Answers
Answer:
b) local minimum at [tex]x=\frac{1}{e}[/tex]
c) Graph of the function is convex
Step-by-step explanation:
We are told that [tex]f'(\frac{1}{e})=0[/tex], which implies there is a turning/stationary point at [tex]x=\frac{1}{e}[/tex].
Substituting [tex]x=\frac{1}{e}[/tex] into [tex]f''(x)[/tex] will tell us if the turning point is a minimum or a maximum:
[tex]f''(\frac{1}{e})=\frac{1}{\frac{1}{e} } =e>0 \implies \textsf{local minimum}[/tex]
Therefore, statement a) is false and statement b) is true.
If the function has a minimum turning point, then this implies that the curve is convex. Therefore, statement c) is true.
Extremum = local min and max points.
We have already established that there is a local minimum at [tex]x=\frac{1}{e}[/tex], therefore statement d) is false.
I know this is not needed for this question, but here are the workings to detemine the equation of the function (I've also attached a graph). This supports the answers above.
[tex]\textsf{if} \ f''(x)=\frac{1}{x}\\\\\implies f'(x)=\int f''(x) \ dx \\\\\implies f'(x)=ln|x|+C\\[/tex]
[tex]\textsf{if} \ f'(\frac{1}{e})=0\\\\\implies ln|\frac{1}{e}|+C=0\\\\\implies -1+C=0\\\\\implies C=1\\\\[/tex]
[tex]\implies f'(x)=ln|x|+1\\[/tex]
[tex]\textsf{if} \ f'(x)=ln|x|+1\\\\\implies f(x)=\int f'(x) \ dx\\\\\implies f(x)=xln(x)-x+x+C\\\\\implies f(x)=xln(x)+C[/tex]
Related Questions
Alejandra has been practicing her free-throw shots as she gets ready for basketball season. At her last practice, she made 70% of her shots from the free-throw line. If
she shot the ball 130 times:
a. How many times did she make a free-throw?
b. How many times did she miss? What percentage of her shots did she miss?
Answers
Answer:
Behold... your answers are...
A. 91
B. 39, 30%
3.If ABCD is a parallelogram with AB = 2x + 1, AD = x + 13, and DC = 3x -11. Determine if ABCD is
rhombus. Show algebraic work to justify your answer.
Answers
Answer:
ABCD is a rhombus
Step-by-step explanation:
Sides AB and DC are opposite and equal in parallelogram ABCD. This means ...
AB = CD
2x +1 = 3x -11
12 = x . . . . . . . . add 11-2x to both sides
Sides AB and CD have length ...
2x +1 = 2(12) +1 = 24 +1 = 25
Then the length of side AD is ...
AD = x +13 = 12 +13 = 25
Adjacent sides AB and AD of the parallelogram have the same length, The figure is a rhombus.
A boat is heading towards a lighthouse, whose beacon-light is 102 feet above the water. From point AA, 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 12. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Answers
Answer:
351 ft (nearest foot)
Step-by-step explanation:
Model the problem as a right triangle, where the horizontal leg is the water (where the boat is at the vertex with the hypotenuse), and the vertical leg is the lighthouse. The angle of elevation is between the boat and the top of the lighthouse. (see attached diagram)
Horizontal distance from point A to the lighthouse
Using the trig ratio tan(x) = O/A where x is the angle, O is the side opposite to the angle and A is the side adjacent to the angle:
Given:
x = 7O = 102 A = ?⇒ tan(7) = 102/A
⇒ A = 102/tan(7)
⇒ A = 830.7233357... ft
Horizontal distance from point B to the lighthouse
Given:
x = 12O = 102 B = ?⇒ tan(12) = 102/B
⇒ B = 102/tan(12)
⇒ B = 479.8722712... ft
Therefore, distance from A to B:
⇒ distance = A - B
⇒ distance = 830.7233357... - 479.8722712...
⇒ distance = 350.8510645...
⇒ distance = 351 ft (nearest foot)
wich is greter 6/10 or 9/8
Answers
Answer:
9/8
Step-by-step explanation:
There are a few ways to look at this.
Starting with the easier way, we see that 9/8 is a fraction above one (this is when the numerator is greater than the denominator), while 6/10 is not, therefore 9/8 is the greater fraction.
Next, we can find the common denominator of the fractions. The least common multiple of 10 and 8 is 40. Now, we can multiply 6/10 by 4 (because 10 x 4 = 40) and 9/8 by 5 (because 8 x 5 = 40)
As a result, we get 24/40 and 45/40, and we can see that 45 is greater than 24.
Find three decimals that make the number sentence true.
-0.01 <
0.01
-0.001
-0.1
-5
-0.009
-200
Answers
Answer:
−0.01≤
So we need to put the right number to make the sentence true.
In this case, we just need to put same or bigger number then -0.01.
So the correct answer can be: -0.01,1,2,3,260
pls answer the question (I'll give brainliest)
Answers
Answer:
10.6 oz
Step-by-step explanation:
To find the answer, we need to divide 2.65/0.25
This will give us how many ounces she bought
So our final answer is…
10.6 oz!
If this was helpful, please award brainliest I would REALLY appreciate it!
Winning The Jackpot In A Particular Lottery Requires That You Select The Correct Four Numbers Between 1 And 54 and, in a separate drawing, you must also select the correct single number between 1 and 37. find the probability of winning the jackpot
Answers
It can be deduced that the probability that an individual wins the jackpot will be 0.0000001.
How to calculate the probabilityFrom the information, the required four numbers will be:
= 54! / 4!(54 - 4)!
= 54! / 4!50!
= 316251
The required single number will be:
= 37! /1! (37 - 1)!
= 37
Therefore, the probability of winning the jackpot will be:
= 1 / (316251 × 37)
= 1/11701287
= 0.0000001
Learn more about probability on:
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What is 3/4 divided by 7/8?
Answers
Answer:
0.85714285714
Answer:
6/7
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Hope this helps! Have a great day!!
ames paid off the loan on his motorboat in the year 2006. He originally borrowed $6500 to buy the boat, but with simple annual interest, he discovered that he paid a total of $8775 over the life of the loan. If James’s annual interest rate was 7%, in what year did his loan begin?
Answers
Answer:
C/2001
Step-by-step explanation:
I did it and got it right
Hope this helps and have a good day :)
Jan is making a logo for her company. She begins with a 6-cm-by-12-cm rectangle. Two points along the bottom side divide that side into three equal pieces. A point on the top side divides that side into two equal pieces. The logo itself is the total shaded area, as shown. What is the area of the shaded logo, in square cm?
Answers
The area of a shape is the amount of space the shape occupies
The area of the shaded region in square cm is 48 square cm
How is the area of the logo calculatedThe logo is a trapezoid with the following dimensions
Height = 12 cmParallel sides: 6 cm and 2 cmThe area of a trapezoid is:
Area = 0.5 * Height * (Sum of parallel sides)
Substitute known values
Area = 0.5 * 12 cm * (6cm + 2cm)
Evaluate
Area = 48 square cm
Hence, the area of the logo i.e. shaded region is 48 square cm
Read more about areas at:
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What is the volume of this sphere?
Use a ~ 3.14 and round your answer to the nearest hundredth.
4 m
Answers
Answer:
Step-by-step explanation:
volume of the sphere=4/3 π (4)³=256 /3 π=256/3 ×3.14≈267.95 m³
The equation e^y= 2x is equivalent to
y = In 2
y = In x
y = In 2x
Answers
Answer:
y = ln(2x)
Step-by-step explanation:
Neat document provided.
Suppose that y varies directly with x, and y=6 when x= 15.
(a) Write a direct variation equation that relates x and y
Equation: ?
1 (b) Find y when x = 20
y = ?
Answers
y = 1 when x = 10
y = 11
(20,9)
15-6=9
9=3/5(20)
9=12
-12/-12
12-9=3
Raghav scod18 out of 20 in the method test his friends only scored 22 out of 25 in the English test who scored more and by how much
Answers
Answer:
sorry but I really don't know the answer
Step-by-step explanation:
What is the measure of angle PBQ
Answers
Answer:
m∠PBQ=51
Step-by-step explanation:
By vertical angles theorem, ∠PBQ ≅ ∠LBM, so m∠PBQ=m∠LBM.
And since ∠LBM & ∠LBQ are supplementary, we'll write,
m∠LBM+LBQ=180°
3x+(4x+61)=180°
Let's solve for x:
7x=119
7x/7=119/7
x=17
So...
m∠LBM=3(17)
m∠LBM=51
This means that m∠PBQ=51
Hope this helps! :)
NO LINKS!!! Use the following graph of f(x) to answer the following below.
Answers
Answer:
a) inc: (-6, 2) ∪ (8, 11); dec: (2, 8)
b) (2, 4) and (8, -2)
c) min: (-8, -3); max: (2, 4)
d) D: [-6, 11]; R: [-3, 4]
e) -2
f) {0, 4}
g) up: (6, 10); down: (0, 6) ∪ (10, 11)
Step-by-step explanation:
a)The graph is increasing where the slope is positive. The graph is decreasing where the slope is negative. Points where the slope is zero are not part of the interval. End points of the domain are generally not included, either.
increasing: (-6, 2) ∪ (8, 11)
decreasing: (2, 8)
__
b)Critical points are points where the slope is zero (tangents are horizontal) or undefined (tangents are vertical).
critical points: (2, 4) and (8, -2)
__
c)Minima and maxima are found either at turning points or the ends of the domain. Here, we have ...
absolute minimum: (-8, -3)
local minimum: (8, -2)
local maximum: (11, 1)
absolute maximum: (2, 4)
__
d)The domain is the horizontal extent of the graph. The range is the vertical extent.
domain: [-6, 11]
range: [-3, 4]
__
e)To find the function value for a given value of x, locate that value of x on the graph and see where the function crosses that vertical grid line. Here, the point is marked (8, -2).
f(8) = -2
__
f)Points where f(x) = 3 will have y-coordinates of 3. They will be at the intersection of the horizontal line y=3 and the graph. Here, they are marked for you:
f(0) = 3
f(4) = 3
The values of x where f(x) = 3 are 0 and 4.
__
g)Concavity switches from up to down, or vice versa, at points of inflection. Here, the points of inflection are hard to determine. We will assume they are the points marked (6, 0) and (10, 0).
Where the graph has a ∩ shape (slope is decreasing), the concavity is down. Where the graph has a ∪ shape (slope is increasing), the concavity is up. The slope on the interval (-6, 0) is constant at +1, so is neither increasing nor decreasing. There is no concavity on that interval.
concave down: (0, 6) ∪ (10, 11)
concave up: (6, 10)
Câu 33, 36, 47, 48, 59, 78, 83, 98, 99, 109.
Answers
Answer:
Following ungrouped data of Sales of a company (in millions) is available
52 33 70 95 57 61
57 64 54 94 38 61
50 39 94 63 59 31
68 88 93 48 82 82
74 70 92 76 98 91
32 33 31 75 54 48
36 64 63 66 92 98
36 54 71 86 84 55
91 34 64 67 89 78
97 92 53 56 68 55
93 42 51 77 36 93
44 66 63 33 68 79
83 53 86 76 35 40
55 41 36 39 42 96
60 53 38 51 95 56
48 69 49 33 95 37
83 62 96 34 85 32
39 59 77 62 35 34
54 89 36 45 83 34
39 61 88 86 55 33
69 54 30 38 79 77
95 34 38 91 80 90
88 45 95 71 80 43
61 40 31 61 58 53
91 63 60 94 98 53
50 34 75 74 90 98
1. Make the frequency distribution table with appropiate class interval, frequency,
cumulative frequency.
1. Calculate the mean, median, mode and quartiles of grouped data.
2. Calculate the standard deviation, variance and range
3. Make the following diagrams: Histogram, Frequency Polygon, Olive
Find the value of the variable
Answers
Answer:
q=8
Step-by-step explanation:
The ratio of sides from bigger to smaller is 1/2.
q=1/2(16)
q=8
Hope it helps!
You buy painting supplies for $12,
and you charge $3 per person to paint faces. How
many faces will you need to paint to earn $15
Answers
Answer:
9
Step-by-step explanation:
If you want to get $15 profit, You will need to paint 9 faces. You spent $12 on painting supplies so this is the explanation.
$3 x 9 = $27
$-12 + $27 = $15
That way, you earn $15.
Simplify
(-x)^6
Write your answer with only positive exponents
Answers
[tex] \sf( { - x)}^{6} [/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto \sf {x}^{6} [/tex]
(when ever power is positive - sign removes)
Why?
Cause : - × - = +
Brainliest if correct
Answers
Answer:
x = 19.Step-by-step explanation:
We have to simplify this equation.
Like this:
2 * x + 8 = 46.The closest number to x is 19:
2 * 19 + 8 = 46Solve:
2 * 19 + 8 = 46= 38 + 8 = 46= 46.x = 19.
What shape do these coordinates make? ( 2, 7 ), ( 8, 7 ), ( 8, 3 ), ( 2, 3 )
Answers
If you need more help just comment!
Please like and brainiest
I had 6 bananas and 4 apples. A hungry baboon ate two of the fruits before being chased by a dog.find probability that the baboon ate
1) two bananas
2) different fruit
Answers
Answer:
two bananas because he's a monkey
Step-by-step explanation:
find the mean, median and mode
Answers
Answer:
Mean: 26.88
Median: 27
Mode: 27
Step-by-step explanation:
19,20,20,21,21,21,22,22,23,23,23,25,25,25,25,25,27,27,27,27,27,27,27,27, 27,27,28,28,28,29,29,29,29,29,29,30,30,30,30,33,33,34,35,40
Mean: 26.88
Median: 27
Mode: 27
Sorry if there are any repeating numbers, this is quite long.
Hope this helps!
Anthony read 5 6 hour each day for 5 days.
Answers
The total number of hours for which Anthony has read after 5 days is; 4 1/6 hours
Total number of reading hoursAccording to the question;
Anthony reads for 5/6 hour each day and does this for 5 days.On this note, it follows that his reading rate is 5/6 hours per day and duration is 5 days.
Hence, the total number of reading hours is;
T = (5/6) × 5.T = 25/6T = 4 1/6 hours.
Read more on rate and time;
https://brainly.com/question/1256181
what is 72/-8 simplified.
Answers
9/-1
-9 is your answer
Help me please if you can
Answers
Answer:
perimeter = 1 3/4
Step-by-step explanation:
1. 3/4 x 2 because there are two sides with the fraction 3/4. 3/4 x 2 is 1 1/2
2. 1/8 x 2 because there are two sides with the fraction 1/8. 1/8 x 2 is 1/4
3. 1 1/2 + 1/4 = 1 3/4
The population of a certain city was 3,416 in 1999. It is expected to decrease by about 0.28% per year. Write an exponential decay function, and use it to
approximate the population in 2023
The exponential decay function where f(x) is the population of the city x years after 1999 is f(x)=
Answers
Answer:
f(x) = 3416*(0.0028)^x
Step-by-step explanation:
f(x) = 3416*(0.0028)^x
you are being watched type the secret code for your ticket
( each line below will pass through one point, graph each line to find your code word )
letter 1: y=1/2x-3
letter 2: y=-4x-2
letter 3: y=-1/3x+4
letter 4:y=1/4x+2
letter 5:y=-2x-1
Answers
Answer:
The answer is LSAGE
Step-by-step explanation:
Hope this helps lol
Answer:
SHINE
Step-by-step explanation:
remember : the slope (the factor of x in the equations) is the ratio "y coordinate change / x coordinate change".
and the constant at the end of the equations are the y-intercept (the y value for x = 0).
Choose the exponential form of the logarithmic equation log4(9x+7)=5.
Answers
Answer:
Use the definition of a logarithm,
log b(x)= y ⟹ b^y = x, to convert from the logarithmic form to the exponential form. 10^5 = 4
Step-by-step explanation:
The exponential form of the given logarithmic equation is [tex](9x+7)=4^5[/tex].
Important information:
The logarithmic equation is [tex]\log_4(9x+7)=5[/tex].Logarithmic equation:The given equation can be written as:
[tex]4^{\log_4(9x+7)}=4^5[/tex]
[tex](9x+7)=4^5[/tex] [tex][\because a^{\log_ab}=b][/tex]
Therefore, the exponential form of the given logarithmic equation is [tex](9x+7)=4^5[/tex].
Find out more about 'Logarithmic equation' here:
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