Find the average of f(x)=x^3-x over [0,2]
Answers
9514 1404 393
Answer:
1
Step-by-step explanation:
The average value of the function is the integral over the interval, divided by the width of the interval.
[tex]\displaystyle\overline{y}=\frac{1}{2-0}\int_0^2{f(x)}\,dx=\left.\frac{1}{2}\left(\frac{x^4}{4}-\frac{x^2}{2}\right)\right|_0^2=\frac{1}{2}\left(\frac{2^4}{4}-\frac{2^2}{2}\right)=\frac{4-2}{2}\\\\\boxed{\overline{y}=1}[/tex]
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Related Questions
Is 7 a factor of 18y + 27z?
Answers
Answer:
no
Step-by-step explanation:
Answer:
No, it can't be factored
Step-by-step explanation:
find the value of k if the roots
of 3x²-5x+k=0, differ by 2
Answers
By the fundamental theorem of algebra, we can write the given quadratic in terms of its roots a and b as
3x ² - 5x + k = 3 (x - a) (x - b)
and upon expanding, we have
3x ² - 5x + k = 3x ² - (a + b) x + ab
Two polynomials are equivalent if their coefficients are equal, so
a + b = 5
ab = k
We're given that |a - b| = 2. If we assume a > b (that is, a is the larger root) then |a - b| = a - b = 2, or b = a - 2. Substitute this for b in the first equation above and solve for a :
a + (a - 2) = 5
2a - 2 = 5
2a = 7
a = 7/2
Solve for b :
b = 7/2 - 2
b = 3/2
Solve for k :
k = 7/2 × 3/2 = 21/4
Answer right and you get brainliest
What is the area
Answers
Area of triangle= 1/2 b x h
12 x 25=300/2 =150
Find a equivalent for 24/100
Answers
Answer:
Step-by-step explanation:
Divide the numerator and denominator by 2.
[tex]\frac{24}{100}=\frac{12}{50}[/tex]
To find equivalent fractions, we have to multiply the numerator and denominator by the same number or divide the numerator and denominator by the same number
2344x24553 math question please answer
Answers
Answer:
57552232
Step-by-step explanation:
please help me with all i will give 40 extra points if you answer all of the question for me and brainliest plus 5 stars if the answer you put is absurd i will repo you thanks
Answers
Answer:
This one ?
Step-by-step explanation:
Solve the equation for x, where x is restricted to the given interval.
Answers
Step-by-step explanation:
[tex]y = 3 \csc( \frac{x}{5} ) [/tex]
[tex] \frac{y}{3} = \csc( \frac{x}{5} ) [/tex]
Multiply by 5 on both sides.
[tex]5 \times \frac{y}{3} = \csc(x) [/tex]
Take the inverse of cosecant or arccsc of the function.
[tex]5 \: arccsc( \frac{y}{3}) = x[/tex]
The trigonometric equation for x, where x is restricted to the given interval is x = 5 * arccsc(y/5)
What is trigonometry?Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given
y = 3 CSC(x/5) for x in given domain
y/ 3 = CSC (x/5)
CSC(x/5) = y/3
x/5 = arccsc(y/3)
x = 5* arccsc(y/3)
Therefore, "x = 5 * arccsc(y/5)" is the trigonometric formula when x is limited to the specified range.
Learn more about trigonometry here:
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pls answer fast this is my last assignments is giving 30 points and make the brainiest
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Answer:
obama your mama she looks like joe mama
writing a two column proof (edge)
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At a bookstore Mrs.McIntyre buys three books, one for each of her children. Each book cost the same amount. She also buys $1.50 magazine for herself. Her purchases have a total price of $13.47. The equation 3x+1.50=13.47 models this situation. Solve this equation for x. Explain what this value of x means in terms of the bookstore purchases.
Answers
Answer:
X= $3.99
Step-by-step explanation:
X is the value of each book
Answer:
x=3.99
Step-by-step explanation:
3x + 1.5= 13.47
3x + 1.5 - 1.5 = 13.47 - 1.5
3x = 11.97
3x/3 = 11.97/3
HOPE THIS HELPSSS
what are the real solutions to the equation 5x2 + 29x + 20 = 0?
Answers
Answer:Solutions are: x = -5, x = -4/5.
Step-by-step explanation:
Answer: -30/29
Step-by-step explanation: Let's solve your equation step-by-step.
(5)(2)+29x+20=0
Step 1: Simplify both sides of the equation.
(5)(2)+29x+20=0
10+29x+20=0
(29x)+(10+20)=0(Combine Like Terms)
29x+30=0
29x+30=0
Step 2: Subtract 30 from both sides.
29x+30−30=0−30
29x=−30
Step 3: Divide both sides by 29.
29x/29=-30/29
The 8 in 429.86 has ___________ the value of the 8 in 321.58
Answers
Answer:
more than
Step-by-step explanation:
The 8 in 429.86 is nearest because is 80/100 while the 8 in 321.58 is 8/100
I need Help please in this problem
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Answer:
Answer the question yourself and stop being lazy!
Step-by-step explanation:
PLEASE HELP ME PLEASE!
Answers
Answer:
-4 and d
==============
Please give brainliest, I really want to rank up, thank you!
Answer:
x = d
x = -4
Step-by-step explanation:
not sure i tried
Solve. Write or draw to explain. Amy has 12 stickers. Jen has 9 stickers. They place 7 stickers on each page of a book. How many pages are in the book? Math Spot thpicks
Answers
Answer:
There's 3 pages in the book
Step-by-step explanation:
You add both of the amounts of stickers (12+9=21), then you divide by the amount on each page (21÷7=3)
Hope this helped!
The area of the shape below is
84 square centimeters.
a
10 cm
6 cm
12 cm
What is the length of a?
Answers
Answer:
Its D. 3cm
____________
Answer:
D=3
Step-by-step explanation:
Split this figure into 2 parts. Now you have 2 rectangles. One with sides 6 and 12. Other with sides (10 - 6) =4, and a.
Area of one rectangle is 12 × 6 = 72
Area of 2nd rectangle is 4 × a = 4a.
Since we know the total area of figure is 84
that means
72 + 4a = 84
4a = 84 - 72
4a = 12
a = 12 ÷ 4 = 3
a=3
. A carbon filter is used by a scientist to filter out small particles of soil and rocks
from a water sample taken from a stream. The exponential function f(x) =
500(0.35) * can be used to model the function. Which of the following could be
represented by the value 500 in the function rule?
Answers
Answer:
C- The size of the initial water sample, in gallons.
Step-by-step explanation:
A teacher has an annual income of $55,125.
The income tax the teacher has to pay is
6%. What is the amount of income tax in
dollars and cents that the teacher has to
pay?
FOR BRAINLIST!!
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Answer:
A - 3307,50
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
PLEASE HELP!!! ILL GIVE BRAINLIEST !! Which is the correct answer ? 100 POINTS !! EXPLAIN.
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explanation : as u can see the 2 and 8 are outside of the lines making it exterior, they are also alternate because one is on the outside of the left and one is outside of the right making it an alternate exterior angel
Can someone help me pls
Answers
Answer:
AB is not a tangent
Step-by-step explanation:
yOA^2=OB^2+AB
AB y a tangent
19^2=361,15^2=225, 8^2+64=289
So here the tangent isn't a tangent.
Hope it helps.....
Proving triangles similar
Answers
Answer:
x=11
Step-by-step explanation:
You do 38/3x+3 and 19/x+7 and then cross mulitply and get 57x+57=38x+266. Then yoy subtract 57 from 266 and get 57x=38x+209. Now you have to subtract 38 from 57 and then answer will be 19. So now you have 19x=209. Finally you divide 209 by 19 and get x=11. Good luck!
which statement is most likely true about the place modeled I the diagrams?
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Answer:
The answer is below. I hope this is the answer your looking for.
Step-by-step explanation:
does the graph represent a function
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Answer:
no this is not a function
Step-by-step explanation:
because if you do the line test it touches both of the lines its kinda hard to explain but yeah
Please help me with this
−3+5+6g=11−3g
-Aster
Answers
Answer:
g=1
Step-by-step explanation:
6g+3g=-3g+9+3g, add 3g to both sides and you get closer to the answer
Answer:
g=1
Step-by-step explanation:
solved and got the same answer
Please help !!!!!!!!!!!!!
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Answer:
1) x= sqrt 98 = 7 sqrt 2
Step-by-step explanation:
A tumor is injected with 0.52 grams of Iodine-125. After 1 day, the amount of Iodine-125 has decreased by 1.15%.
Write an exponential decay model with A(t) representing the amount of Iodine-125 remaining in the tumor after t days. Enclose arguments of the function in parentheses and include a multiplication sign between terms. For example, c*ln(t).
Then use the formula for A(t) to find the amount of Iodine-125 that would remain in the tumor after 8.5 days.
Answers
Answer:
The equation is [tex]A(t) = 0.52*(0.9885)^{(t)}[/tex].
0.4713 grams would remain in the tumor after 8.5 days.
Step-by-step explanation:
Exponential equation of decay:
The exponential equation for the amount of a substance that decays, after t days, is given by:
[tex]A(t) = A(0)*(1-r)^t[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
A tumor is injected with 0.52 grams of Iodine-125.
This means that [tex]A(0) = 0.52[/tex]
After 1 day, the amount of Iodine-125 has decreased by 1.15%.
This means that [tex]r = 0.0115[/tex]
So
[tex]A(t) = A(0)*(1-r)^t[/tex]
[tex]A(t) = 0.52*(1-0.0115)^t[/tex]
[tex]A(t) = 0.52*(0.9885)^t[/tex]
Then use the formula for A(t) to find the amount of Iodine-125 that would remain in the tumor after 8.5 days.
This is A(8.5).
[tex]A(t) = 0.52*(0.9885)^t[/tex]
[tex]A(8.5) = 0.52*(0.9885)^{8.5} = 0.4713[/tex]
0.4713 grams would remain in the tumor after 8.5 days.
Use the formula speed distance/time to calculate each speed A train travels 120miles in 2hours speed= Mph
Answers
Answer:
60
Step-by-step explanation:
120 miles divided by 2 hours equals 60 mph
Simplify 5/8+1/2-(-6)
Answers
Answer:
5/8 +4/8 -(-6) =
9/8 + 6 =
9/8 + 48/8 =
57/8
Step-by-step explanation:
PLEASE ANSWER ASAP! NO SCAM LINKS OR REPORTED.
Answers
Answer:
Its A
Step-by-step explanation:
Standard equation: y=mx+b
x+y=0
-x -x
y=-x+0
9)
The delivery van uses 33 litres of diesel to travel 264 miles.
How far would the van travel using 40 litres of diesel?
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Answer:
find how much the truck travels in,a litre