What value of x satisfies the conclusion of the mean value theorem for f(x) = ln(x3) over the interval [1, e2]?
Answers
Answer:
\(x \approx 3.195\) satisfies the conclusion of the Mean Value Theorem for \(f(x) = \ln x^{3}\) over the interval \([1,e^{2}]\).
Step-by-step explanation:
According to the Mean Value Theorem, for all function that is differentiable over the interval \([a, b]\), there is at a value \(c\) within the interval such that:
\(f'(c) = \frac{f(b)-f(a)}{b-a}\) (1)
Where:
\(a\), \(b\) - Lower and upper bounds.
\(f(a)\), \(f(b)\) - Function evaluated at lower and upper bounds.
\(f'(c)\) - First derivative of the function evaluated at \(c\).
If we know that \(f(x) = \ln x^{3} = 3\cdot \ln x\), \(f'(x) = \frac{3}{x}\), \(a = 1\) and \(b = e^{2}\), then we find that:
\(\frac{3}{c} = \frac{3\cdot \ln e^{2}-3\cdot \ln 1}{e^{2}-1}\)
\(\frac{3}{c} = \frac{6\cdot \ln e-3\cdot \ln 1 }{e^{2}-1 }\)
\(\frac{3}{c} = \frac{6}{e^{2}-1}\)
\(c = \frac{1}{2}\cdot (e^{2}-1)\)
\(c \approx 3.195\)
\(x \approx 3.195\) satisfies the conclusion of the Mean Value Theorem for \(f(x) = \ln x^{3}\) over the interval \([1,e^{2}]\).
Answer:
C. 1/2(e^2-1)
Step-by-step explanation:
Edge AP Cal 2022
Related Questions
a bird bath that is 3 ft talk casts a shadow that is 2 ft long.Find the height of a tent that casts a 6 ft shadow.
Answers
Answer:
is it 5ft
Step-by-step explanation:
if the bird bath had a foot taken off in the shadow then wouldn't a foot be taken off for the tent as well
The measure x and y are equal. Which is the value of m
Answers
For this problem we know that the measure of x and y are equal. So then we can set up the following equation:
\(3(m+2)=5m-58\)If we distribute the terms in the left of the equation we got:
\(3m+6=5m-58\)And solving for m we got:
\(58+6=2m\)\(m=\frac{64}{2}=32\)And then the final answer for this case would be m=32
if I have £6507278 and I gave my parents half of my money how much would I have left. guys pls answer this
Answers
Answer
divide by 2? bro come on now you got this
Step-by-step explanation:
...
Complete the equation describing how x
and y are related.
х у
y = [ ? ]x
-2
-1
0
1
2
3
-6
-3
0
3
6
9
Enter the answer that
belongs in [?]
![Complete the equation describing how xand y are related. y = [ ? ]x-2-10123-6-30369Enter the answer thatbelongs](https://i5t5.c14.e2-1.dev/c-qa-images/contents/attachments/okGLNBZxhbSlXOmxyCrxxO3wX3kkwMS4.png)
Answers
Answer:
y=3x
Step-by-step explanation:
-6/-2=3, -3/-1=3, 3/1=3. 6/2=3
are the following ratios equal. write yes or no. use the theroem that the product of the extremes equals the product means.
Answers
The ratios will be equal if the theorem that the product of the extremes equals the product means follows.
Let us understand the equality of ratios through example. The example ratio will be -
7:10 = 21:30
In this ratio, 7 and 30 are first and last numbers and hence they are extremes. The number 10 and 21 are in middle and hence considered mean. Now, we will perform multiplication to if the ratios are equal or not.
Product of extremes = 7 × 30
Extremes product = 210
Product of means = 21 × 10
Means product = 210
Since the products are equal, the ratios are also equal.
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The complete question is -
Are the following ratios equal? write yes or no. use the theroem that the product of the extremes equals the product means.
Ratio = 7:10 and 21:30.
Find the equation whose roots are reciprocal of the roots of x² + 4 + 11 = 0
Answers
I think the equation should be x² + 4x + 11 = 0, so I am giving the solution of the same.
Hope it helps.
If you have any query, feel free to ask.
Que números multiplicados dan 30 y sumados dan 11
Answers
Answer:
5, 6
Step-by-step explanation:
Answer:
Los números son:
6 y 5
Step-by-step explanation:
Planteamiento:
a * b = 30
a + b = 11
Desarrollo:
De la segunda ecuación del planteamiento:
a = 11-b
Sustituyendo esta última ecuación en la primer ecuación del planteamiento:
(11-b)*b = 30
11*b + b*-b = 30
11b - b² - 30 = 0
-b² + 11b - 30 = 0
b = {-11±√((11²)-(4*-1*-30))} / (2*-1)
b = {-11±√(121-120)} /-2
b = {-11±√1} / -2
b = {-11±1} / -2
b₁ = {-11-1} / -2 = -12/-2 = 6
b₂ = {-11+1} / -2 = -10/-2 = 5
Comprobación:
6*5 = 30
6+5 = 11
I can prove that 2=1, where is the error?
X = 1
X+X = 1+X
2x = 1+X
2x = X+1
2X-2 = X+1-2
2x-2 = X-1
2 (x-1)/(x-1) = X-1/X-1
2 times 1 = 1 1-1 / 1-1
2 = 1
I subtracted -2
because thats the # I chose to subtract with.
Answers
The mistake is when you try to divide by X - 1, because you can't divide by zero.
Where is the problem in this procedure?Here we start by defining:
X = 1
The second step makes sense, we are adding the same value in both sides:
X + X = X + 1
2X = X + 1
Now subtract 2 in both sides:
2X - 2 = X + 1 - 2
2X - 2 = X - 1
Here is the mistake, you divide both sides by X - 1
But we already defined that X = 1
Then you are trying to divide by zero, and that opeartion is not defined, that is why you reach a false equation.
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In the formula, l = a + (n - 1)d make d as the subject. Find d when l = 10, a = 2, n = 5.
Answers
I = a + (n - 1)d [Given formula]
To Find:-Find d when I = 10, a = 2, n = 5
Solution:-I = a + (n - 1)d [Given]
Putting the value of I = 10, a = 2, n = 5 we get,
10 = 2 + (5 - 1)d
10 = 2 + 4d
10 - 2 = 4d
8 = 4d
d = \( \frac{8}{4} \)
d = 2
Value of d is 2. [Answer]Which expression is represented by the model shown below?
brit of beau ad noo noiz
Srodeq nislame
Answers
Answer:
4*9
Step-by-step explanation:
It's obvious.
Which property justifies Step 3?
Answers
On a map, 1 inch equals 17.9 miles. If two cities are 2.5 inches apart on the map, how far are they actually apart?
Answers
Answer:
44.75 miles
Step-by-step explanation:
(17.9 mi/in)(2.5 in) = 44.75 mi
Natasha packs a single layer of a prism with 5 cubes. Each cube measures 1 centimeter long on each edge. If 5 layers completely fill the prism, what is the volume of the prism?
Answers
Answer:25
Step-by-step explanation
5 x 5 = 25. Got this problem correct on Imagine Math.
Hello, just need the answer for this question. Thank you for your help if you do so.
Answers
Answer:
In the first one you are missing (x - 3) so it will be 4(x - 3) and if you factor it out it will be 4x - 12
In the second one you are missing a (x -5)which means 9x(x -5) or when you factor it out it will be 9x^2 - 45x
Step-by-step explanation:
3x^2 -23x + 40 = (3x - 8) (x - 5)
3x^2 -17x + 24 = (3x -8) ( x - 3)
Polygon ABCD is a scaled copy of polygon EFGH.
Which segment in the scaled copy corresponds to segment
EF?
Answers
Answer:
AB
Step-by-step explanation:
AB, because it is the same side as EF
SLOPE DIGITAL ESCAPE ROOM
I need help finding the code
Answers
By finding all the four slopes, we can see that the word is ECHA.
How to find the word?We know that the general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
We know that if the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:
s = (y₂ - y₁)/(x₂ - x₁)
With that formula we can get the slopes.
1) Using the points (0, 3) and (2, 4).
m = (4 - 3)/(2 - 0) = 1/2, so the letter is E.
2)Using (-1, -12) and (1, -8)
m = (-8 + 12)/(1 + 1) = 4/2 = 2, so the letter is C.
3) We have (2, -6) and (-4, -3) so:
m = (-3 + 6)/(-4 - 2) = 3/-6 = -1/2, so the letter is H
4)we can use the points (0, 3) and (1, 1), so:
m = (1 - 3)/(1 - 0) = -2, so the letter is A
Then the word is ECHA
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Jessica needs to rent a moving truck for one day. She can choose to rent a moving truck from Rentals Plus or from Speedy Move. At Rentals Plus, it costs $5.24 to rent a moving truck for one day, plus $4.46 per mile driven. At Speedy Move, it costs $85.24 to rent a moving truck for one day, plus $0.46 per mile driven. How many miles would Jessica have to drive for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move?
Answers
Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.
How find how many miles would Jessica have to driveLet's assume the number of miles driven is represented by 'm'. The cost of renting a moving truck for one day at Rentals Plus can be calculated using the equation:
Cost at Rentals Plus = $5.24 + $4.46 * m
Similarly, the cost of renting a moving truck for one day at Speedy Move can be calculated using the equation:
Cost at Speedy Move = $85.24 + $0.46 * m
To find the number of miles that makes the costs equal, we can set up the equation:
$5.24 + $4.46 * m = $85.24 + $0.46 * m
By rearranging the equation, we can solve for 'm':
$4.46 * m - $0.46 * m = $85.24 - $5.24
$4 * m = $80
m = $80 / $4
m = 20
Therefore, Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.
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What is the unit cost?
Answers
Answer:
The unit cost is 6
Step-by-step explanation:
Notice how the first point lands on (2,12) and how a "unit cost" is per one unit. So, if you divide 12 by 2, you would get a unit cost of 6.
What is the inmage of A(2, 1) after reflecting it across x =4 and then across the x-axis? a.16. 1)b. (6,-1) c(-6,-1) d. -6, 1)
Answers
If we reflect the point A (2, 1) across x=4, the point will be at (6, 1). Then if we reflect it again across the x axis, the point will be at (6, -1)
Answer: (6, -1)
A mug has a diameter of 8 centimeters and a height of 11 centimeters. Which of the following is the closest to the volume of the mug?
Answers
Identify the variable and constant in 15-x
Answers
Simplify the expression:
(4k – 4) + ( –9k – 5)
Answers
Answer:
The answer is
- 5k - 9Step-by-step explanation:
(4k – 4) + ( –9k – 5)
Remove the bracket and simplify
That's
4k - 4 + - 9k - 5
4k - 4 - 9k - 5
Group like terms
4k - 9k - 4 - 5
We have the final answer as
- 5k - 9
Hope this helps you
We can use FOIL to solve:
(4k - 4) + (-9k - 5)
(4k * -9k) + (4k * -5) + (-4 * -9k) + (-4 * -5)
-36k - 20k + 36k + 20
-20k + 20
Best of Luck!
Express the following as a fraction in their lowest term 25%
Answers
Answer:
Answer is ¼
Step-by-step explanation:
\({ \tt{25\% = \frac{25}{100} }} \\ \\ { \tt{ \frac{25}{100} = \frac{1}{4} }}\)
Hunter measured the middle school and made a scale drawing. The scale he used was 1 inch : 10 feet. The gym is 7 inches wide in the drawing. How wide is the actual gym?
Answers
Answer:
70 ft
Step-by-step explanation:
You want the actual width of a gym that is represented as 7 inches on a drawing with a scale of 1 in : 10 ft.
Scale factorEach inch represents 10 feet, so 7 inches will represent ...
7 × 10 ft = 70 ft
The gym is 70 ft wide.
__
Additional comment
You can also write and solve an equation that shows the measures are proportional:
actual width / drawing width = (10 ft) / (1 in) = (gym width) / (7 in)
Multiplying both sides of this proportion by 7 in, we have ...
gym width = (7 in) × (10 ft)/(1 in) = 7 × 10 ft = 70 ft
John is painting parallel lines in the parking lot to create parking spaces. The measure of angle A is 60°. What is the measure of angle B? A. 60° B. 90° C. 120° D. 180° E. any acute angle
Answers
Answer:60°
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me....
Answer:
A.
60°
Hope its right.
Step-by-step explanation:
Read paragraphs 4-5 from the passage.
(4) Springing to my feet I received my first Martian surprise, for the effort, which on Earth would have brought me standing upright, carried me into the Martian
air to the height of about three yards. I alighted softly upon the ground, however, without appreciable shock or jar. Now commenced a series of evolutions
which even then seemed ludicrous in the extreme. I found that I must learn to walk all over again, as the muscular exertion which carried me easily and safely
upon Earth played strange antics with me upon Mars.
(5) Instead of progressing in a sane and dignified manner, my attempts to walk resulted in a variety of hops which took me clear of the ground a couple of feet
at each step and landed me sprawling upon my face or back at the end of each second or third hop. My muscles, perfectly attuned and accustomed to the
force of gravity on Earth, played the mischief with me in attempting for the first time to cope with the lesser gravitation and lower air pressure on Mars.
How do the underlined words help establish a sense of place and circumstance?
A. They suggest that the narrator is clumsy and careless, making him unable to explore Mars because he is unable to walk properly.
B. They demonstrate how frustrated the narrator is becoming due to his inability to stay on the ground without gravity.
C. They create vivid imagery, which reinforces that the narrator has landed somewhere that is extremely different from Earth.
D. They help establish a mood of joy and lightness as the narrator begins to enjoy the weightlessness of being on Mars.
Answers
Answer: C
Step-by-step explanation:
I recognize this as coming from an old 1912 novel published as "A Princess of Mars", by Edgar Rice Burroughs. I read the book as a teenage boy. A 2012 movie, called "John Carter", was based on this same book.
Answer A - No, because the character (Carter) says, "My muscles, perfectly attuned and accustomed to the force of gravity on Earth". Perfectly attuned is an athlete, not a clumsy person.
Answer B - No, because the character just doesn't sound all that frustrated. The experience is strange and inconvenient, yet he is handling his emotions pretty well for how weird it must be. It is more like he is writing about an amazing experience, not just complaining.
Answer D - No, because he never says that the experience was making him happy. He does not say that he was laughing or smiling or that it reminded him of some pleasant time he had as a boy.
Answer C - Yes. - Creation of vivid imagery. In a novel, the author must paint pictures with their words. Part of how the author does this is by giving you the picture of a man who feels very comfortable with his coordination on Earth, but keeps winding up about 9 feet off the ground without trying. He doesn't just "I kept falling". He tells you in vivid detail - "... landed me sprawling on my face or back ..."
Hope this helps!
Can someone please give me the answer I will mark u brilliant
Answers
Answer:
choice 1) x + 1.5 = 50.75
Step-by-step explanation:
Paxton invests $4850 at 7.6%/a simple interest. If she wants the money to increase to $8000, how long will she need to invest her money?
Answers
Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.
To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest earned
P = Principal (initial investment)
r = Interest rate per year (expressed as a decimal)
t = Time (in years)
Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:
4850 * 0.076 * t = 8000
Simplifying the equation:
369.8t = 8000
To find t, we divide both sides of the equation by 369.8:
t ≈ 8000 / 369.8 ≈ 21.62 years
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What is the average rate of change of h(x) over the interval [4, 8]?
-2/3
-3/2
-2
-6
![What is the average rate of change of h(x) over the interval [4, 8]?-2/3-3/2-2-6](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/Y4NMtnNK0JU4BzCmvVad9Ew2crcscR9p.png)
Answers
Answer:
B
Step-by-step explanation:
the average rate of change of h(x) in the interval [ a, b ] is
\(\frac{h(b)-h(a)}{b-a}\)
here the [ a, b ] = [ 4, 8 ] , then
h(b) = h(8) = 3 ← point (8, 3 ) on graph
h(a) = h(4) = 9 ← point (4, 9 ) on graph
then
average rate of change = \(\frac{3-9}{8-4}\) = \(\frac{-6}{4}\) = - \(\frac{3}{2}\)
Find the equation of a line passing through the points (3,-4) and (1,2)
Answers
Explanation:
The equation of a line in slope-intercept form is:
\(y=mx+b\)Where m is the slope and b is the y-intercept.
The formula for the slope of a line with points (x1, y1) and (x2, y2) is:
\(m=\frac{y_1-y_2}{x_1-x_2}\)In this case the slope is:
\(m=\frac{-4-2}{3-1}=\frac{-6}{2}=-3\)For now we have:
\(y=-3x+b\)To find the y-intercept b, we have to replace (x,y) for one of the given points and solve for b. If we use point (1,2):
\(\begin{gathered} y=-3x+b \\ \text{ replacing x = 1 and y = 2} \\ 2=-3\cdot1+b \\ 2=-3+b \\ b=2+3=5 \end{gathered}\)Answer:
The equation of the line is: y = -3x + 5
Answer:
y=\neg;[3]x+5
Step-by-step explanation: