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
Solve the problem using long division
Answer and Step-by-step explanation:
[tex](m^{2} - 3m - 7) (\frac{1}{m+2})[/tex]
1m -5
____________
[tex]m+2 |m^{2} - 3m - 7[/tex]
- m^2 + 2m
___________________
-5m - 7
- -5m - 10
___________________
3
(The negatives cancel out).
[tex]m - 5 + \frac{3}{m+2}[/tex] <- This is the answer.
#teamtrees #WAP (Water And Plant)
m^2+5=14
[tex] {x}^{2} [/tex]
x2+5=14
Answer:
okeed
Step-by-step explanation:
3 to 4 is equivalent to the ratio of x to 36. What will x be?
Answer:
x = 27
Step-by-step explanation:
(28 points) In the drawing, a regular polygon is partially covered by a rectangle. what is the number of sides of this polygon?
A: 6
B: 7
C: 8
D :60
Answer:
c:8
Step-by-step explanation:
✔
Answer:
C: 8
Step-by-step explanation:
28800000, 1440000, 72000, 3600, 180, ...
Answer: I'm confused. What are you asking here?
Step-by-step explanation:
Convert 6 months to years
Answer: 0.500001
Step-by-step explanation: Hope that helps!
The sum of three consecutive even integers is 486. find all three integers
160 and 162 and 164
Step-by-step explanation:
To find the three even integers, use the equation
x + (x + 2) + (x + 4) = 486
Then solve:
Add the common terms (the xs and numbers)
3x + 6 = 486
Subtract the 6 from both sides
3x = 480
Then divide
x = 160
So 160 + (160 + 2) + (160 + 4) = 486
160 + 162 + 164 = 486
So your three consecutive even integers are
Could someone answer and explain. Will mark the brainliest
Answer: I think you’re right??
Step-by-step explanation:
which expression is equivalent to (2m+3)+(m-1)?
A.5m
B.3m + 2
C.2m+2
D.3m-2
Answer:
i think the correct is D so 3m-2
Factor the trinomial below COMPLETELY
5x^2 - 20x + 60
Answer:
± [tex]\sqrt{-800}[/tex] / 2 or ±800i
Step-by-step explanation:
there are no rational roots because the square root of a negative
i got the answer by using the quadratic formula: (-b ±√b2 - 4ac) /2a
of the last 60 people who went to the cash register at the department store, 16 had blomd hair, 20 had black hair, and 3 had red hair. determine the empirical probability the next person will have brown hair
Answer: 20
Step-by-step explanation:
Answer: Plz don't come for me if its wrong but I think the answer is 21
Step-by-step explanation: Because there are 60 people in all and 16 had blond hair, 20 had black hair and 3 had red hair and 60-16-20-3=39 then you have to take 60-39 and you get 21
What is the solution to (4/2)4 + (1 + 3)?
The total profit made by an engineering firm is given by the function p=x^2 - 24x +5000 where x is the number of clients the firm has and p is the profit.
1. Find the maximum profit made by the company.
2. How many clients are necessary to reach the profit outlined in part one?
Answer:
[tex]5144[/tex]
[tex]12[/tex]
Step-by-step explanation:
The function [tex]p=x^2-24x+5000[/tex] is incorrect as its roots are imaginary [tex]b^2-4ac=576-4\times 5000=-19424<0[/tex].
So, the correct function is
[tex]p=-x^2+24x+5000[/tex]
Differentiating with respect to [tex]x[/tex] we get
[tex]p'=-2x+24[/tex]
Equating with zero
[tex]0=-2x+24\\\Rightarrow x=\dfrac{24}{2}\\\Rightarrow x=12[/tex]
Double derivative of the function
[tex]p''=-2<0[/tex]
So, the function is maximum at [tex]x=12[/tex]
Maximum profit is
[tex]p=-x^2+24x+5000=-12^2+24\times 12+5000\\\Rightarrow p=5144[/tex]
The maximum profit made by the company is [tex]5144[/tex]
The number of clients required to make the maximum profit is [tex]12[/tex].
Can anyone help me pls
10g of Copper reacts with 5g of Sulfur
Write the ratio of Copper to Sulphur
Find the product of (1)(3)(x).
Your
answer
Answer:
2/5.
Step-by-step explanation:Start with fractions for which you need to find the product. In this example, we will multiply the fractions 4/6 and 3/5.
Simplify the fractions to the lowest terms. A fraction needs to be simplified if the same number can divide both the numerator and denominator of a fraction. So 4/6 would become 2/3 and you would multiply by 3/5.
Multiply the numerators. Multiply the top number in one fraction by the top number in the other fraction. In this case 2 x 3 = 6.
Multiply the denominators. Multiply the bottom number of one fraction by the bottom number in the other fraction. In this case 3 x 5 = 15
Simplify the product again if necessary. Your product of 6/15 can be converted into 2/5 by dividing both the numerator and denominator by 3. So the product of 4/6 and 3/5
Convert 7% as a decimal
Answer:
0.07
Step-by-step explanation:
7/100
Answer:
it would be .07 i believe
A 2-pound package of hamburger costs $7.00, and you pay $10.50 for a 3-pound package of hamburger. Use a double number line to complete the table.
Weight (lb)
2
3
4
5
Cost ($)
7.00
10.50
14.00
17.50
What is the unit rate in this relationship?
Step-by-step explanation:
fresco didn't Divo ratify jdndodnswjskd ksosbwjw
Silvia has a coupon for 25% off an item that regularly costs $8. How much will Silvia pay if she uses the coupon?
Answer:
0.32
Step-by-step explanation:
just divide
Answer:
$6
Step-by-step explanation:
25%= 1/4
8 divided by 4 =2
$2 is what is taken off
$8-$2 which is $6
Snowflake the snowman wants to buy new scarves if each scarf cost $4.27 how much did snowflake spend if he buys 5
Answer:
21.35
Step-by-step explanation:
4.27 * 5 i hope this is one of your answers
HELP!! will give brainliest!
ху
7 21
8 24
9 27
Function B
Function B
6
4
2
0
2
4
6
8
10
Which statement best compares the rate of change of the two functions?
The rate of change of both functions is 2.
The rate of change of both functions is 3.
The rate of change of function A is greater than the rate of change of function B.
The rate of change of function B is greater than the rate of change of function A.
The rate of change of function A is greater than the rate of change of function B.
Paul is a newspaper boy who received a total piecework
paycheck of $265.72. He receives 73 cents for every
newspaper he delivers. How many newspapers did he
deliver?
Answer:
364
Step-by-step explanation:
265.72 ÷ 0.73 is 364
Check:
364 x 0.73
265.72
What’s the answer pls
Answer:
168.75 because u put a dot infront of 32 divide it by 54
Alaina baked a cake that weighs 28 ounces. Her family has eaten 49% of it. About how many ounces of cake have they eaten?
Answer:
I think the answer is that her family has eaten 13.72 ounces.
Step-by-step explanation:
So it weighs 28 ounces and her family has eaten 49% of it.
28 multiplied by 49% or 0.49 is 13.72.
I hope this helps!
hich expression is equivalent to -4(7 - 2m) + 11m?
Answer:
[tex] - 4(7 - 2m) + 11m \\ = - 28 + 8m + 11m \\ = \boxed{19m - 28}[/tex]
Expression (19m-28) is equivalent to -4(7 - 2m) + 11m.
Let N* be the total number of ranchers in Uruguay, and N(t) be the number of ranchers who have adopted an improved pasture technology there. Assume that the rate of adoption, , is proportional to both the number who have adopted the technology and the fraction of the ranchers who have not (and so are susceptible to conversion). Let a be the proportionality constant.
a. Write down the differential equation modeling N(t).
b. According to Banks (1993), N* = 17000, N(0) = 170, a = 0.5 per year.
Determine how long it takes for the improved pasture technology to spread to 80% of the population of the ranchers.
Answer:
A) dN / dt = aN( N* - N ) /N*
B) 12 years
Step-by-step explanation:
attached below is a detailed description of the solution
A) Write down the differential equation modelling N(t)
The differential equation of the modelling = dN / dt = aN( N* - N ) /N*
B) Determine how long it takes for improved pasture technology to spread to 80% of the population of the ranchers
firstly we will resolve the ODE and apply partial fractions, integrate and exponentiate before inputting the given data. attached below is a detailed solution
calculate the pay for the following day of a weekly time card given a wage of $16/hr
Answer:
24x16x7
Step-by-step explanation:
Answer:
$2,688 a week
Step-by-step explanation:
16 x 7 x 24 would be 2,688
Brandon has a jar of quarters and dimes with a total value of $7.85. The number of quarters is 7 less than twice the number of dimes. How many quarters and how many dimes does Brandon have?
Answer:
dimes=8
quarters=12
Step-by-step explanation:
the total value 380 cents
The area A of a circle in square feet with a radius r in feet is given by the formula, A=πr2. What is the area of a circle with a radius of 3 feet? Round your answer to the nearest thousandths.
Answer:
28.29
Step-by-step explanation:
A=πr2
=3.14(3^2) (btw the ^2 is exponent)
=3.14(9)
=28.29
Iman’s favorite colors are \blue{\text{blue}}bluestart color #6495ed, start text, b, l, u, e, end text, end color #6495ed and \pink{\text{pink}}pinkstart color #ff00af, start text, p, i, n, k, end text, end color #ff00af.
She has \blue{\text{1 blue shirt}}1 blue shirtstart color #6495ed, start text, 1, space, b, l, u, e, space, s, h, i, r, t, end text, end color #6495ed, \pink{\text{1 pink shirt}}1 pink shirtstart color #ff00af, start text, 1, space, p, i, n, k, space, s, h, i, r, t, end text, end color #ff00af, \blue{\text{1 blue hat}}1 blue hatstart color #6495ed, start text, 1, space, b, l, u, e, space, h, a, t, end text, end color #6495ed, \blue{\text{1 blue belt}}1 blue beltstart color #6495ed, start text, 1, space, b, l, u, e, space, b, e, l, t, end text, end color #6495ed, \blue{\text{1 blue pair of pants}}1 blue pair of pantsstart color #6495ed, start text, 1, space, b, l, u, e, space, p, a, i, r, space, o, f, space, p, a, n, t, s, end text, end color #6495ed, and \pink{\text{1 pink pair of pants}}1 pink pair of pantsstart color #ff00af, start text, 1, space, p, i, n, k, space, p, a, i, r, space, o, f, space, p, a, n, t, s, end text, end color #ff00af.
Iman selects one of these garments at random. Let AAA be the event that she selects a pink garment and BBB be the event that she chooses a shirt.
What is P(A\text{ or }B)P(A or B)P, left parenthesis, A, start text, space, o, r, space, end text, B, right parenthesis, the probability that the garment Iman chooses is pink or a shirt?
Answer:
1/2
Step-by-step explanation:
i got this from camellarosegarcia. thank you camellarosegarcia!!!
also got it right on Khan :)
The answer of probability that the garment Iman chooses is pink or a blue shirt is 1/2
What is Probability ?Probability means possibility.
It is a branch of mathematics that deals with the occurrence of a random event.
The value is expressed from zero to one.
The meaning of probability is basically the extent to which something is likely to happen.
Divide the number of events by the number of possible outcomes. This will give us the probability of a single event occurring.
In this case Iman has 2 choices pink or blue
So the probability that the garment Iman chooses is pink or a blue shirt
is 1/2 .
To know more about Probability
https://brainly.com/question/23298290
#SPJ2