(\int\limits^5_2 {x^{2} -8x+10} \, dx\)
Here, a=2
b=5
f(x) =x2 – 8x + 10
f = 1/3 (x³/3 - 8x²/2+10x)5/2
f = -25/9 -20/9
f = -45/9
= -5
Mean Value Theorem
If f(x) = continous on (a, b)
If f(x) = differentiable on (a, b)
Then f(c) = f(b) -f(a)/b-a
were c∈ (a,b)
Here, f(c) = f(-5)-f(2)/5-2
f(c) = -5+2/3
f(c) = -1 ......................(1)
Here, f(x) = x²-8x+10
f(c) = c²-8c+10
f(x) = 2c-8...................(2)
equating 1&2
2c -8 = -1
2c = -1 +8
c = 7/2
c∈ (2,5)
(b) f(x) = Vx on [1, 16]
f = \(\sqrt{x}\) on (1 ,16)
f= 1/b-a \(\int\limits^b_a {f(n)} \, dx\)
f = 1/16-1 \(\int\limits^6_1 {\sqrt{x} } \, dx\)
f = ( 2x (3/2)/45)₁¹⁶
f = 128/45-2/45
f = 126/45
= 14/5
Mean Value Theorem
f(x) = \(\sqrt{x}\)
f(c) =\(\sqrt{c}\)
f(c) = 1/2\(\sqrt{c}\)....................(1)
we know that
f(c) = f(b)-f(a)/b-a
f(c) = f(16)-f(1)/16-1
f(c) = \(\sqrt{16}\) -\(\sqrt{1}\)/15
f(c) = 4-1/15
= 3/15.....................(2)
Equating (1) and (2)
1/2\(\sqrt{c}\) = 3/15
2\(\sqrt{c}\) = 15/3
2\(\sqrt{c}\) = 5
\(\sqrt{c}\) = 5/2
c = (5/2)²
=25/4
c≅ 6.25
6.25 = (1 ,16)
The average value of the given function on the given interval is = 7/2 and 6.25 respectively
To learn more about Average visit
brainly.com/question/27193544
#SPJ4