Question 3 1 pt 1 Given 4 < f'(x) < 8 for all values of x. Determine the possible range of possible values for f(1) - f( - 6) using mean value theorem. The minimum possible value for f(1) – f( – 6): the maximum possible value for f(1) – f( – 6):
Answers
To use the mean value theorem, we know that there exists a c between 1 and -6 such that f'(c) = (f(1) - f(-6))/(1 - (-6)) = (f(1) - f(-6))/7. Since 4 < f'(x) < 8 for all values of x, we know that 4 < f'(c) < 8.
To find the minimum possible value for f(1) - f(-6), we use the smallest possible value for f'(c), which is 4. Therefore, we have:
f'(c) = (f(1) - f(-6))/7
4 = (f(1) - f(-6))/7
28 = f(1) - f(-6)
So the minimum possible value for f(1) - f(-6) is 28.
To find the maximum possible value for f(1) - f(-6), we use the largest possible value for f'(c), which is 8. Therefore, we have:
f'(c) = (f(1) - f(-6))/7
8 = (f(1) - f(-6))/7
56 = f(1) - f(-6)
So the maximum possible value for f(1) - f(-6) is 56.
Therefore, the possible range of values for f(1) - f(-6) is from 28 to 56.
Using the Mean Value Theorem, there exists a value c in the interval (-6, 1) such that f'(c) = (f(1) - f(-6))/(1 - (-6)). Given that 4 < f'(x) < 8 for all values of x, we can apply these bounds to f'(c).
4 < (f(1) - f(-6))/7 < 8
To find the minimum and maximum possible values for f(1) - f(-6), we can solve for this expression in the inequalities:
Minimum possible value:
4 < (f(1) - f(-6))/7
f(1) - f(-6) > 4 * 7
f(1) - f(-6) > 28
Maximum possible value:
(f(1) - f(-6))/7 < 8
f(1) - f(-6) < 8 * 7
f(1) - f(-6) < 56
So, the minimum possible value for f(1) - f(-6) is 28, and the maximum possible value for f(1) - f(-6) is 56.
Learn more about mean value theorem here: brainly.com/question/30403137
#SPJ11
Related Questions
)The area of a rectangular painting is 4636 cm 2 .
If the width of the painting is 61 cm , what is its length?
Answers
The length of the rectangular painting is equal to 76 cm.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
The area of a rectangular painting is 4636 cm². The width of the painting is equal to 61 cm.
The length of the painting is calculated as,
Area of rectangle = Length x Width
4636 = Length x 61
Length = 4636 / 61
Length = 76 cm
The length is 76 cm for the rectangle.
To know more about an area follow
https://brainly.com/question/25292087
#SPJ1
Aubrey used
4
7
liter
7
4
literstart fraction, 4, divided by, 7, end fraction, start text, space, l, i, t, e, r, end text of paint for a mural in her room and
2
10
liter
10
2
literstart fraction, 2, divided by, 10, end fraction, start text, space, l, i, t, e, r, end text for a wall in her bathroom.
Answers
The total amount of paint Aubrey used is more than 1/2 liter but less than 1 liter
Estimating the total amount of paint Aubrey usedTo estimate the total amount of paint that Aubrey used for both the mural and the wall, we can add the fractions of paint used
So, we have
Total = 4/7 + 2/10
Evaluate the sum in decimals
This gives
Total = 0.77 (approximated)
This value is between 0.5 liters and 1 liter
Hence, the estimate is between 0.5 liters and 1 liter
Read more about fractions at
https://brainly.com/question/1330447
#SPJ1
Complete question
Aubrey used 4/7 liter of paint for a mural in her room and 2/10 for a wall in her bathroom.
Determine a reasonable estimate for the total amount of paint Aubrey used
Answer: B or the one that is more than 1/2 but it is less than 1
Step-by-step explanation: Took quiz on khan
The scores on the statistics test was normally distributed with a mean of 86 and a standard deviation of 5. Jose scored a 93 on his test. What percentage of the class scored less than he did?
Answers
The scores on the statistics test was normally distributed with a mean of 86 and a standard deviation of 5. Jose scored a 93 on his test then 1.4% of the class scored less than he did.
What is Normal Distribution?A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
The scores on the statistics test was normally distributed with a mean of 86, a standard deviation of 5, and Jose scored a 93 on his test.
We need to find the percentage of the class scored less than he did
z=(x-mean)/ S.D
=93-86/5
=7/5
=1.4
Therefore 1.4 percentage of the class scored less than Jose did.
To learn more on Normal Distribution click: https://brainly.com/question/25394084.
#SPJ1
The perimeter of an equilateral triangle is 6x - 24. Which expression represents the length of one side?
Answers
Answer:
side = 2x - 8
Step-by-step explanation:
An equilateral triangle has 3 equal sides.
The perimeter is 3 times one side
In this case P = 6x - 24
Side = p/3 = (6x - 24)/3
Side = 2x - 8
Find the area of the shaded region (s) of each figure. Explain or show your thinking
Answers
Answer:
ok
Step-by-step explanation:
ok so the answer is thx for the points
Passes through 5,4 slope -3 ASAP
Answers
Y=-3x+19
Combine these radicals
-6 v/100 + v/36
A.)-66
B.) -54
C.) -6 v/ 136
D.) -6 v/16
(dont delete my question please I only use this for work ok).
Answers
Answer: B.) -54
Step-by-step explanation: view screenshot
The width of a rectangular garden is 4 meters less than 2 times the length. The area of the garden is 6 square meters. Which is the function to find the dimensions of the the garden?
a) 2l^2−4l−6=0
b) 2w^2+4w+6=0
c) 2w^2+4w−6=0
d) 2l^2−4l+6=0
Answers
The dimensions of the the garden are 8 x 12
What is Quadratic Equation?
The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f. (x).
A = l x w
l = 2w-4
A = w (2w-4)
A = 2w² -4w
96m² = 2w² - 4w
0 = 2w² - 4w - 96 divide both sides by 2
0 = w² - 2w -48
(w-8) ( w +6) = 0
w = 8 since it can't equal -6
length therefore = 2w-4 = 16-4 = 12
Hence, the dimensions of the garden are 8 x 12
Know more about dimensions
https://brainly.com/question/19819849
#SPJ4
Full question:
A rectangular garden has a length that is 4 meters less than twice its width. Can you set up a quadratic equation to find the dimensions of the garden if its area is 96m^2?
If f(x, y) = xy, find the gradient vector ∇f(4, 7) and use it to find the tangent line to the level curve f(x, y) = 28 at the point (4, 7). a) gradient vector b) tangent line equation c)Sketch the level curve, the tangent line, and the gradient vector.
Answers
To find the gradient vector ∇f(4, 7), we need to compute the partial derivatives of f(x, y) = xy with respect to x and y.
Given:
f(x, y) = xy
Partial derivative with respect to x (keeping y constant):
∂f/∂x = y
Partial derivative with respect to y (keeping x constant):
∂f/∂y = x
So, the gradient vector ∇f(4, 7) is (∂f/∂x, ∂f/∂y) evaluated at (4, 7):
∇f(4, 7) = (7, 4)
The equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) can be written as:
z - f(4, 7) = ∇f(4, 7) · (x - 4, y - 7)
Substituting the values:
z - 28 = (7, 4) · (x - 4, y - 7)
Expanding the dot product:
z - 28 = 7(x - 4) + 4(y - 7)
z - 28 = 7x - 28 + 4y - 28
z = 7x + 4y - 56
Therefore, the equation of the tangent line to the level curve f(x, y) = 28 at the point (4, 7) is z = 7x + 4y - 56.
To sketch the level curve, the tangent line, and the gradient vector, you can plot the points on a graph with x and y coordinates and represent the tangent line as a straight line passing through the point (4, 7) with a slope of 7/4. The gradient vector (7, 4) can be represented as an arrow starting from the point (4, 7) in the direction of the vector.
learn more about vector here
https://brainly.com/question/24256726
#SPJ11
Which is the graph of x - y = 1?
Answers
the title pattern shown was used in pompeii for paving. if the diagonals of each rhombus are 2 and 3 inches, what area makes up each cube in the pattrn
Answers
Each cube in the pattern has an area of 3 square inches.
To determine the area of each cube in the pattern, we need to find the area of each rhombus formed by the pattern.
The pattern consists of rhombuses, and we know that the diagonals of each rhombus are 2 inches and 3 inches.
The formula to find the area of a rhombus is given by:
Area = (d1 * d2) / 2,
where d1 and d2 are the lengths of the diagonals.
In this case, d1 = 2 inches and d2 = 3 inches.
Plugging the values into the formula, we get:
Area = (2 * 3) / 2
= 6 / 2
= 3 square inches.
Know more about rhombus here:
https://brainly.com/question/12665650
#SPJ11
A region is prone to flooding once every 20 years. If the probability of flooding in that region any one year is >o. What is the probabilit, of not flooding the next year
Answers
The probability of the region not flooding the next year is 19/20.
Given that a region is prone to flooding once every 20 years, we can calculate the probability of flooding in any one year as:
Probability of flooding in any one year = 1/20 = 0.05
Since the probability of flooding in any one year is greater than 0, the probability of not flooding in any one year would be:
Probability of not flooding in any one year = 1 - 0.05 = 0.95
Therefore, the probability of not flooding the next year in this region would be 0.95 or 95%.
Hi, I'd be happy to help you with your probability question.
The probability of flooding in the region any one year is 1/20 (once every 20 years). To find the probability of not flooding the next year, we need to find the complement of the probability of flooding.
Step 1: Determine the probability of flooding.
P(Flooding) = 1/20
Step 2: Find the complement probability.
P(Not Flooding) = 1 - P(Flooding)
Step 3: Calculate the probability of not flooding.
P(Not Flooding) = 1 - (1/20) = 19/20
The probability of the region not flooding the next year is 19/20.
To know more about probability visit:
https://brainly.com/question/13604758
#SPJ11
We can approach this problem using the concept of probability and complement rule.
Given that a region is prone to flooding once every 20 years, we can assume that the probability of flooding in any given year is 1/20 or 0.05 (since once in 20 years means once in 20 trials, and the probability of success in any one trial is 1/20).
Now, the probability of not flooding in the next year can be calculated using the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.
Therefore, the probability of not flooding in the next year can be calculated as follows:
P(not flooding) = 1 - P(flooding)
P(not flooding) = 1 - 0.05
P(not flooding) = 0.95
So, the probability of not flooding in the next year is 0.95 or 95%. This means that there is a high likelihood that the region will not experience flooding in the next year.
However, it's important to note that the probability of flooding in any given year is still greater than 0, which means that there is always a possibility of flooding occurring, regardless of whether it occurred in the previous year or not.
To know more about probability visit -
brainly.com/question/31469353
#SPJ11
a certain statistic dˆ is being used to estimate a population parameter d. the expected value of dˆ is not equal to d. what property does dˆ exhibit?a. The sampling distribution of d hat is normal.b. The sampling distribution of d hat is binomial.c. The sampling distribution of d hat is uniform.d. d hat is unbiased.e. d hat is biased.
Answers
The right answer is: E, according to the Central Limit Theorem for proportionality. The statistic is inaccurate.
In probability theory, the central limit theorem establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.
The Central Limit Theorem establishes that for a proportion p in a sample of size n:
The expected value is μ=р
The standard error is s=\(\sqrt{\frac{p(1-p)}{n} }\)
In this problem, the expected value is different of the expected of μ=р , hence, the statistic is biased, and the correct option is E.
To learn more about Central limit theorem visit: brainly.com/question/4086221
#SPJ4
Given vectors u = ⟨–2, 1⟩ and v = ⟨4, –2⟩, which statement is true concerning u and v? a. The vectors form an obtuse angle of approximately 93°. b. The vectors form an obtuse angle of approximately 96°. c. The vectors form an obtuse angle of approximately 127°. d. The vectors point in opposite directions.
Answers
Answer:
D) The vectors point in opposite directions.
Step-by-step explanation:
got it right on edge :)
see graph below
Answer:
D. The vectors point in opposite directions.
Step-by-step explanation:
Two 1.0 g spheres are charged equally and placed 2.0 cm apart. when released, they begin to accelerate at 150 m/s2. what is the magnitude of the charge on each sphere?
Answers
The charge on each sphere is 3. 337× 10^-13 C
How to determine the chargeThe formula for force in an electric field is given as;
F = kQ/ r²
Where:
F is the force between the chargesk is the electric field constant = 8.99 × 10^9 N ⋅ m 2 /C 2.r is the distance between the charges = 0. 02mQ is the chargeNote that;
F = ma
F = 1. 0 × 150
F = 150N
Substitute the value into the formula
150 = 8.99 × 10^9 Q/ (0. 020)^2
150 = 8.99 × 10^9 Q/4× 10^-4
cross multiply
150× 4× 10^-4 = 8.99 × 10^9 Q
Q = 6 × 10^-3 /8.99 × 10^9
Q = 6. 67 × 10^-13 C/ 2 = 3. 337× 10^-13 C
Thus, the charge on each sphere is 3. 337× 10^-13 C
Learn more about electric field here:
https://brainly.com/question/14372859
#SPJ4
Find the value of x: please help me!
Answers
Answer:
6
Step-by-step explanation:
19x=114
Divide both sides
X=6
NEED HELP INSTANTLY.
QUICK
20 POINTS
Answers
Answer:
with what? there is no picture
Devi’s mother is three times as old as Devi. Five years ago, Devi’s mother was four times as old as Devi was then. Find their present ages
Answers
Answer:
Devi's present age = 15 years
Devi's Mother's present age = 45 years
Step-by-step explanation:
Let the present age of Devi be x years.
Therefore, mother's present age = 3x
Five years ago:
Devi's age = (x - 5) years
Mother's age =( 3x - 5) years
According to the given condition:
Five years ago:
Devi's mother's age = 4 times Devi's age
3x - 5 = 4( x - 5)
3x - 5 = 4x - 20
20 - 5 = 4x - 3x
15 = x
x = 15 years
3x = 3* 15 = 45 years
Hence,
Devi's present age = 15 years
Devi's Mother's present age = 45 years
3. The ratio of the width to the length of a rectangle is 4:5. If the area of the rectangle is 500 square centimeters, what is the length of the rectangle?
5 centimeters
9 centimeters
20 centimeters
25 centimeters
Answers
Answer:
25 centimetersStep-by-step explanation:
Ratio 4:5 means:
width: W = 4x
length: L = 5x
Area of rectangle: A = W×L
Therefore:
500 = 4x×5x
500 = 20x²
50 = 2x²
x² = 25
x = 5
W = 4×5 = 20 cm
L = 5×5 = 25 cm
Martin had 24
5
pounds of grapes left. Which expression shows the pounds of grapes Martin has if he doubles his current amount?
(2) + (2) (Four-fifths)
(2) (2) + (four-fifths)
(2) (2) + (2) (four-fifths)
(2) + (2) + (four-fifths)
Answers
Answer:
its C
Step-by-step explanation:
Answer:
16/3 pounds
Step-by-step explanation:
We are give that each friend took 2/3 pound of grapes from the bowl. Therefore, to know the total amount taken by the four friends, we will simply do cross multiplication as follows:
1 friend .................> 2/3 pounds
4 friends ...............> ?? pounds
Amount taken by the 4 friends = [4*(2/3)] / 1 = 8/3 pounds
The bowl originally had 8 pounds and 8/3 pounds were taken, therefore:
remaining amount = 8 - 8/3 = 16/3 pounds hope this helps!
math how do you times
Answers
What percent of students in grade 8 prefer to joun a dance club?
Answers
The percent of students in grade 8 those who like to join dance club is equal to 25%.
Total number of students in grade 8 = 20
Total number of students of grade 8 join in dance club = 5
Percent of students of grade 8 prefer to join dance club
= ( total number of students prefer dance club ) / ( Total number of students in grade 8 ) × 100
Substitute the value in the formula we get,
⇒ Percent of students of grade 8 prefer to join dance club
= ( 5 ) / ( 20 ) × 100
⇒ Percent of students of grade 8 prefer to join dance club = 0.25 × 100
⇒ Percent of students of grade 8 prefer to join dance club = 25%
Therefore, percent of grade 8 students who preferred to join dance club is equal to 25%.
learn more about percent here
brainly.com/question/29391170
#SPJ4
The above question is incomplete, the complete question is:
What percent of students in grade 8 prefer to join a dance club?
Dance club Hiking club Total
Grade 7 15 15 30
Grade 8 5 15 20
Total 20 30 50
I need these fast I have midterms and I’m horrible at math
Answers
4. Specifically, a correspondence between two triangles is a pairing of each vertex of one triangle with one (and only one) vertex of the other triangle.
5. Line symmetry is when there exists a line (or lines) such that the image of a figure when reflected over the line is itself.
6. 2 to 1 or 2:1 ___________________________________________________________
hope it helps,can i plz get brainliest,have a great day/night
please i need ASAPPPPP ILL GIVE BRAINLIEST!!!!
Hans baked 51 cookles. His family ate m of them. Using m, write an expression for the number of cookles that remained. + ローロ ロメロ
Answers
Answer:
\(51-m=n\)
Step-by-step explanation:
M - Number of cookies his family ate
N - The remaining number of cookies left
which pair of functions are inverse of eachother ?
Answers
Answer: a
Step-by-step explanation:
does a chemical change create a new substance?
Answers
Answer:
True
In a chemical change, the molecules in the reactants interact to form new substances. In a physical change, like a state change or dissolving, no new substance is formed. Explain that another way to say that no atoms are created or destroyed in a chemical reaction is to say, “Mass is conserved.”
Step-by-step explanation:
Hope it helps :)
Have a good day/night
Brainliest pls?
the measure of 2 angles are (3y+11) and (11 y+15). What is the value of y if the angles are congruent
Answers
As a result, if the two angles' measurements are (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.
What is angle?An angle is a geometric figure formed by two rays that have a common endpoint, called the vertex. The rays are also known as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees. Angles can also be measured in radians, which are another unit of angular measurement used in mathematics and physics. One radian is equal to the angle subtended by an arc of a circle that has a length equal to the radius of the circle. The size of an angle is determined by the amount of rotation that occurs between the two rays. This is typically measured relative to the positive x-axis, with counterclockwise rotations being considered positive and clockwise rotations being considered negative. Angles are used in a wide range of mathematical and scientific applications, including geometry, trigonometry, physics, engineering, and architecture. They are also used in many everyday situations, such as measuring the size of an opening or the angle of incidence of sunlight on a surface.
Here,
If the two angles are congruent, then they must have the same measure.
So we can set the expressions for the measures of the two angles equal to each other and solve for y:
3y + 11 = 11y + 15
Subtracting 3y from both sides:
11 = 8y + 15
Subtracting 15 from both sides:
-4 = 8y
Dividing both sides by 8:
y = -1/2
Therefore, if the measure of the two angles is (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.
To know more about angle,
https://brainly.com/question/14569348
#SPJ1
The following circular spinner has 10 sections of equal size. If the spinner is spun twice, what is the probability that the spinner lands on an odd number both times?
Answers
Answer:
The chance of anding on A for one spin is 90+45360=38. So the probability of that happening twice in a row is 38×38=964.
Step-by-step explanation:
hope this helps you mark me brinilylist
select all the statements that are true. 7.107 > 7.017 0.200 = 0.200 10.220 < 10.022 8.008 < 8.080 13.190 > 13.090
Answers
Answer:
7.107 > 7.017
0.200 = 0.200
8.008 < 8.080
13.190 > 13.090
27 is 30% of what number?
A 8585
B 9292
C 1212
D 90
Answers
Answer:
27 is 30% of what number?
D. 90
Step-by-step explanation:
You're welcome.