Answer:
: let's recall that the average value of a function for an interval of (a,b) is given by formula: k=1b−a∫baf(x)dx where; k:average value k=16−2∫62(x2−2x+5)dx k=14(∣∣∣x33−2x22+5x∣∣∣62) k=14(∣∣∣x33−x2+5x∣∣∣62) k=14[(633−62+5⋅6)−(233−22+5⋅2)] k=14[(2163−36+30)−(83−4+10)] k=14[(2163−6)−(83+6)] k=14[216−183−8+183] k=14[1983−263] k=14[1723] k=17212
QuestionThe average of a function over an interval is computed as (1/width of interval) times the definite integral of the function evaluated over the interval. The indefinite integral of e^2x is (1/2)e^2x. So the answer is found by evaluating:(1/2)*[(1/2)[e^8 - e^4]], or (1/4)[e^8 - e^4]which equals about 731.6.
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Brainly.com
Question
Find the average value of f(x)=2/x over the interval [1, 3].
Answer · 0 votes
[tex] \bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll}average~rate\of~change\end{array}\\-------------------------------\\f(x)= \cfrac{2}{x} \qquad \begin{cases}x_1=1\x_2=3\end{cases}\implies \cfrac{f(3)-f(1)}{3-1}\implies \cfrac{\quad \frac{2}{3}-\frac{2}{1}\quad }{2}\\\\cfrac{\quad \frac{2-6}{3}\quad }{2}\implies \cfrac{\quad \frac{-4}{3}\quad }{\frac{2}{1}}\implies \cfrac{-4}{3}\cdot \cfrac{1}{2}\implies -\cfrac{2}{3} [/tex]
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Wyzant
Question
Find the average value of the function f(x)=x^3 over the interval [0,2] and find the value(s) of x at which the function assumes the average values
Answer · 0 votes
The average value of f is defined as: 1/(b-a)∫ f(x) dx (where integral is evaluated from a to b) If we are to integrate f(x) = x3 we get: (1/4)* (x4) Applying formula for average value: [1/(b-a)]*[(1/4)*(x4)]a to b Evaluating this result where a = 0 and b = 2: [1/(2-0)]*[(1/4)*(x4)]a to b =(1/2)*[((1/4)*x4)]a to b =(1/2)*[((1/4)*(2)4) - (2*(0^4))] =(1/2)*[((1/4)*16)-0] =(1/2)*(4) =2
The average rate of change over the interval [a,b], or the secant line between the points a and b on the function f(x), is [f(a) - f(b)]/[a-b]. So, substitute a for 1 and b for 5, and you get [f(1) - f(5)]/[1–5]. The quotient of that is your average rate of change.
the average value of f(x) on [a,b] is ∫[a,b] f(x) dx ----------------------- b-a f' = 3x^2-6x f = x^3-3x^2+4 so, you want ∫[-1,3] x^3-3x^2+4 dx -------------------------- 3 - (-1) which I'm sure you can do.
1/2 e 2 - 1/2 or 3.19 Given: f(x)=2x 2 e 2x [0, 1] The average value of a function is: Where: a and b -intervals [a,b] f(x) - given function Substitute the values to the formula: In the integration of the function, we will use integration by parts: Let: u = 2x 2 dv = e 2x dx For du, get the derivative of u: du = 2(2x 2-1 ) = 4x dx For v, integrate dv: v = 1/2 e 2x Substitute the values to the integration by parts formula, and plug it in the solution: Get the integration by parts of xe 2x dx and let: u = x dv = e 2x dx for du,get the derivative of x du = dx For v, integrate dv v = 1/2 e 2x Substitute the values to the integration by parts formula, and plug it in the solution: Final answer: The average value of the function is 1/2 e 2 - 1/2 or 3.19
Step-by-step explanation:
plz brian list Oh and the real answer is k=17212
A semi-circle with a diameter of 6 cm sits on top of an isosceles trapezoid. Find the area of the entire figure.
Answer:
86.13 cm²
Step-by-step explanation:
the area of the entire fig =
(½×3.14×3²) + (½×(10+6)×9)
= (14.13)+(72) = 86.13
The average (also called mean) number of calories I consumed in the last 4 days is 2100. Today I decided to splurge and consumed 3000 calories. What is my new average consumed calories, now accounting for 5 days?
your friend borrowed 1050 from you to buy a new dirt bike. your friend pays you back the principal plus 7.25% interest per year for 3 years. what is the total amount your friend will owe you at the end of 3 years
Answer:
12.78375
Step-by-step explanation:
7.25% of 10.50 = 0.76125
0.76125 × 3 = 2.28375
10.50 + 2.28375 = 12.78375
So his friend will owe him 12.78375
The perimeter of this rectangle is 30 units. How long is the longer side?
a. 24 units
b. 9 units
c. 5 units
d. 6 units
Answer:
b. 9 units
Step-by-step explanation:
30/2 -6 = 15-6 = 9
Answer:
9
Step-by-step explain
6+6=12
12+x=30
30-12=18
18/2 =9
the equation s=2√5x can be used to estimate the speed ,s,of a car in milles per hour, given the length in feet ,x, of the tire marks it leaves on the ground .A card travelling 90 miles per hour came to a sudden stop according to the equation ,how long would the tire marks be for this car A 355 feet B 380 feet C 405 feet D 430 feet
Answer:
405 feet
Step-by-step explanation:
s = 2 * (√5) * 90
s = 2 * 201.246117975
s = 402.49223595
Closest estimate
405 feet
Answer:
Since The equation that depicts the motion of the Car is given.
The speed in terms of the tire marks...
s= 2√5x
where x is the tire marks(in feet.)
s is the speed(miles per hr)
We can't use the speed in Miles per hr when the tire mark is feet.
1mile = 5280ft
90miles x 5280ft/1mile = 475,200ft/hr
Making x the subject
x= s/2√5
x= 475/200/(2√5 )
=106,257ft
I still can't see what I'm missing or You sure you didn't forget to add something else to the question?
Can I get help with number 16.
Plz help me well mark brainliest if correct
Answer:
B) producers
Step-by-step explanation:
producers use water, air, and sunlight to make there own food and energy.
A rectangular prism has a length of 2 feet, a width of 6 feet, and a height of 3, teet. What is the volume of the prism? Enter your answer in the box as a simplified mixed number or a decimal
Answer:
V = 36 ft3
Step-by-step explanation:
2*6= 12
12*3= 36ft
Plz help me well mark brainliest if correct,.....???.
Answer:
B: 6
the heights between 45 and 55 are : 46, 49, 50, 50, 52,52
thats 6 students
Step-by-step explanation:
please mark brainliest
In the triangle below..
Answer:
44
Step-by-step explanation:
Step 1: Create an equation to solve for ∠Z
Recall that trig ratio tangent = Opposite over Adjacent
Opposite of ∠Z = 75 and adjacent of ∠Z = 79
Hence, [tex]tan(z)=\frac{75}{79}[/tex]
We now solve for z
Step 1: Multiply each side by the inverse of tan ( tan ) ^-^1
[tex]tan(z)*tan^-^1=z\\tan^-^1(\frac{75}{79} )=43.51213147[/tex]
We're left with z = 43.51213147
Our last step is to round to the nearest degree,
We get that ∠Z = 44
To make a newspaper with 60 pages you need 15 sheets of paper which are on top of each other. Then they are folded together. Page 7 is missing. Which other pages are missing in this newspaper?
Answer: here’s your answer
Step-by-step explanation:
pages are 60
sheet 15
on one sheet we get no of
pages=60/15=4
on one sheet we get 4 pages
they are stuck each other
so
let we consider
on1st sheet page no 1=60
2=59
so 7pageno. missing with also 8
(because attaching each other)
7=60-7
8=60-8
answer is 7,8,52,53pages are 60
sheet 15
on one sheet we get no of
pages=60/15=4
on one sheet we get 4 pages
they are stuck each other
so
let we consider
on1st sheet page no 1=60
2=59
so 7pageno. missing with also 8
(because attaching each other)
7=60-7
8=60-8
answer is 7,8,52,53
Could someone answer for this for me?
PROBLEM 1. Veldora walked around the circular pool. The circular pool has a
diameter of 3 meters. What is the distance that Veldora has walked?
Step 1 – Read and understand
What is asked in the problem? ____________________________
What do you know of the problem?________________________
Step 2 – Plan
What must be done to solve the problem? _________________
Step 3 – Solve and answer ___________________________
Carry out the plan & write the final answer. _______________
Step 4 – Check
Is the answer correct? _______________________
PROBLEM 2. How much greater is the circumference of the circle with a diameter of
12m than another circle with a radius of 5m?
Step 1 – Read and understand
What is asked in the problem? ____________________________
What do you know of the problem?_______________________
Step 2 – Plan
What must be done to solve the problem?_________________
Step 3 – Solve and answer ________________________
Carry out the plan & write the final answer._______________
Step 4 – Check
Is the answer correct?_________
Answer:
9.42m
Step-by-step explanation:
I took this on a test. Was extremely difficult, but I remembered the answer after my 4th retake
To solve a system of inequalities, you just need to graph each inequality and see wich points are in the overlap of the graphs.
True or false?
This is often how many math teachers and textbooks approach problems like this. The overlapped region is the region in which satisfies every inequality in the system. Be sure to note the boundary of each region whether you're dealing with a dashed line or a solid line. Dashed lines mean points on the boundary do not count as solution points, whereas solid boundaries allow those points as part of the solution set.
Side note: This is assuming you're dealing with 2 variable inequalities. If you only have one variable, you don't need to graph and instead could use algebra. Graphing doesn't hurt though.
Calculate the radius of the below. Show all work.
Area -0.25 ft
Answer:
r ≈ 0.28
Step-by-step explanation:
[tex]r=\sqrt{\frac{A}{\pi } }[/tex]
[tex]r=\sqrt{\frac{0.25}{\pi } }[/tex]
0.28209
≈ 0.28
Can someone answer this?
Answer:
Step-by-step explanation:
6x-1+3x+5x+3+4x+8+5x+5=360 degree(sum of exterior angle of a pentagon is 360 degree)
23x+15=360
23x=360-15
x=345/23
x=15
therefore the value of x is 15 degree.
A) Do the following lengths form a right triangle? Prove it by SHOWING YOUR WORK. 0 6 8 9
Answer:
friend me on here and imma send you the link Step-by-step explanation:
A football field is a rectangle 80 meters wide and 110 meters long. Coach Trevor asks his players to run from one corner to the other corner by running diagonally across the field. What is the distance from one corner of the field to the other corner? Answer choices are rounded to the nearest meter.
Answer:
136
Hypothenus² = Opposite² + Adjacent²
H²= 110² + 80²
H²= 18500
H= √18500
H = 136m
Estimate the difference of the decimals below by rounding to the nearest whole number.
23.827
- 1 .218
Answer:
23
Step-by-step explanation:
The difference between the 23.827 - 1.218
23.827 - 1.218 = 22.609
By rounding to the nearest whole number it is 23.
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 7 minutes. Find the probability that a randomly selected passenger has a waiting time
greater than 1.25 minutes.Find the probability that a randomly selected passenger has a waiting time greater than 1.25 minutes.
Answer:
0.8214
Step-by-step explanation:
We have
F(x) = 1/b-a
With b = 7
And a = 0
Such that we have
1/7-0
= 1/7
Probability of x> 1.25
7-1.25
= 5.75
1/7 x 5.75
= 0.8214
Therefore the probability that a randomly selected passenger has a waiting time more than 1.25 minutes is = 0.8214.
Thank you!
Let g(t)= t−16 t−4. a. Make two tables, one showing the values of g for t=15.9, 15.99, and 15.999 and one showing values of g for t=16.1, 16.01, and 16.001. b. Make a conjecture about the value of limt→16 t−16 t−4.
Answer:
[tex]\lim_{t \to \ 16} (t-16)(t-4) =0[/tex]
Step-by-step explanation:
g(t)= (t-16)(t-4)
(a) Then, we have,
t g(t)
15.9 -1.19
15.99 -0.1199
15.999 -0.011999
Also, we have,
t g(t)
16.1 1.21
16.01 0.1201
16.001 0.012001
(b) We can see, from the above table that as 't' tends to 16 from the left hand side, the value of g(t)= (t-16)(t-4) is tending to 0 from the negative direction.
Similarly, from the second table, we can see that as 't' tends to 16 from the right hand side, the value of g(t)= (t-16)(t-4) is tending to 0 from the positive direction.
Thus, we can say that [tex]\lim_{t \to \ 16-} (t-16)(t-4)[/tex] & [tex]\lim_{t \to \ 16+} (t-16)(t-4)[/tex], i.e., the left hand limit and right hand limit of g(t)= (t-16)(t-4), at t=16, both exist and is both equal to 0.
Since both these limits exist and are equal, we can say, [tex]\lim_{t \to \ 16-} (t-16)(t-4) = \lim_{t \to \ 16+} (t-16)(t-4) = \lim_{t \to \ 16} (t-16)(t-4) = 0[/tex]
for homework lawl
Evaluate each expression when x is 4 and y is 6.
(6-x)3 + y
Easy variable question pls help
Answer:
z = -4 1/2
Step-by-step explanation:
1. First change the mixed fractions to improper fractions so it's easier
[tex]\frac{16}{5\\}/(z-\frac{1}{2}) = \frac{8}{3}/(z+\frac{1}{3})[/tex]
2. Simplify
[tex]\frac{32}{5(2z-1)} = \frac{8}{3z+1}[/tex]
3. Cross multiply
[tex]32(3z+1) = 5(2z-1) * 8[/tex]
4. Simplify again (distributive property)
[tex]32(3z+1) = 40(2z-1)[/tex]
5. Distributive property
[tex]32(3z+1) -> 96z+32[/tex]
[tex]40(2z-1) -> 80z-40[/tex]
[tex]96z+32=80z-40[/tex]
6. Subtract 32 from both sides
[tex]96z+32-32 = 80z-40-32[/tex]
7. Simplify
[tex]96z = 80z-72[/tex]
8. Subtract 80 from both sides
[tex]96z-80z=80z-72-80z[/tex]
9. Simplify
[tex]16z=-72[/tex]
10. Divide both sides by 16
[tex]\frac{16z}{16}=\frac{-72}{16}[/tex]
11. Simplify
[tex]z=-\frac{9}{2} -> also = -4\frac{1}{2}[/tex]
Sorry if it was too long but hope this helps! :)
And also try using symbolab cuz it gives step by step explanations it's really good!
The mean of a standard normal probability distribution _____. a. can be any value b. can be any value as long as it is positive c. is always equal to 1 d. None of these answers are correct.
Answer:
D
Step-by-step explanation:
The mean of a standard normal distribution is always = 0 with the standard deviation being equal to. Therefore a standard normal distribution is a normal distribution described with a mean of 0 and standard deviation of 1. Since a standard normal distribution is centered at the middle with equal distribution to both the left and right of the distribution. The centre point is 0, which is the mean and the standard deviation is 1 to either side of the distribution.
PLEASEEEEEE PLEASEEEEEE HELPPPPPP IM BEGGING SOMEONE PLEASEEEEEEE I REALLY NEED HELPPPPPPPPPP
Answer:
Step-by-step explanation:
4x-5+3x+5+40=180 degree(sum of interior angles of a triangle)
7x+40=180
7x=180-40
x=140/7
x=20
Find the sum of the first four terms of the geometric series 5 + 50 + 500+....
The answer is 5 + 50 + 500+5000= 5555
Solve 1/3(3.2×1.4)2.8
Simplify your answer
4 68⁄375 is the purpose answer
Philip wants to buy a new video game system that costs
$349.99 including tax. Philip has $125.50 saved. If
Philip mows grass for $15.00 per yard, what is the least
amount of yards he could cut to purchase the new video
game system?
Answer:
I think the answer I think the answer would be 14
5(k+2)-3(k+2) combine to make simpiler
Answer:
2k + 4
Step-by-step explanation:
David,
Start by performing the indicated multiplication:
5(k+2)-3(k+2) becomes 5k + 10 - 3k - 6.
Next, combine like terms: 5k - 3k + 10 - 6 becomes 2k + 4
This 2k + 4 is the desired simpler result.
An advertising company charges $40 per half - page advertisement and $75 per full-page advertisement. Michael has a budget of $800 to purchase 13 advertisements. A) Define a variable for each unknown. Write a system of equations to represent the situation. B( How many half-page advertisements does Michael purchase? Show Your Work. C) How many full-page advertisements does Michael purchase? Show your Work. ( Will Mark Brainliest but have to show work) Answer A, B & C. No links or nonsense answers please.
The number of half page advertisements that Michael purchased is 5 while the full page advertisements is 8.
Let the number of half page ads be represented by h
Let the number of full page ads be represented by f.
Therefore, the system of equations to represent the situation will be:
h + f = 13 ....... i
40h + 75f = 800 ........ ii
From equation i,
h = 13 - f ....... equation iii
Put the value of h into equation ii
40h + 75f = 800
40(13 - f) + 75f = 800
520 - 40f + 75f = 800
Collect like terms
75f - 40f = 800 - 520
35f = 280
f = 280/35
f = 8
The number of full-page advertisements that Michael purchased is 8.
Since h + f = 13
h + 8 = 13
h = 13 - 8
h = 5
The number of half page advertisements that Michael purchased is 5.
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https://brainly.com/question/24429956