Suppose f has absolute minimum value m and absolute maximum value M. Between what two values must 7 f(x) dx 4 lie?Which property of integrals allows you to make your conclusion?
Answers
Answer:
3m ≤ ∫ f(x) dx ≤ 3M, at limit of b, a
Step-by-step explanation:
Like the question asked, which property of integral was used.
Property 8 of integrals was the basis upon which the question was solved.
The property of the integral is used to solve the problem. The function is given below.
[tex]3m & \leq \int_a^b f(x)dx \leq 3M \end{aligned}[/tex]
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
Suppose f has absolute minimum value m and absolute maximum value M.
We know that the property of the integral can be used.
If m ≤ f(x) ≤ M ∀ a ≤ x ≤ b. Then we have
[tex]m (b-a) \leq \int_a^b f(x) dx \leq M(b-a)\\[/tex]
Then we have
[tex]m \leq f(x) \leq M \ \ and \ \ 4 \leq x \leq 7[/tex]
This means that
[tex]\begin{aligned} m(7-4) & \leq \int_a^b f(x)dx \leq M(7-4)\\\\3m & \leq \int_a^b f(x)dx \leq 3M \end{aligned}[/tex]
More about the function link is given below.
https://brainly.com/question/5245372
Related Questions
A diamond ring cost $3500 in 2018. However, it increased in value by 4% in 5 point
2019 and 8% in 2020. What does the ring cost in 2020 ?
Answers
Answer:
The ring in 2020 costs around $3,931.2.
Step-by-step explanation:
We know how much the ring cost in 2018 and we know the percentages of the value as years go by.
To solve this, we will need to put the percentages into decimals, and since we are adding value, add an additional 1 [whole] in both decimals.
Should look like this:
2019: 1.04
2020: 1.08
Multiply the cost with the first year:
3500 x 1.04 = 3640
The ring costs $3,640 in 2019.
Then it says the ring went up by %8 percent in 2020.
Multiply the cost from last year with the current year:
3500 x 1.08 = 3931.2
The ring costs $3,931.2 in 2020.
I hope this helps!
find the position vectors of the points which trisect the line joining the points whose position vectors are i+2j+7k and 3i+j-k
Answers
Answer:
Step-by-step explanation:
you should have to find two position vectors between the given positional vectors . to find the first position vector take the ratio 1:2 internally and for the second positon vector take the ratio 2:1 as it is trisectedusing the position vector formula we get the respective answer's
3. While trick or treating with his buddies, Albert noticed he received 7 Kit Kat bars after
visiting 10 houses. If they plan on visiting 65 houses, how many Kit Kat bars might he receive
by the end of the night?
Answers
So all you have to do in this problem is multiply the amount with 6 and you can get the amount for 60 houses: 42
And then you can divide half of 7 to get the amount for 5 houses. However, we cannot use decimals in this problem. So round the amount: 3.5=4
So approximately Albert should get somewhere near 46 kk bars.
ANSWER FAST!!!!!! 25 POINTS!!!!!!!!
Answers
Answer:
X,Z,Y
Step-by-step explanation:
9π=28.27
√3/2=0.866
z=27.5
remember all are in cm^2 so no conversion is needed
Answer:
Circles X, Z, Y.
what's the answer for the question find the following Figure angle x and y angle z
from the degrees and go 47 degrees
Answers
where is figure????????????????????
What is Half a cup in a fraction? .........
Answers
Answer:
1/2
Step-by-step explanation:
One cup is 1.
Half of a cup in decimals is 0.5, and in fraction 1/2
Answer:
it would be 1/2
1/2 a cup
train A arrives at the station at 11:50 Am and leaves the station at 1:50 PM.how long does it stay in the station?
Answers
Answer:
2 hrs.
Step-by-step explanation:
11:50am ----> 12:50pm (1 hr.)
+
12:50pm ---> 1:50pm (1 hr.)
= 2 hrs
If m<TUV = (9x + 1), m<TUW = (7x-9), and m<WUV = (5x - 11), find the value of x.
Answers
Answer: x = 7
Step-by-step explanation:
Suppose ray UW divides ∠TUV into two angles ∠ TUW and ∠ WUV.
Then, m∠TUV = m∠ TUW + m ∠ WUV (i)
Given, m∠TUV = (9x + 1) , m∠ TUW = (7x-9) and m ∠ WUV = (5x - 11)
Substitute these values in (i), we get
[tex]9x+1=7x-9+5x-11\\\\\Rightarrow\ 9x+1= 7x+5x-9-11\\\\\Rightarrow\ 9x+1=12x-20\\\\\Rightarrow\ 12x-9x= 1+20\\\\\Rightarrow\ 3x= 21\\\\\Rightarrow\ x=\dfrac{21}{3}\\\\\Rightarrow\ x=7[/tex]
Hence, the value of x = 7.
Answer:
x=7
Step-by-step explanation:
write the interval in set builder notation (-2,3)
Answers
Answer:
helium,nitrogen
Step-by-step explanation:
A set-builder notation describes or defines the elements of a set instead of listing the elements. For example, the set { 1, 2, 3, 4, 5, 6, 7, 8, 9 } list the elements. The same set could be described as { x/x is a counting number less than 10 } in set-builder notation.
simplify the fraction 34%
Answers
The questions asks us to simplify the fraction 34%, first convert that into a decimal which would be .34, then change that as a fraction which would be [tex]\frac{17}{50}[/tex]
Answer:
brainliest plssssss
Step-by-step explanation:
answer is in the img below
What's the difference between 2x+2 and 2x+2=10?
Answers
Answer:
10Step-by-step explanation:
Given both expression
2x+2 and
2x+2=10
the difference inlvosves basically the subtraction of one expression from the other expression.
now before we perform the subtraction operation, let us do some preprocessing.
let us equate the first and second expression to zero
2x+2=0 and
2x+2-10=0
we can now subtract
(2x+2)-(2x+2-10)=0
open bracket
2x+2-2x-2+10=0
collect like terms
2x-2x+2-2+10=0
0+0+10=0
the answer is 10
HELP ASAP PLS pls help with all the questions thank you!
Answers
answer 2. min= 30.5
max=31.5
answer 3. 5 s.f
answer 4. False
Answer:not an answer but do you go to Cwcs because I go there too
Step-by-step explanation:
PLEASE SOMEONE HELP ME
The bar graph shows changes in price of regular gasoline from 1996–2010.
For example, at the end of 1996, the price per gallon for regular gasoline was
$0.15 more than the price per gallon at the end of 1995, the price at the end
of 1997 was $0.12 less than the price at the end of 1996, and so on.
1. Find the average change in the price of regular gasoline for the given years.
a. 1996–2002 b. 2003–2010 c. 1996–2010
2. The price per gallon for regular gasoline at the end of 1995 was $1.08. In what
year was the price per gallon for regular gasoline the lowest? What was the
price? Explain how you found your answer.
3. How many times greater is the price per gallon in 2010 than the price per
gallon in 1996? Price change (dollars per gallon)
Answers
Answer:
The answer is 5 times
Step-by-step explanation:
First, we need to read the change in price in 2000 and 2007, from the graph.
So, the change in price in 2000 was $0.14 and in 2007 it was $0.71.
Now, we do the same thing we always do when comparing two values - we divide them. So:
0.71 / 0.14 = 5.07
Of course, we could multiply these values with 100, in order to avoid decimal numbers. Then we would get:
71 / 14 = 5.07
We could also divide this in the form of fractions:
71/100 / 14/100 = 5.07
There are several ways we could divide rational numbers, but the result will always be the same.
Change in price in 2007 was around 5 times greater than the change in 2000.
I hope this helps!!;-)
Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15.b. 2x−4y=12 −5x+3y=10.a. 2x−4y=12 −3x+6y=−18.
Answers
Answer:
a. No solution, parallel lines.
b. One solution.
Step-by-step explanation:
Given the system of equations:
a. [tex]2x-4y=12[/tex]
[tex]-3x+6y=-15[/tex]
b. [tex]2x-4y=12[/tex]
[tex]-5x+3y=10[/tex]
To give a geometric description of the given system of equations.
The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.
i.e.
Number of planes = Number of variables
Number of lines = Number of equations in the system.
Here, we are given 2 variables and 2 equation in each system.
So, they can be represented in the xy-coordinates plane.
And the number of solutions to the system depends on the following condition.
Let the system of equations be:
[tex]A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0[/tex]
1. One solution:
There will be one solution to the system of equations, If we have:
[tex]\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}[/tex]
2. Infinitely Many Solutions: (Identical lines in the system)
[tex]\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}= \dfrac{C_1}{C_2}[/tex]
3. No Solution:(Parallel lines)
[tex]\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}[/tex]
Now, let us discuss the system of equations one by one:
a. [tex]2x-4y=12[/tex] OR [tex]2x-4y-12=0[/tex]
[tex]-3x+6y=-15[/tex] OR [tex]-3x+6y+15=0[/tex]
[tex]A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -3, B_2 = 6, C_2= 15[/tex]
Here, the ratio:
[tex]\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2} = -\dfrac{2}{3}\\\dfrac{C_1}{C_2} = -\dfrac{4}{5}[/tex]
[tex]\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}[/tex]
Therefore, no solution i.e. parallel lines.
b. [tex]2x-4y=12[/tex] OR [tex]2x-4y-12=0[/tex]
[tex]-5x+3y=10[/tex] OR [tex]-5x+3y-10=0[/tex]
[tex]A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -5, B_2 = 3, C_2 = -10[/tex]
[tex]\dfrac{A_1}{A_2}= -\dfrac{2}{5}\\\dfrac{B_1}{B_2} = -\dfrac{4}{3}\\\dfrac{C_1}{C_2} = -\dfrac{6}{5}[/tex]
[tex]\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}[/tex]
So, one solution.
Kindly refer to the images attached for the graphical representation of the given system of equations.
the low temperature in Anchorage, Alaska today was -4°F. The low
temperature in Los Angeles, California was 63°F. What is the difference in
the two low temperatures?
Answers
Answer:
67°F
Step-by-step explanation:
-4-63 = - 67°F
Therefore temperature difference=67
What is the profit percentage if the selling price is Rs 3000 and the cost price is RS 2000? * 5% 15% 50% 100%
Answers
Answer:
100% 50% 5% RS2000 Rs 3000
Square root 50 as a decimal
Answers
Answer:
I got 7.0 try that.
Find an equation for the surface obtained by rotating the line x = 6y about the x-axis.
Answers
Answer:
[tex]\frac{x^2}{36}=y^2+z^2[/tex]
Step-by-step explanation:
If we loo at the xy plane and consider the point (6y, y, 0), it looks like a circular path that is a cone as the curve is rotated about the x axis. The equation of the cone has the form:
[tex]\frac{x^2}{c^2}=\frac{y^2}{a^2}+\frac{z^2}{b^2}[/tex]
Given that x = 6y, to make the equation to be in the form as seen above, we square x = 6y, hence:
x² = (6y)²
x² = 36y²
The path parallel to yz axis are circles, so the equation should be as that of a circle. We need to add 36z², hence:
x² = 36y² + 36z²
[tex]\frac{x^2}{36}=y^2+z^2[/tex]
[tex](\frac{x}{6})^2=y^2+z^2[/tex]
This equation is that of a circle with radius of r = y = x/6, the resulting surface is that of a cone
Triangle ABC has coordinates A(2, -5), B(1, -3), and C(6, 1). If the triangle is
rotated 180° clockwise about the origin, what are the coordinates of A'?
Answers
Answer:(2,5)
Step-by-step explanation:
3(n+1)=5.4 Solve for n
Answers
Answer:
n =0.8Step-by-step explanation:
[tex]3(n+1)=5.4[/tex]
Expand ; 3(n+1)
[tex]3(n+1) =3n +3\\\\3n+3 =5.4[/tex]
Collect like terms and simplify
[tex]3n =5.4-3\\3n=2.4[/tex]
Divide both sides of the equation by 3
[tex]\frac{3n}{3} = \frac{2.4}{3} \\\\n = 0.8[/tex]
Answer:
The value of n is 0.8 .
Step-by-step explanation:
First, you have to expand to get rid of brackets :
[tex]3(n + 1) = 5.4[/tex]
[tex]3n + 3 = 5.4[/tex]
Next, you have to subtract 3 on both sides to remove 3 at the left side :
[tex]3n + 3 - 3 = 5.4 - 3[/tex]
[tex]3n = 2.4[/tex]
Lastly, you have to divide 3 on both sides :
[tex]3n \div 3 = 2.4 \div 3[/tex]
[tex]n = 0.8[/tex]
That’s a Meanie Genie. On an archeological dig near the highlands of Tibet, Alley discovered an ancient oil lamp. Just for laughs she rubbed the lamp. She quickly stopped laughing when a huge puff of magenta smoke spouted from the lamp and an ornery genie Murray appeared. Murray gave her two balance scales and nine identical stones as per her three wishes. Alley may use each of the scales exactly once. Choose a possible way for Alley to select the slightly heavier stone containing Ramanujan from among the nine identical-looking stones.
Answers
Answer:
Step-by-step explanation:
Arrange the stones into 3groups of 3and place one group on one side of the first balance scale and another group on the other side.
If both sides weigh the same, then she knows that the (heavier) jewel must be in the third group of three. However, if one side is heavier than the other, then she knows that the jewel is one of the three that weighed more. In either case, after only one weighing, Alley is able to identify a group of only three stones among which is the Rama Nujan.
Then take 2 of the 3 stones and place one on each side of the second scale. If one weighs more than the other, then she knows that this stone is the one containing the jewel. If they both weigh the same, then she knows that the third stone must contain the jewel.
A Meanie Genie.
An archeological dig was performed by a team of researchers near the highlands of the Tibet and alley found an ancient oil lamp. She rubbed the lamp and saw a huge puff of magenta smoke coming from it. Later in the genie appeared. She gave him a balance scale and nine identical stones.
Hence answer is the third stone contains jew.
After the arrangement, of the 3 types of stones one side of the first balance scale and another on the group of the other side. Both balances scale to weight the same the heavier consists of the jew than the others.Taking two and three on the scale she knows that the third is having the jewel.Thus alley choose a slightly heavier stone which continued the Ramanujan from the 9 identical ones.Learn more about the Meanie Genie.
brainly.com/question/12420511.
The graph of the function f is shown. The domain of f is [0, 50]. What is the range of g(x) = 4f(x)? PLEASE HELP!
Answers
Answer: the range of g(x) is [0, 7]
Step-by-step explanation:
The domain is the set of the possible values of y.
We can see that, for y = f(x) in the domain [0, 50]
The smallest possible value of y is 0, and the largest possible value of y is 1.75 (at x = 25).
Then the range of f(x) is [0, 1.75]
Now, if we have the function g(x) = f(x)*4
Let's analyze the possible values of g(x) in these extremes of the range of f(x).
when f(x) is in the minimum, f(x) = 0, we have that g(x) is:
g(x) = f(x)*4 = 0*4 = 0.
So 0 is the minimum in the range of g(x).
Now, for the maximum of f(x) (f(x) = 1.75) we have:
g(x) = f(x)*4 = 1.75*4 = 7
Then the range of g(x) is [0, 7]
What is the difference in kilowatt hours of monthly energy production between an a erage local wind speed of 15 miles per hour and an average local wind speed of 10 miles per hour?
Answers
Answer:
The difference in energy production in kilowatt hours of monthly energy produced between an average local wind speed of 15 miles per hour and an average local wind speed of 10 miles per hour is approximately 9 kWh
Step-by-step explanation:
We note that the energy produced is given by the formula;
Energy = 1/2 × m × v²
From which we have the energy per unit mass = 1/2 × v²
The energy produced by the wind traveling at 15 miles per hour is given as follows;
15 mph = 6.705 m/s
The energy per unit mass produced in a month of 30 days is therefore;
1/2×6.705²×60×60×24×30 = 58264304.4 J/kg
We note that 1 Kilowatt hour = 3.6 × 10⁶ Joules
Therefore;
58264304.4 J = 58264304.4 J/(3.6 × 10⁶) kWh = 16.184529 kWh
The energy produced by the wind traveling at 10 miles per hour is given as follows;
10 mph = 4.47 m/s
The energy per unit mass produced in a month of 30 days is therefore;
1/2×4.47²×60×60×24×30 = 25,895,246.4 J/kg
We note that 1 Kilowatt hour = 3.6 × 10⁶ Joules
Therefore;
25,895,246.4 J = 25,895,246.4 J/(3.6 × 10⁶) kWh = 7.193124 kWh
The difference in energy production in kilowatt hours of monthly energy produced between an average local wind speed of 15 miles per hour and an average local wind speed of 10 miles per hour is therefore;
16.184529 kWh - 7.193124 kWh = 8.991405 kWh. ≈ 9 kWh
Find the square root of this complex number -5+12i ? Solve
Answers
Answer:
Well you can't simplify the question anymore so I believe the question is the answer
Step-by-step explanation:
There is no equal sign so it can't be simplified anymore because it says 12i you can't combined 12i with -5 because of the variable
Find f(-7) if f(x) = 2x+8.
-6
03
02
22
Answers
2(-7)+8
-14 +8
-6
9 200 711 to the nearst ten
Answers
Answer:
9,200,711 rounded would be 9,200,710
Hope this helps!! - Maddy
(if this helps please make brainliest, rate, and thank so I know how I did!)
╰(*°▽°*)╯
Drag each equation to the correct to the correct location on the table
Answers
Answer:
x=3
2(2x-3)=65x - (3x-1)=75x-2x-4=5x=2
5(x+3)=254x-(2x+1)=3x+2x+3=9
Answer:
x=3
2(2x-3)=6
5x - (3x-1)=7
5x-2x-4=5
x=2
5(x+3)=25
4x-(2x+1)=3
x+2x+3=9
=> Please Help Me With My Math <=
Answers
Answer:
B
Step-by-step explanation:
A political scientist surveys 38 of the current 153 representatives in a state's congress.
Answers
Answer:
What is the question? Is this a true or false question ?
Step-by-step explanation:
The percentage of surveys done if, A political scientist surveys 38 of the current 153 representatives in a state's congress is 25%.
What is percentage?As it is clear from the term, percent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.
Given:
The number of surveys done = 38,
The representatives in a state's congress = 153,
Calculate the percentage as shown below,
Percentage of survey = The number of surveys done / total representative × 100,
Percentage of survey = 38 / 153 ×100
Percentage of survey = 0.25 × 100
Percentage of survey = 25 %
To know more about percentages:
https://brainly.com/question/26080842
#SPJ2
The complete question is: A political scientist surveys 38 of the current 153 representatives in a state's congress. Calculate the percentage of the survey.
Sandy and Steve share some prize money in the ratio 4:3. The prize money totaled $1400 How much
does Sandy receive ?
Answers
Answer:
Sandy will receive $800
Steve will receive $600
Step-by-step explanation:
Sandy : Steve = 4 : 3
Sandy = 4
Steve = 3
Total ratio = 4 + 3 = 7
Total prize money = $1400
How much does Sandy receive ?
Sandy's share = Sandy's ratio / total ratio × Total prize money
= 4 / 7 × 1400
= 4 × 200
= $800
Sandy will receive $800 out of $1400
Steve's share = Steve's ratio / total ratio × Total prize money
= 3 / 7 × $1400
= 3 × $200
= $600
Steve will receive $600 out of $1400
Check:
Sandy's share + Steve's share
= $800 + $600
= $1400