The value of constant c between 1 and 9 such that the average value of the function f(x) on the interval [1,9] is equal to is 5.
What is mean value theorem?Mean value theorem is the theorem which is used to find the behavior of a function.
The function given as,
[tex]f(x) = 6x^2 - 4x + 2[/tex]
The value of function at 0,
[tex]f(0) = 6(0)^2 - 4(0) + 2\\f(0)=2[/tex]
Differentiate the given equation,
[tex]f(x)' = 6\times2x - 4\times1 + 0\\f(x)' = 12x - 4\\f(x)' = 12x -4[/tex]
If the constant c between 1 and 9 such that the average value of the function f(x) on the interval (1,9], then,
[tex]f(c)'=12c-4[/tex]
Using Lagrange's mean value theorem,
[tex]f(c)'=\dfrac{f(9)-f(1)}{9-1}\\12c-4=\dfrac{452-4}{9-1}\\12c=54+4\\c=\dfrac{60}{12}\\c=5[/tex]
Thus, the value of constant c between 1 and 9 such that the average value of the function f(x) on the interval [1,9] is equal to is 5.
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Answer:
5.5402
Step-by-step explanation:
First you need to find the average value of the function, you can use a calculator to do that, which you will find is 164.
The questions asks you to find a number between 1 and 9 so that f(c) (which is just f(x)) equals the average value of the function.
Since you already know the average value (164), you can set the equation equal to 164 and solve for x, which should give you 5.5402.
If you want more information: the function equals the average value, which is 164=6x^2-4x+2, is the equation you want to set up and solve for x.
You may get two answers and I can't explain why because I don't understand it that well, just use the one that is in the 1 to 9 range.
The second answer should be negative which is out of the 1 to 9 range, which leaves you with the other number that rounds up to 5.5402
I hope this helps any other struggling students
Based on the graph how many distinct real number solutions does the equation x^3-3x^2+4=0 have
Answer:
2 solutions
Step-by-step explanation:
In order to answer a question "based on the graph," we need to have a graph of the equation. A graph provided by a graphing calculator is attached.
The cubic intersects the x-axis at two distinct points.
There are two (2) distinct real solution to the equation. (x = -1, x = 2).
Elise, Jake, Malik, and Xiao each solved the same inequality.
Random Reply:
Indeed, so they have.
PLEASE HELP ME! If an arithmetic sequence has a4 = 107 and a8 = 191, what is a₁? (I need the steps too please).
Answer:
[tex]\displaystyle a_1 = 44[/tex]
Step-by-step explanation:
Recall the direct formula for an arithmetic sequence:
[tex]\displaystyle a_n = a_1 + d(n-1)[/tex]
Where d is the common difference.
Therefore, we can write the following two equations:
[tex]\displaystyle \left \{ {a_4 = 107 = a_1 + d(4-1)\atop {a_8 = 191 = a_1 + d(8-1)}} \right.[/tex]
Solve the system. Simplifying yields:
[tex]\displaystyle 107 = a_1 + 3d\text{ and } 191 = a_1 + 7d[/tex]
Subtracting the two equations into each other yields:
[tex]\displaystyle \begin{aligned} (191) - (107) & = (a_1 + 7d) - (a_1 + 3d) \\ \\ 84 & = 4d \\ \\ d & = 21 \end{aligned}[/tex]
Using either equation, solve for the initial term:
[tex]\displaystyle \begin{aligned} 107 & = a_1 + 3(21) \\ \\ a_1 & = 107-63 \\ \\ & = 44\end{aligned}[/tex]
In conclusion, the initial term is 44.
Answer:
[tex]\huge\boxed{\bf\:a_{1} = 44}[/tex]
Step-by-step explanation:
In the given arithmetic series,
[tex]a_{4} = 107[/tex][tex]a_{8} = 191[/tex][tex]a_{1} = ?[/tex]We know that,
[tex]\boxed{a_{n} = a + (n - 1)d}[/tex]
Therefore,
[tex]a_{4} = a + 3d = 107 -----(1)\\a_{8} = a + 7d = 191 -----(2)[/tex]
By solving the two equations (1) & (2)....
[tex]\:\:\:\:a + 7d = 191 \\-\underline{a + 3d = 107 }\\ \underline{\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:4d = 84\:\:\:\:\:\:\:\:}}\\\\\\\\4d = 84\\d = 84 \div 4\\\boxed{d = 21}[/tex]
Now, we have the value of the common difference (d). To find [tex]a_{1}[/tex] or a, let's substitute the value of 'd' in (1).
[tex]a + 3d =107\\a + 3(21)=107\\a + 63 = 107\\a = 107 - 63\\\boxed{\bf\:a_{1} = 44}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
How many kilograms in 1 1/2 pounds?
Answer:
67.5 kgs.
Step-by-step explanation:
1 pound = 0.45 kg
1 1/2 pounds = 0.45 + 1/2 * 45
= 67.5 kgs.
Find the area of the shaded regions
your answer would be 254 I just did it and I got it right ✨
17) Find sine and cot
Answer:
79/156
Step-by-step explanation:
we know that cosx is the adjacent side over the hypotenuse.
hence, we can find the opposite side using the pythagorean theorem.
sqrt(13^2 - 5^2)
therefore, the opposite side is 12
opposite: 12
adjacent: 5
hypotenuse: 13
not that cot is adjacent over opposite while sin is opposite over hypotenuse.
So,
12/13 - 5/12
the answer is 79/156
Which linear inequality represents the solution set graphed?
Answer:
Your Answer is D.
Step-by-step explanation:
There isn't much to explain but look at the graph.
The slope of m = rise/run.
m = 1/2
b = -3/2
y = mx + b
Miquel runs 5 days a week. He runs 2 7/10 miles each day that he runs. What is the total number of miles Miguel runs each week?
Answer:
13.5
Step-by-step explanation:
If he runs five times a week and his route is 2 7/10 then you do 5x2 7/10
Which of the following describes the polynomial function?
8
==
4
-2
2
09
00
8
X
1
-5
do
9
The function has a negative leading coefficient.
O The function has an even degree.
O The function has zero turning points.
The function has one x-intercept.
Answer:
the function has one x intercept is the correct answer of given statement
who wan na ta lk? im bo red
Answer:
So this is what hello means :):):):):):):)
Step-by-step explanation:
Leo drew a line that is perpendicular to the line shown on the grid and passes through point (F, G). Which of the following is the equation of Leo's line?
A) y - F = -2(x - G)y
B) y + F = 2(x + G)
C) y - G = -1/2(x - F)
D) y - G = -1/2(x + F)
The equation of the perpendicular line drawn by Leo is [tex]y-G=\dfrac{-1}{2}(x-F)[/tex]. Option C is the correct answer.
The equation of the line is [tex]y-y_1=m(x-x_1)[/tex] where, [tex]m[/tex] is the slope of the line and [tex](x_1,y_1)[/tex] is the point through which it is passing.
How to determine the equation of a line?
A line is drawn perpendicular to the line shown in the image. The perpendicular line passes through the coordinate point [tex](F,G)[/tex].
The slope of the line from the graph is-
[tex]m=\dfrac{y-intercept}{x-intercept}\\=2[/tex]
Therefore, the slope of the perpendicular line is [tex]\dfrac{-1}{2}[/tex].
Also, it is being given that Leo's line is passing through the coordinate point [tex](F,G)[/tex].
So, the equation of the Leo's line is-
[tex]y-G=\dfrac{-1}{2}(x-F)[/tex]
Thus, the equation of the perpendicular line drawn by Leo is [tex]y-G=\dfrac{-1}{2}(x-F)[/tex].
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The maximum grain yield for corn is achieved by planting at a density of 37,000 plants per
acre. A farmer wants to maximize the yield for the field represented on the coordinate grid.
Each unit on the coordinate grid represents one foot. How many corn plants, to the nearest
thousand, does the farmer need? (Hint: 1 acre = 43,560 ft?)
у
5001
E
F
F
х
lo
-500
500
G
-500
H
The farmer needs approximately
corn plants.
Since there are 37000 plants per hectare, the total corn plan required is 475,665.75 corn plants
How to determine the area of a trapezium?The trapezium is a 2 -dimensional shape consisting of a triangle and a square.
The formula for calculating the area of a trapezoid is expressed as:
Area = 0.5(a + b)h
Area = 0.5(500 + 900) * 800
Area = 700 * 800
Area = 560000 square feet
Since 1 acre is equivalent to 43560 square feet, hence the total acre required is expressed as:
Required acre = 560000/43560
Required acre = 12.856 acres
Also since there are 37000 plants per hectare, the total corn plan required is 475,665.75 corn plants
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Assume that the weights of ripe watermelons grown at a particular farm are normally distributed with a mean of 30 pounds and a standard deviation of 1.9 pounds. If the farm produces 400 watermelons, how many will weigh less than 27.87 pounds?
We know that,
[tex] \rightarrow \: z = \frac{x - \mu}{\sigma} \\ [/tex]
z = standard scorex = measuring valueμ = meanσ =standard derivationinserting the given values in the formula
[tex]\rightarrow \: z = \frac{27.87 - 30}{1.9} \\\rightarrow \: z = - 1.121[/tex]
Area that's left to z = -1.121
Area that's left to -1.121 = 0.1311
= 13.11%
Hence ,
13.11% of the watermelons weigh less than 27.87 pounds
To find the number of watermelons,
We'll find 13.11% of 400
= 13.11% x 400
= 13.11/100 x 400
= 52.44
hence , approx 52 watermelons would be lesser than 27.87 pounds
please help! a point is chosen at random in the square, what percent of the time will the point be in the circle,round to the nearest tenth of a percent?
Answer:
78.5%
Step-by-step explanation:
You take the area of the circle which is pie*r^2
and divide it by the area of the square
Which fraction make comparison 3/4
Answer:
6/8, 12/16, and so on. I wasn't sure how you wanted this question to be answered, but 3/4 is also 0.75
Step-by-step explanation:
What is the value of x in |-6|=x
which angle is conterminal with a 645 degree angle
a. an angle measuring 75 degrees
b. an angle measuring 265 degrees
c. an angle measuring 345 degrees
d. an angle measuring 285 degrees
Answer:
D. An angle measuring 285 degrees
Step-by-step explanation:
An angle that is coterminal is congruent to the other angle whether negative or positive or more than 360.
An angle that is 645 degrees can be broken down into 360 + 285.
Since 360 is one revolution the angle would finish with 285 degrees.
Therefore the coterminal angle to 645 is 285.
Help me pls lol
I don’t understand
[tex]J'= (-5,-6)[/tex]
[tex]K'=(-5,-1)[/tex]
[tex]L'=(-10,-2)[/tex]
See graph below.
[tex]Hope[/tex] [tex]this[/tex] [tex]helps![/tex] [tex]Have[/tex] [tex]a[/tex] [tex]good[/tex] [tex]day![/tex] [tex]:)[/tex]
Find the area of the shape based on the provided measurements
Answer:
375 units²
Step-by-step explanation:
A = bh/2
A = (75)(10)/2
A = 750/2
A = 375
A box contains 3 orange pencils, 9 yellow pencils, and 5 green pencils.
Two pencils are selected, one at a time, with replacement.
Find the probability that the first pencil is green and the second pencil is yellow.
Express your answer as a decimal, rounded to the nearest hundredth.
The probability that the first pencil is green and the second pencil is yellow is 0.16.
What is the probability?Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that the first pencil is green and the second pencil is yellow = (number of green pencils / total number of pencils) x (number of yellow pencils / total number of pencils)
5/17 x 9/17 = 0.16
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OLZ HELP ILL MARK AS BRAINLEST
find the slope
Answer:
-1
Step-by-step explanation:
Find the perimeter of the figure. Round to the nearest hundredth and show work.
Answer:
38 cm
Step-by-step explanation:
The perimeter of the figure is the sum of the lengths of all its sides.
We have two unknown length, so let's find their lengths first.
x= 10 -6= 4 cm
y= 9 -2= 7cm
Let's add all the lengths together to find the perimeter:
Perimeter
= 9 +10 +2 +6 +7 +4
= 38 cm
Function or not a function pls help giving brainlest
Answer:
function
Step-by-step explanation:
For every value of 'x' ....there is only ONE value of 'y'
so it IS a function
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
Step-by-step explanation:
I NEED HELP SOON! THESE ARE DUE SOON!
Answer:
Q2: J. all real numbers.
Q4: [tex]f(3)=-20[/tex]
Q15: [tex]y=-3x+5[/tex]
Step-by-step explanation:
Q2: J. All real numbers.
Range: It can be [tex]y\geq 1[/tex].
It can't be [tex]y\geq 2[/tex].
Domain: It can't be [tex]x\geq 1[/tex] because it is going from (-∞,+∞)
Q4:
[tex]f(x)=-2x^2+x-5,f(3)=?[/tex]
Plugin x with 3 into the equation.
[tex]f(3)=-2(3)^2+(3)-5\\f(3)=-2*9+3-5\\f(3)=-18+3-5=-20\\f(3)=-20[/tex]
Q15: point-slope form.
[tex]y-(y_1)=m(x-x_0)[/tex], plugin [tex](2,-1)=(x_0,y_0)[/tex] and m=-3
[tex]y-(-1)=-3(x-(2))\\y+1=-3(x-2)\\y+1=-3x+6\\y=-3x+5[/tex]
Please help!! What do I do
Answer:
a(5) = 1.080
a(10) = 0.393
a(20) = 0.122
Step-by-step explanation:
Take the derivative of velocity v(t) -> acceleration a(t)
v(t) -> a(t)
Quotient Rule: [tex]\frac{u*dv-du*v}{u^2}[/tex]
[tex]120*\frac{x}{5x+13}[/tex]
Make u= 5x+13 and v=x
[tex]120*\frac{x'*(5x+13)-x*(5x+13)'}{(5x+13)^2}\\\\120*\frac{1*(5x+13)-x*(5)}{(5x+13)^2}\\\\120*\frac{(5x+13)-5x}{(5x+13)^2}\\120*\frac{13}{(5x+13)^2} \\\\a(t)=\frac{1560}{(5x+13)^2}[/tex]
Now Subsitute your a(5) , a(10) , a(20). Also, round to 3 decimal place.
a(5) = 1.08033241 = 1.080
a(10) = 0.3930461073 = 0.393
a(20) = 0.122170826 = 0.122
Answer:
(a) 1.080 ft/s²
(b) 0.393 ft/s²
(c) 0.122 ft/s²
Step-by-step explanation:
Acceleration is the derivative of velocity. You are being asked to differentiate the given function and evalutate the derivative at three different times. The function is a rational function, so the formula for the derivative of a ratio is applicable.
(u/v)' = (vu' -uv')/v²
__
For the given velocity function, the accleration is ...
v(t) = (120t)/(5t +13)
a(t) = v'(t) = ((5t +13)(120) -(120t)(5))/(5t +13)² = 1560/(5t +13)²
(a)At t=5, the acceleration is ...
a(5) = 1560/(5·5 +13)² = 1560/1444 ≈ 1.080 . . . ft/s²
(b)At t=10, the acceleration is ...
a(10) = 1560/(5·10 +13)² = 1560/3969 ≈ 0.393 . . . ft/s²
(c)At t=20, the acceleration is ...
a(20) = 1560/(5·20 +13)² = 1560/12729 ≈ 0.122 . . . ft/s²
_____
Additional comment
Many graphing calculators are capable of finding the numerical value of the derivative of a function.
If the following line segment is reflected across the y-axis, what are the coordinates of the new endpoints?
A. (1, 6) and (3, 2)
B. (-1, -6) and (-3, -2)
C. (6, -1) and (2, -3)
D. (-6, 1) and (-2, 3)
Answer:A
Step-by-step explanation: im right im a god at answering these kind of equations.
6) Find the approximate perimeter of the following shape. Use 3.14 for pi
Answer:
where is the shape ???????
A rental car company charges $72.37 per day to rent a car and $0.06 for every mile
driven. Colton wants to rent a car, knowing that:
• He plans to drive 275 miles.
• He has at most $450 to spend.
Answer:
5.99 days.
Step-by-step explanation:
If you are asking how many days he can rent the car then this is the correct answer.
So first multiply 275 x .06 to get how much money he will spent on the mileage. Which is $16.50. Then subtract that from $450 which is $433.50 and divided by $72.37.
Ashley makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working h hours
Answer:
twin what does H mean?
Step-by-step explanation: if you mean 8 the answer is 72.