Answer:
[tex]x \approx 3.195[/tex] satisfies the conclusion of the Mean Value Theorem for [tex]f(x) = \ln x^{3}[/tex] over the interval [tex][1,e^{2}][/tex].
Step-by-step explanation:
According to the Mean Value Theorem, for all function that is differentiable over the interval [tex][a, b][/tex], there is at a value [tex]c[/tex] within the interval such that:
[tex]f'(c) = \frac{f(b)-f(a)}{b-a}[/tex] (1)
Where:
[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds.
[tex]f(a)[/tex], [tex]f(b)[/tex] - Function evaluated at lower and upper bounds.
[tex]f'(c)[/tex] - First derivative of the function evaluated at [tex]c[/tex].
If we know that [tex]f(x) = \ln x^{3} = 3\cdot \ln x[/tex], [tex]f'(x) = \frac{3}{x}[/tex], [tex]a = 1[/tex] and [tex]b = e^{2}[/tex], then we find that:
[tex]\frac{3}{c} = \frac{3\cdot \ln e^{2}-3\cdot \ln 1}{e^{2}-1}[/tex]
[tex]\frac{3}{c} = \frac{6\cdot \ln e-3\cdot \ln 1 }{e^{2}-1 }[/tex]
[tex]\frac{3}{c} = \frac{6}{e^{2}-1}[/tex]
[tex]c = \frac{1}{2}\cdot (e^{2}-1)[/tex]
[tex]c \approx 3.195[/tex]
[tex]x \approx 3.195[/tex] satisfies the conclusion of the Mean Value Theorem for [tex]f(x) = \ln x^{3}[/tex] over the interval [tex][1,e^{2}][/tex].
Answer:
C. 1/2(e^2-1)
Step-by-step explanation:
Edge AP Cal 2022
Starting at 1:00 p.M., The temperature changes -4 degrees Fahrenheit per hour. Write and solve an equation to find how many hours (x) it will take to reach -1 °F. please say the equation.
Answer:
0.25 hours
Step-by-step explanation:
The equation for a linear function is given by:
y = mx + b,
where y and x are variables, m is the rate of change of y with respect to x and b is the initial value of y (value of y when x = 0).
Let x represent the number of hours after 1:00 P.M and let y represent the temperature in degree Fahrenheit.
Let us assume that initial the temperature is 0°F. The temperature changes -4 degrees Fahrenheit per hour. From the equation of a linear function y = mx + b:
m = -4 degrees Fahrenheit per hour, b = 0. Hence:
y = -4x
The time taken to reach -1°F is gotten by substituting y = -1 and finding x:
y = -4x
substituting:
-1 = -4x
x = -1 / -4
x = 0.25 hours
0.25 hours = 0.25 hours * 60 minute / 1 hour = 15 minute
Therefore at 1:15 P.M, the temperature is -1°F
Sonu's mother is 12 years more than twice Sonu's age. After 8 years,she will be 20 years less than three times Sonu's age. Find Sonu's age and mother's age.
Answer
sonu's age=16years
mothers age=44years
Step-by-step explanation:
sonu's age be x
then, mothers age will become 2x+12
after 8years,
sonu's age=x+8
mother's=2x+12+8
a/q
3(x+8)-20=2x+12+8
3x+24-20=2x+20
3x+4=2x+20
3x-2x=20-4
x=16
sonu's age=16years
mothers age=44years
Service improves society, impacting the helpers as well as those needing assistance. It means being an active participant in one's community, taking action where it can be of benefit. Every person should make it a priority to serve at least two hours per week. It's an extremely important civic responsibility that is invaluable to citizens most in need. Service creates improved communities where people care about each other.
What are the key details from the article that should appear in its summary?
(5 points)
Group of answer choices
Service is performed by millions of Americans each year, saving tax dollars.
Service is being an active helper in the community and taking action that can be of benefit.
Service comes from those who have the time and money to not work.
Service comes from citizens who care and accept their responsibility.
Answer:
Service is being an active helper in the community and taking action that can be of benefit.
Service comes from citizens who care and accept their responsibility.
Use those
C. or D is the answer I think its D
maybe.
what is 1 17/8 + 1 1/4 =
Answer:
39/8
Step-by-step explanation:
Suppose that a scientist captures 20 fiddler crabs in a small freshwater pond and marks them before releasing them back to the pond. The following week, the scientist returns and captures 30 fiddler crabs, six of which are marked. What is the estimated size of the fiddler crab population
Answer:
100 fiddler crabs
Step-by-step explanation:
If the 30 crabs are a representation of the entire population, then 6 marked crabs in a population of 30 would mean that
6 / 30 = 0.20 or 20%
20% of the entire crab population are marked. Since we know that a total of 20 fiddler crabs are marked in the pond then we can divide this number of marked crabs by 20% in decimal form to get the estimated total size of the fiddler crab population
20 / 0.20 = 100 fiddler crabs
A jet plane can carry up to 200,000 liters of fuel. It used to 130,000 liters of fuel during a flights. What percentage of the fuel capacity did it use on this flight?
Sprinters who run 100 yards now often run 100 meters.
How many meters longer to the nearest tenth is 100 meters than 100 yards?
Answer:
100 meters is 8.6 meters longer than 100 yards.
Step-by-step explanation:
Conversion of yards to meters.
Each yard has 0.914 meters.
So 100 yards is 100*0.9144 = 91.4 meters.
How many meters longer to the nearest tenth is 100 meters than 100 yards?
100 yards = 91.4 meters
100 - 91.4 = 8.6
So 100 meters is 8.6 meters longer than 100 yards.
4 7/8 in decimal form
Answer:
4.875?
convert it into an improper fraction
4 7/8 in decimal form is equal to 4.875.
To convert the mixed number 4 7/8 into decimal form, we need to add the whole number part to the fraction part.
The whole number part is 4.
To convert the fraction 7/8 into decimal form, divide the numerator (7) by the denominator (8):
= 7 ÷ 8
= 0.875
Now, add the decimal result to the whole number:
= 4 + 0.875
= 4.875
Therefore, 4 7/8 in decimal form is equal to 4.875.
Learn more about Decimal here:
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Need help please and thank you!!
9514 1404 393
Answer:
y = 6·2^x
Step-by-step explanation:
The general form can be written as ...
y = a·b^x
The value of 'a' is the value of y when x=0. That is 6.
The value of 'b' is the ratio of y-values when x differs by 1. b = 12/6 = 2.
So, the equation of interest is ...
y = 6·2^x
Gordon types 3,572 words in 47 minutes. Find the unit rate.
Answer:
Gordon types at 76 wpm
Step-by-step explanation:
You can find this by dividing the number of words typed by the number of minutes:
[tex]\frac{3572w}{47m}\\\\= \frac{3572}{47}\frac{w}{m}\\\\= 76\frac{w}{m}\\\\[/tex]
Answer:
78 Words per minute
Step-by-step explanation:
Unit Rate = 3666 Words in 47 minutes
Unit Rate = 78 Words per minute
An art teacher has 16 pieces of blue chalk, 14 pieces of red chalk, and 10 pieces of yellow chalk. She
randomly gives a piece of chalk to each student in her class. What is the probability that the first
student will receive a piece of blue chalk? PLEASE ANSWER QUICKLY THANK YOU
Answer:
there is a 40% or a 16/40 chance the the student will receive blue chalk
Step-by-step explanation:
If gas costs $1.95 per gallon, how many whole gallons of gas could you buy with $36.00? (Make sure to answer with a whole number.)
dentify as an increase or decrease. Then find the percent of increase or decrease. If necessary, round to the nearest percent.
Original: 150
New: 130
Answer:
Step-by-step explanation:
The difference is 130-150 = -20, a decrease.
-20/150 ≅ -0.133, a decrease of 13.3%
What is the inverse of the function f(x) = 2x+1
Answer:
The answer is b. h(x) = one-halfx – one-half
Step-by-step explanation:
Answer:
hey everyone its b!!!
Step-by-step explanation:
John wants to make a glider and he needs to
make sure that XM is the same length as XB
so that his glider will fly smoothly. Can you
help John calculate the length of XM 2 Find
the length of XM if XB = 7k- 3 and XM =
9k-9.
M
B
The length of XM =
If you Start with $10 in the bank and each month you add $20 which line equation will give you your total amount after X months?
Answer:
y=20x+10
Step-by-step explanation:
You start with $10, so this will be added on, and is not affected by the number of months.
You add $20 each month, so the 20 is dependant on x.
ANSWER: y=20x+10
Help please ............
Answer:
1
Step-by-step explanation:
We use PEMDAS, so we do the parenthese first, which is 6 x 2 = 12 and 12 / 12 gets you 1!
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the graph shows the voltage in a circuit changing as temperature increases from 100° to 600°. which is the best estimate for the rate of change of the voltage over the interval?
1.5 volts
3 5 volts
5.5 volts
7.5 volts
Answer:
3.5?
Step-by-step explanation:
The best estimate for the rate of change of the voltage over the interval will be 3.5 volts. Then the correct option is B.
What is the average rate change of a function?It is the average amount by which the function is modified per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph that represents the function. The average rate of change of the function is given as,
Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]
The graph shows the voltage in a circuit changing as temperature increases from 100° to 600°.
We know that v = 1750 at t = 600° and v = 0 at t = 100°. Then the Average rate of change is given as,
Average rate = (1750 - 0) / (600 - 100)
Average rate = 1750 / 500
Average rate = 3.5
The best estimate for the rate of change of the voltage over the interval will be 3.5 volts. Then the correct option is B.
More about the average rate change of a function link is given below.
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Find the perimeter of the following shape:
1 Rose factored the expression below. Is her answer correct? Why or why not? x2.5x + 6 + (x - 1)(x - 6)
Answer:
(x+3)(x+2)
Step-by-step explanation:
Given the quadratic equation x²+5x + 6
Factorize
x²+2x+3x+6 = 0
x(x+3)+3(x+2) = 0
(x+3)(x+2)
Hence the factored form is (x+3)(x+2)
Rose was incorrect because she uses the wrong factors
What is the correct expanded form and value of
5
?
Answer:
[tex]\frac{4}{5} .\frac{4}{5} .\frac{4}{5} =\frac{64}{125}[/tex]
Step-by-step explanation:
An "exponential form" is being used for "repeated multiplication." The value of [tex](\frac{4}{5} )^3[/tex] is equal to [tex]\frac{4}{5}[/tex] being repeatedly multiplied by itself.
[tex]\frac{4}{5}[/tex] x [tex]\frac{16}{25}[/tex] x [tex]\frac{4}{5}[/tex] = [tex]\frac{64}{125}[/tex]Choice A is incorrect because it is an addition of fraction and also an incorrect way of adding the numerators. Choice C is also incorrect because it also used the addition operation. Choice D is incorrect because it repeatedly multiplied the reciprocal of [tex]\frac{4}{5}[/tex], which is [tex]\frac{5}{4}[/tex], instead of the fraction itself.
A certain forest covers an area of 2100 km^2. Suppose that each year this area decreases by 5.25%. What will the area be after 6 years
Answer:
The area after 6 years is [tex]1519.49km^2[/tex]
Step-by-step explanation:
Given
[tex]a = 2100[/tex] --- Initial Value
[tex]r = 5.25\%[/tex] --- Rate
Required
Determine the area after 6 years
Because the area reduces,, the following formula will be used to solve the question.
[tex]y = a*(1 - r)^t[/tex]
Here
[tex]t = 6[/tex]
So, we have:
[tex]y = 2100*(1 - 5.25\%)^6[/tex]
Convert percentage to decimal
[tex]y = 2100*(1 - 0.0525)^6[/tex]
[tex]y = 2100*(0.9475)^6[/tex]
[tex]y = 1519.47866516[/tex]
[tex]y = 1519.49[/tex] -- approximated
The area after 6 years is [tex]1519.49km^2[/tex]
what is the solution to the equation below
Answer:
x=-4
Step-by-step explanation:
Cross multiply to get:
3x=4(x+1)
3x=4(x+1)
3x=4x+4
x=-4
Answer:
x=-4
Step-by-step explanation:
cross multiply you get 3x=4x+4. solve algebraically you get x=-4
If you sleep 30% of the day, how many hours do you sleep?
Answer:
7.2 hours.
Step-by-step explanation:
Search up "30% of 24"
Answer:
You sleep 7.2 hours.
Step-by-step explanation:
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emily sold 2 small boxes of grapefruits and 3 large boxes of grape fruit for a total $61 chelsea sold 3 small boxes of grapefruit and 3 large boxes of grapefruit for a total of $72
what is the cost of one small box of grape fruit and one large box of grapefruit
Answer:
small box costs $11, large box costs $13
Step-by-step explanation:
2S + 3L = 61
3S + 3L = 72
Eliminate the L terms: subtract first equation from second equation
2S + 3L = 61
-3S - 3L = -72
-------------------
-S = -11
S = 11
2S + 3L = 61
2(11)+3L = 61
3L = 39
L = 13
small box costs $11, large box costs $13
Answer:
no tienes idea de lo que estoy diciendo, chico
Step-by-step explanation:
One Season The Cougars won 20 games. They played a total of 25 games. Use the equation 20 + g = 25 to find g, the number of games the team lost.
Answer:
Step-by-step explanation:
20 + g = 25
-20 -20
g = 5
Help on number 2 please
Answer:
y=12.73 x=9
Step-by-step explanation:
could you help me understand cross sections of three-dimenstional object its harder than it sound.
A section, or cross-section, is a view of a 3-dimensional object from the position of a plane through the object. A section is a common method of depicting the internal arrangement of a 3-dimensional object in two dimensions. It is often used in technical drawing and is traditionally crosshatched.
Cross sections of three-dimensional objects are two-dimensional shapes of various sizes. They may be parallel to a side or base of the object or at an angle to these surfaces. A cross section may resemble the shape of the object’s side or base, or it may have a completely different shape.
So far this month you have achieved $100.90 in sales which is 50% of your monthly goal l. With 5 more workdays this month, how much do you need to sell each day to reach your goal?
3. A cube has a length of 9 inches. Find its volume.
A. 486 in^3
B.639 in^3
C.729 in^3
D. 819 in^3
Answer:
C
Step-by-step explanation:
[tex]x^{3}[/tex]=volume of cube
x= length, width, or height
9*9*9=729
C