In 2.2, recall that on an open interval, the end points are not included in the interval. For example, the open interval (2, 4) represents the real numbers between, but not including, 2 and 4. In a closed interval, the end points are included in the interval. For example, the closed interval [5,8] represents the real numbers between and including, 5 and 8. In some text books (including ours), they define increasing, decreasing, and constant on open intervals. Other texts do not require the intervals to be open, meaning they can be defined on closed intervals. What do you think? Should increasing, decreasing, and constant intervals be defined on open intervals or do you think they should be defined on closed intervals? Why?
Answers
9514 1404 393
Answer:
it depends
Step-by-step explanation:
The ideas of "increasing" or "decreasing" have to do with the sign of the derivative of a function. The derivative of a function is a limit, which is only defined if the point can be approached from both sides. For a function that is only defined on an interval, the derivative is undefined (hence "increasing" or "decreasing" are undefined) at the end points of the interval.
When the function is defined on an interval, "increasing" or "decreasing" can only be determined on that open interval. There may also be critical points within an interval at which the derivative is either zero or undefined. Those points must also be excluded from any interval of "increasing" or "decreasing".
__
If a function is defined over a domain that extends beyond the interval of interest, then the derivative may very wll be defined a the end points of the interval of interest. As a simple example, consider a line with defined non-zero slope: y = kx, k≠0. For k>0, the line will be increasing everywhere. The slope is defined at the end points of any finite interval, so the function can be said to be "increasing" on the closed interval.
Similarly, if the (finite) interval of interest includes the vertex of a parabola defined for all real numbers, the function will be "increasing" on one side of the vertex, and "decreasing" on the other side. Both the "increasing" and "decreasing" intervals will be half-open intervals. The point at the vertex will not be included in either of them.
Related Questions
I need some help with this question. "A scale drawing of a school bus has a scale of an inch to 5 feet. If the length of the school bus is in inches on the scale drawing, what is the actual length of the bus?"
Answers
Answer:
45 Feet
Step-by-step explanation:
4.5 divided by 0.5=9
9 times 5=45
Hoped this helped!
The sum of three numbers is 97. The third number is 9 less than the first. The second number is 2 times the third. What are the numbers
Answers
Answer:
Step-by-step explanation:
x + y + z = 97 eq1
x - z = 9 eq2
y = 2z eq3
Since y is already defined in eq3, we can substitute eq3 into eq1.
x + 2z + z = 97
x + 3z = 97 new eq1
Now, we have only 2 equations to work with that have two variables.
x + 3z = 97 new eq1
x - z = 9 eq2
Subtract eq2 from new eq1 to eliminate the x terms.
4z = 88
z = 22
Next, substitute this value of z into eq3 to solve for y.
y = 2(22)
y = 44
Finally, we can substitute the values of y and z into eq1 to solve for x.
x = 97 - 44 - 22
x = 31
The three numbers are 22, 31, and 44.
Find the measure of
Answers
Answer:
A
Step-by-step explanation:
28 + 39 + 86 = 153
180 - 153 = 27
Elijah can spend up to $23 on groceries. He wants to buy 3 pounds of tomatoes, 4 pounds of oranges, and x pounds
of lean ground beef. The tomatoes cost $1.35 per pound, the oranges $1.65 per pound, and the ground beef $4.94
per pound. Write an inequality that represents the possible number of pounds of ground beef, x, he can buy. Find
the value of x.
A. 1.35 x 3 +
B. 1.35 x 3 +
1.65 x 4 +
1.65 x 4 +
c.
1.35 x 3 + 1.65 x 4 +
D. 1.35 x 3 + 1.65 x 4 +
4.94x < 23; x<25
4.94x ≤ 23; x ≤ 25
4.94x >
23; x > 25
4.94x ≥
23;x ≥ 25
Answers
Answer1.35+ 4:
Step-by-step explanation:
Please help, 30 points.
What are the domain and range of the relation given in the table?
x y
-12 0
-8 12
0 0
1 8
A. domain: {−12,−8, 0, 1} range: {0, 8, 12}
B. domain: {x|x∈R} range: {0, 8, 12}
C. domain: {−12,−8, 0, 1} range: {y|y∈R}
D. domain: {0, 8, 12} range: {−12,−8, 0, 1}
Answers
Answer:
Domain (-12,-8,0,1) range (0,8,12)
Answer:
THE CORRECT ANSWER IS
domain: {−12,−8, 0, 1} range: {0, 8, 12}
I took testttttttt
what is the relationship between angle a and angle b
Answers
Answer:
A
Step-by-step explanation: Because of the fact that vertical angles revolve around angles for top to bottom, its A. Correct me if im wrong.
A direct mail appeal for contributions from a university’s alumni and supporters is considered to be too costly if less than 13% of the alumni and supporters provide monetary contributions. To determine if a direct mail appeal is cost effective, the fundraising director sends the direct mail brochures to a simple random sample of 204 people on the alumni and supporters mailing lists. They receive monetary contributions from 19 people. Does this evidence demonstrate that the direct mail campaign is not cost effective? Use a 0.02 level of significance. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. H0Ha: p=0.13: p⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0.13
Answers
The null hypothesis (H0) is that the proportion of alumni and supporters who provide monetary contributions is equal to or greater than 13%.
The alternative hypothesis (Ha) is that the proportion of alumni and supporters who provide monetary contributions is less than 13%.
What is a statistical hypothesis?A statistical hypothesis is usually formulated to test whether there is a significant difference or relationship between two or more variables.
There are two types of statistical hypotheses:
Null hypotheses, which assume that there is no significant difference or relationship between variables
Alternative hypotheses: these assume that there is a significant difference or relationship between variables.
We have,
From the situation given we can create the null and the alternative hypothesis as,
The null hypothesis (H0) is that the proportion of alumni and supporters who provide monetary contributions is equal to or greater than 13%.
i.e
(p ≥ 0.13).
The alternative hypothesis (Ha) is that the proportion of alumni and supporters who provide monetary contributions is less than 13%.
i.e
(p < 0.13)
Now,
Mathematically,
H0: p ≥ 0.13
Ha: p < 0.13
Where p represents the true proportion of alumni and supporters who provide monetary contributions.
Thus,
The null hypothesis (H0) is that the proportion of alumni and supporters who provide monetary contributions is equal to or greater than 13%.
The alternative hypothesis (Ha) is that the proportion of alumni and supporters who provide monetary contributions is less than 13%.
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1. A target is divided into 100 squares colored in dark blue, white, and light blue. Amber throws a beanbag that lands on the target.
co
9 25
dark blue
What is the probability that it will land on a dark blue square?
26
white
light blue
Answers
The probability of landing on the dark blue target is 2/5.
Finding probabilityProbability is the ratio of required to the total possible outcomes of an event.
The required outcome = dark blue= 25Total possible outcomes= entire sample Space = 100P(dark blue ) = 40/100
divide through by 20
P(dark blue ) = 2/5
Therefore, the probability of landing on target is 2/5
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Build me a 100ft roller coaster ride using math?
Answers
Classify the polynomial by the number of terms.
ar2 + bxtc
Binomial
Trinomial
Polynomial
Monomia
Answers
4(3r - 8)
Simplify the expression
Answers
An 8-sided number cube is rolled 4000 times. The number 2 appeared 200 times. Determine the theoretical and experimental probability of rolling a 2 in order to determine the fairness of the number cube. Drag values or words to the boxes to correctly complete the statements.
Answers
Theoretical Probability of rolling a 2= 1/20
Experimental Probability of rolling a 2 = 1/20
Theoretical probability of rolling a 2:
The theoretical probability of an event is the ratio of the number of favourable outcomes to the total number of possible outcomes. Since there are 8 sides to the cube, the total number of possible outcomes is 8. Since the number 2 appeared 200 times out of 4000 rolls, the number of favorable outcomes is 200. Therefore, the theoretical probability of rolling a 2 is:
Theoretical Probability of rolling a 2 = Number of favourable outcomes / Total number of possible outcomes = 200/4000 = 1/20
Experimental probability of rolling a 2:
The experimental probability of an event is the ratio of the number of times the event occurred to the total number of trials. In this case, the event is rolling a 2, which occurred 200 times out of 4000 rolls.
Therefore, the experimental probability of rolling a 2 is:
Experimental Probability of rolling a 2 = Number of times the event occurred / Total number of trials = 200/4000 = 1/20
Comparing theoretical and experimental probability:
If the cube is fair, we would expect the theoretical probability and the experimental probability to be similar. In this case, both probabilities are 1/20, which means that the cube appears to be fair. However, we would need to conduct more trials to be more confident in our conclusion.
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Simplify the expression: 42x3y6 6xy6 A) 7x2y12 B) 7x2y C) 36x2y12 D) 7x2
Answers
Answer:
D
Step-by-step explanation:
So first you simplify
Step 1: (2•3•7x3y6) (2•3xy6)
Step 2: you divide x3 by x1 = x (3-1) = x2
step 3: You cancel out y6 as it appears on both sides of the fraction line.
step 4: cancel out 2 as it appears on both sides.
step 5: cancel out 3 as it appears on both sides.
step 6: final result 7x2
degree and classification of 4x^2+32x+63?
nvm its quadratic trinomial
Answers
Answer:
Pertaining to the mathematical expression conveyed, the answer to such proposed interrogate is acknowledged as the following:
Degree: 2nd degree term.
Classification: Quadratic trionomial.
Step-by-step explanation:
Evaluating the Degree:
The degree is acknowledged as the predominating term adjacent to a base of a peculiar value that denotes the particular allocation within a polynomial.
4x^2 has the highest degree of 2.
32x has the degree of one, being that x individually is x^1.
Since polynomials are defined by the term in which obtains the greatest degree, ^2 is referred to as quadratic, whereas ^3 is cubic, ^4…
Classification Evaluation:
Such could be determined by evaluating for the quantity of terms present within the mathematical expression or statement.
4x^2 is the first term.
32x is the second term.
63 is the third term (considered a constant).
Thus, the correct answer is a quadratic trinomial.
*I hope this helps.
the equation below represents the total price of Michigan State University per semester where c represents the number of classes and t represents the total cost for the semester including a one time fee for room and board
Answers
The equation that represents the total price of Michigan State University per semester is determined by the number of classes taken (c) and the total cost for the semester, which includes a one-time fee for room and board (t).
The equation captures the relationship between these variables and calculates the overall cost for a student attending the university. It is important to note that the equation provides a quantitative representation and does not take into account other factors such as scholarships, financial aid, or additional expenses. Therefore, the equation serves as a useful tool for estimating the total cost of attending Michigan State University, allowing students and their families to plan and budget accordingly for their education.For such more question on equation
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Identify the focus and directrix of the parabola represented by the equation (y-2)^2= 24 (x-5)
Answers
Answer: Directix= -1
Focus (11, 2)
Step-by-step explanation:
Explanation it’s 1
Plz Help. Euler Equations are hard!
Find the general solution to the following differential equation.
Answers
An
2 pie/3
Step-by-step explanation:
How can I simplify this
The result should be three
Answers
The image you provided is a mathematical expression written in a non-standard format. To simplify it and obtain the result of 3, we can break it down step by step.
The expression can be written as follows:
(8c8) * (8x83)
Let's simplify each part separately:
(8c8):
The term "8c8" represents the combination or binomial coefficient. In general, the combination "nCr" is calculated as n! / (r! * (n-r)!), where "!" denotes factorial. When r = n (as is the case here with 8c8), the combination simplifies to 1. Therefore, 8c8 equals 1.
(8x83):
The term "8x83" represents multiplication between the numbers 8 and 83, which equals 664.
Now, let's put it all together:
(8c8) * (8x83) = 1 * 664 = 664
According to the given expression, the simplified result is 664, not 3. Please double-check the expression or provide further clarification if needed.
number 150 please!
Answers
Answer:
ABCDEFGHIJKLMNOP
Answer:
please follow me pleaseWhat 2 numbers can multiply to -40 and add up to 6
Answers
Answer: 10 and -4
Step-by-step explanation: 10 + - 4 = 6 and 10 x -4 = -40
The parent function f ( x ) = 3 √ x is transformed to g ( x ) = 2 f ( x − 3 ) Which is the graph of g ( x ) ?
Answers
The graph of the function g(x) has an equation of g(x) = 6√(x - 3)
Identifying the graph of the function g(x)?From the question, we have the following parameters that can be used in our computation:
f(x) = 3√x
The transformed function g(x) is given as
g(x) = 2f (x − 3)
In f(x) = 3√x , we have
f(x - 3) = 3√(x - 3)
Multiply both sides by 2
So, we have
2f(x - 3) = 2 * 3√(x - 3)
Evaluate the products
2f(x - 3) = 6√(x - 3)
Recall that
g(x) = 2f (x − 3)
So, we have
g(x) = 6√(x - 3)
This means that the graph of the function g(x) has an equation of g(x) = 6√(x - 3)
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A baseball pitcher has made 53 pitches in the first four innings of a baseball game and plans to pitch 3 mote innings. The manager of the team has committed to allowing his pitcher to throw, at most, pitches during the game. Write an inequality to find the average number of pitches the pitcher can throw over the next three innings Solve the inequality from Part 1. What is the maximum number of pitches the pitcher can make in cach of the next 3 innings ? Graph your solution from Part 2 on a number line and explain what your solution means. If the pitcher threw just 6 pitches in the fifth inning, what is the greatest number of pitches the pitcher can throw per inning he wishes to pitch nine innings? Write and solve an inequality to answer this part.
Answers
Answer:
at most 17 pitches per inning
Step-by-step explanation:
It is given that a baseball pitcher makes 53 pitches in the first 4 innings of a game and plans to pitch in the next 3 innings.
We need to write and solve an inequality to find the possible average pitches per inning the pitcher made in the next 3 innings if the pitcher is assigned a maximum of 105 pitches.
From part (a) we know 3 p + 53 3p+53 represents the total number of pitches made if the pitcher makes an average of p pitches per inning in the next 3 innings.
If the pitcher can make at most 105 pitches, then:
3 p + 53 ≤ 105 3p+53≤105
To solve the inequality, first subtract 53 on both sides of the inequality to isolate the variable term:
3 p + 53 − 53 ≤ 105 − 53 3 p ≤ 53
3p+53≤105 \(p\leq 17\frac{1}{3}\)
at most 17 pitches per inning
(Hope this helps can I pls have brainlist (crown)☺️)
What is the property of the first step in the equation?
Answers
9514 1404 393
Answer:
(c) addition property of equality
Step-by-step explanation:
Each side of the equation after the first step is 2 more than it was before the first step. The first step consisted of adding 2 to both sides of the equation.
The "addition property of equality" tells you that the value of the variable remains unchanged if you add the same thing to both sides of the equation. That is, the addition property of equality justifies the fist step of adding 2 to both sides of the equation.
please help me im very behind
Answers
Answer:
y=4/3x+4
Step-by-step explanation:
The change is Y is +4 and in X in +3, which is how we get the slope..4/3.
And the y-intercept would be 4, which is when x is at 0.
Hope this helps!
Answer:
y=4/3x+4
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
A. x= 3, y= -2
Step-by-step explanation:
[2] 2x= 4y+14
[1] 3y+5x=9
Solve equation [2] for the variable x
[2] 2x = 4y + 14
[2] x = 2y + 7
// Plug this in for variable x in equation [1]
[1] 5•(2y+7) + 3y = 9
[1] 13y = -26
// Solve equation [1] for the variable y
[1] 13y = - 26
[1] y = - 2
// By now we know this much :
x = 2y+7
y = -2
// Use the y value to solve for x
x = 2(-2)+7 = 3
good luck, I hope this helps!!!
5. A ski slope is 310 yards long with a vertical drop of 220 yards. Find the
angle of elevation of the ski run. Round to the nearest degree.
Answers
310 is the hypotenuse of the ski slope and the side length across from the angle you’re looking for is 220, the vertical drop.
You can use sin to find theta.
sinx= 220/310
sinx=0.70967...
x = sin inverse of 0.70967....
x = 45°
Someone please want to do my algebra assignments all due at 11 tn I need help at least ;(
Answers
Answer:
-48
Step-by-step explanation:
I think!! :)
-2(4g - 3) = 30 what is the answer
Answers
Answer:
g=-3
Step-by-step explanation:
-8g+6=30
-6
-8g=24/-8
Answer:
g = -3
Step-by-step explanation:
8+8?
Pls help will mark you or whatever
Answers
Answer:
8+8=16
Step-by-step explanation:
Lets say you have 8 apples and your friend gives you 8 more apples. So, you count 9,10,11,12,13,14,15,16 which was 8 times.
Hope this helps.
Calculate the area of a circle with a radius of 5 meters
Answers
Ans: pi (5)^2 = 78.5( cor. to 3 sig. fig)/ 25 pi