If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then
m(b − a) ≤
b
f(x) dx
a
≤ M(b − a).
Use this property to estimate the value of the integral.
2
3
1 + x2
dx
0
Answers
Answer:
smaller value is 1.2
larger value is 6
Step-by-step explanation:
[tex]f(x)=\frac{3}{1+x^{2} }[/tex]
when x=a=0, one has
[tex]f(0)=\frac{3}{1+0^{2} } \\f(0)=3[/tex]
now, when x=b=2, one has
[tex]f(2)=\frac{3}{1+2^{2} } \\f(2)=\frac{3}{5}[/tex]
Therefore, the absolute minumun is
[tex]m=\frac{3}{5}[/tex]
and the absolute maximun is
[tex]M=3[/tex]
The approximation to the integral is
[tex]\frac{3}{5}(2-0)\leq \int\limits^2_0 {f(x)} \, dx \leq 3(2-0)[/tex]
hence
[tex]\frac{3}{5}(2)\leq \int\limits^2_0 {f(x)} \, dx \leq 3(2)\\\frac{6}{5} \leq \int\limits^2_0 {f(x)} \, dx \leq 6\\1.2 \leq \int\limits^2_0 {f(x)} \, dx \leq 6[/tex]
Related Questions
Zeke has swim club every 2 days and robotics Club every 8 days.
This month, he has swim club on the 2nd day of the month and robotics club on the 8th day of the month.
Zeke says that the first time he will have both clubs on the same day is the 16th day of the month because the LCM of 2 and 8 is 16.
Answers
Answer: No. Zeke found the LCM to be the product of two and eight but because eight is a multiple of two the LCM is eight so the first day he will have both clubs is the 8th day of the month
Step-by-step explanation:
all you have to do is fine the least common multiple of 2 and 8 which is eight so obviously zeke is incorrect because they said the least common multiple was 16 and it is not. zeke multiplied 2 and 8 which is not what you’re supposed to do to get the lcm.
The following equations involve different quantities and use different operations, yet produce the same result (4.13 x 103 = 4130 & 413,000 ÷ 102 = 4130) Use any strategy and words to explain why this is true
Answers
Answer:
fzdgxfmhcgj,hvjb.√∆≤ç˙
Step-by-step explanation:
Answer:
heyyyyyyyyyyyyyyy
Step-by-step explanation:
-100x - 100 = 0
-100x = ?
x = ?
Answers
Answer:
x = 100
Step-by-step explanation:
-100x - 100 = -100x
+100= +100
-100x= -100x + 100
x=100
Answer:
x = 100
Step-by-step explanation:
Jane has saved 600 dollars in a college fund. She added money to the account over the next year and at the end of the year the account had 890 dollars. Write an equation to represent the amount she saved over the year.
Answers
Answer:
$290.00
Step-by-step explanation:
The equation would be 890-600=290 because if you subtract the base amount from the final savings it would give you how much she saved altogether.
Two lines are perpendicular. The slope of the first line is 3/5. What is the slope of the second line?
Answers
-5/3
Step-by-step explanation:
m1 = 3/5
m1 * m2 = - 1. For a pair of perpendicular line.
Usking that m2 = - 5/3
Please help ASAP I don’t know how to do this
Answers
∆HGJ is isosceles
hence, angleH = angle J
8x = 6x + 18
8x - 6x = 18
2x = 18
x = 18/2
x = 9
angleH = 8x = 8×9 = 72
angleH =72°
what is 903 minus 538
Answers
Answer: Your answer is 365
Step-by-step explanation: Hoped this helped you. And have a wonderful day!!!
The final result of 903 - 538 is 365.
To subtract 538 from 903, you perform the following calculation:
903 - 538 = 365
To explain the process, you start with the number 903 (minuend) and subtract 538 (subtrahend) from it.
1. Begin with the units place: 3 - 8. Since 8 is greater than 3, you borrow 1 from the tens place. The units place becomes 3 + 10 (borrowed) - 8 = 5.
2. Move to the tens place: 0 (in 903) - 3 (borrowed) - 3 (from 538) = -6.
3. Lastly, the hundreds place: 9 - 5 (from 538) = 4.
To know more about final result:
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Sunday by 11:59pm
Points
me di
Hal 0
Question
Laura's sporting goods store purchased a bicycle at the wholesale price of $400. Laura marked up the price 22%. What is
the amount of markup?
Provide your answer below:
B FEEDBACK
MORE INSTRUCTION
SUBMIT
Content attribution
Answers
Answer:
The amount of markup is 88 dollars.
Step-by-step explanation:
Given that the whole sale price of bicycle is: $400
[tex]P = \$400[/tex]
Mark up is the profit that the seller of the product makes after selling the product more in price more than its cost or buying price.
Given that mark up percentage is 22%
It can be written mathematically as:
[tex]Mark\ up = 22\%\ of\ Price\\Mark\ up = 0.22 * P\\Mark\ up = 0.22 * 400\\= \$88[/tex]
Hence,
The amount of markup is 88 dollars.
Evaluate the factorial expression.
19!
16!(3 - 1)!
Answers
Answer:
2907Step-by-step explanation:
19!/16!(3-1)! =16!*17*18*19/16!2! =17*18*19/1*2 = 17*9*19 =2907use the elimination method to solve the system of equations. choose the correct ordered pair. 7x+3y=30 -2x+3y=3
Answers
Answer:
x = 3, y = 3
Step-by-step explanation:
Elimination method to find x:
(7x + 3y = 30) * -1 ===> -7x - 3y = -30
-2x + 3y = 3
add two equations to eliminate y ______________
-9x = -27 ===> x = 3
substitution to find y:
-2x + 3y = 3
-2(3) + 3y = 3
-6 + 3y = 3
3y = 9
y = 3
Elimination method to find y:
(7x + 3y = 30) * 2 ===> 14x + 6y = 60
(-2x + 3y = 3) * 7 ===> -14x + 21y = 21
add two equations to eliminate x ______________
27y = 81 ===> y = 3
Lin rode her bike 2 miles in 8 minutes. She rode at a constant speed. Complete the table to show the time it took her to travel different distances at this speed Enter
your answer as a decimal
What is the value of A?
distance traveled ]
Answers
you're not specific enough, but i took the test and..
miles minutes
2 ║ 8
1 ║ 4
1/4 ║ 1
What is the ratio of the rise over runof the line 2x -6y = 12?
Answers
Answer:
1/3
Step-by-step explanation:
Write Word form for 6 (16+27)
Answers
Answer:
two hundred and fifty eight
Step-by-step explanation:
cause 6 (16+27) is equal to 258.
Or the equations is said six multiplied by 16 plus 27
Ella is selling baked goods to raise money for charity. She spent $25.00 on baking
supplies. If each baked good sells for $0.75, what is the minimum number of baked
goods Ella needs to sell in order to raise $125.00 after the cost of supplies?
HELP
Answers
Answer:
I think the answer might be 141 baked goods. but I dont know don't trust me.
Step-by-step explanation:
Answer:
200.
Step-by-step explanation:
I know math. But if you want an explanation, here it is.
First, you have to add 25 to 125 because you're trying to gain 25 more dollars than 125 dollars to make up for the money you already spent. Next, you need to dive 150, the result of 125 plus 25, by .75 because you're trying to figure out how many goods you need to sell for .75 cents, to get 150 dollars. So, you do the division, and the answer is 200 dollars.
A mountain road rises 10 feet over a 206-foot run. What is its slope?
Answers
It's slope is 5/103 , by using simple calculation for slope.
What is slope?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively. The ratio of the "vertical change" to the "horizontal change" among (any) two distinct points along a line is used to calculate slope. The ratio can also be written as a quotient (also known as "rise over run"), which gives the same number for each and every two distinct points on same line.
Mathematically, it's calculated as "rise over run".
Here,
Rise is given i.e. 10feet.
and foot-run=206.
So, slope = Rise/foot-run
= 10/206
= 5/103 .
Hence, slope = 5/103.
Learn more about slope from given link:
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3
If a is 63% of x and c is of x, which of the following is
8
the closest equivalent of the ratio of a to c?
3
Answers
Answer:
The closet equivalent of the ratio of 'a' to 'c' is:
[tex]\frac{a}{c}=1.680\:[/tex]
Step-by-step explanation:
Given
a is 63% of xi.e.
a=0.63x
c is 3/8 of x.i.e.
c=3/8x
Hence,
[tex]\frac{a}{c}=\frac{0.63x}{\frac{3}{8}x}[/tex]
[tex]\frac{a}{c}=1.680\:[/tex]
Thus, the closet equivalent of the ratio of 'a' to 'c' is:
[tex]\frac{a}{c}=1.680\:[/tex]
Find the value of k so that the line going through the points A(2,7) and B(k, 5)
is parallel to the line y=12x-1
Answers
Answer:
Step-by-step explanation:
parallel line y=12x+c
put this point A(2,7)
7=12*2+c
c=-17
so the equation is y=12x-17
now put the point B
k=12*5-17
k=43
(s+12)+(-3s-8) equals?
Answers
Answer:
-2s + 4
General Formulas and Concepts:
Combining like termsStep-by-step explanation:
Step 1: Define expression
(s + 12) + (-3s - 8)
Step 2: Simplify
Combine like terms (s): -2s + 12 - 8Combine like terms (constants): -2s + 4Translate the phrase into an algebraic expression.
2 more than y
Answers
Answer:
2 + Y
Step-by-step explanation:
Two more than Y would be adding 2 to y, therefore adding 2 to y.
2 + Y
Joe’s Car service charges $5 to pick up passengers, plus 1.25 for each mile. Write an equation for the function that relates to the total cost of a trip to the distance. Also identify the slope and the y-intercept of the function.
Answers
Answer:
Initial fee charged = $5
Fee charged for a mile = $1.25
No. of miles traveled = x
Total fee charged = 5 + 1.25x
Slope = 1.25
y-intercept = 5
De’Shaun is 5 years younger than Nemo. Adela is twice as old as Nemo. Jefferson is 3 times as old as De’Shaun. Altogether their ages total 50. Find each person’s age
Answers
Answer:
Nemo: 10
De'Shaun: 5
Adela: 20
Jefferson: 15
Step-by-step explanation:
Let Nemo's age be x
De'Shaun's age= x-5
Adela's age= 2x
Jefferson's age= 3(x-5)
= 3x-15
x+x-5+2x+3x-15= 50
7x-20= 50
7x= 50+20
7x= 70
x= 10
Nemo's age= 10
De'Shaun's age= 10-5
= 5
Adela's age= 2(10)
= 20
Jefferson's age= 3(10)-15
= 30-15
= 15
Answer:
Age of Nemo = 10 years
De'shaun's age = 5 years
Adela's age = 20 years
Jefferson's age = 15 years
Step-by-step explanation:
Age of Nemo = x years
So, De'shaun's age = x - 5
Adela's age = 2*x = 2x
Jefferson's age = 3* (x -5) = 3*x - 3*5 = 3x -15
Total age = 50
x + x - 5 + 2x + 3x - 15 = 50 {Combine like terms}
x + x + 2x + 3x - 5 - 15 = 50
7x - 20 = 50
7x = 50 + 20
7x = 70
x = 70/7 = 10
Age of Nemo = 10 years
De'shaun's age = 10 - 5 = 5 years
Adela's age = 2* 10 = 20 years
Jefferson's age = 3*10 -15 = 30 - 15 = 15 years
Ellon has 10 cups of flour. A special cake she make to sell in her bakery requires 2 1/3 cups of flour
Answers
Jalil and Victoria are each asked to solve the equation ax – c = bx + d for x. Jalil says it is not possible to isolate x because each x has a different unknown coefficient. Victoria believes there is a solution, and shows Jalil her work
Answers
Answer:
[tex]x=\frac{d+c}{a-b}[/tex]
Step-by-step explanation:
The equation is:
a x - c = b x + d
so we subtract b x from both sides to group the terms that contain x on the left:
a x - b x - c = d
add c to both sides to isolate the terms in x on the left:
a x - b x = d + c
extract "x" as common factor on the left:
x (a - b) = d + c
divide both sides by the quantity (a - b) to isolate the "x":
x = (d + c) / (a - b)
or: [tex]x=\frac{d+c}{a-b}[/tex]
52.35 for 15 gallons
Answers
which multiplication expression is equal to 5/6 ÷1/2
Answers
Answer:
enjoy that's the answer
Step-by-step explanation:
the answer is 5/3
Answer:
it would be 5/3 or 1 2/3
Step-by-step explanation:
Is this a function please help I’m failing
Answers
Answer:
Yes
Step-by-step explanation:
The relation is a function. For a relation to be a function there must be a unique x value for each y value. So this means x's can not repeat, and in this relation, the x-values never repeat. Therefore this is a function.
what is the missing number in the pattern?
Answers
Answer:
where's the pattern?
Step-by-step explanation:
you didn't post the pattern
Please help I’m struggling on this topic
Answers
explanation: in the corner of (2x+18)°, it would be 90° as it is a right angle, 90-18=72 72/2=36, putting it into the equation 2(36)+18=90°. for (3x+6), putting 36 as x 3(36)+6=114° since every 3-sided triangle and a line with another line crossing through has angles that add up to 120°, if you add up 90 and 24 you get 114°, 120-114=6. if you add 6 to the 114° from the (3x+6)° equation you also get 120°, therefore x=36
I would appreciate the help!
Answers
Answer:
its b I'm pretty sure. it makes the most sense i
Answer:
A
Step-by-step explanation:
Multiply 15 by 8 to get 120. 120 + 15 × 11 = 285. 285 + 15 × 22 = 615. 615 + 20 × 7 = 755. 755 + 20 × 6 = 875. 875 + 20 × 14 = 1,155. 1,155 - 292.58 = 862.42. 862.42 - 292.58 = 569.84. Remember PEMDAS.
Irina’s basketball team has a 1 in 6 chance of winning the first-place trophy. She rolled a six-sided number cube repeatedly, assigning her team a number from 1 to 6 to demonstrate the probability that her team would win. Which method did she use to collect her data? survey simulation experiment observational study
Answers
Answer:
b is right (simulation)
Step-by-step explanation:
edg
The method of data collection used is the simulation method
What is a number cube?A number cube (also known as a die) is a device that is used in simulating probabilities
Below is how to determine the method she used.
From the question, we have the following highlights:
Chance of winning = 1/6She rolls a number cubeThe outcome is assigned to the team that would winThe highlight 3 above implies that the method of data collection used in this question is the simulation method
This is so because the winning team is determined by rolling a number cube
Read more about random sampling at:
https://brainly.com/question/14470673