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How do you find the average rate of change of
f
(
x
)
=
2
x
2
+
1
on [x,x+h]?
Calculus Derivatives Average Rate of Change Over an Interval
1 Answer
Steve M
Feb 28, 2017
4
x
+
2
h
Explanation:
The average rate of change of a continuous function,
f
(
x
)
, on a closed interval
[
a
,
b
]
is given by
f
(
b
)
−
f
(
a
)
b
−
a
So the average rate of change of the function
f
(
x
)
=
2
x
2
+
1
on
[
x
,
x
+
h
]
is:
A
r
o
c
=
f
(
x
+
h
)
−
f
(
x
)
(
x
+
h
)
−
(
x
)
=
f
(
x
+
h
)
−
f
(
x
)
h
...
.
.
[
1
]
=
2
(
x
+
h
)
2
+
1
−
(
2
x
2
+
1
)
h
=
2
(
x
2
+
2
x
h
+
h
2
)
+
1
−
2
x
2
−
1
h
=
2
x
2
+
4
x
h
+
2
h
2
−
2
x
2
h
=
4
x
h
+
2
h
2
h
=
4
x
+
2
h
Which is the required answer.
Additional Notes:
Note that this question is steered towards deriving the derivative
f
'
(
x
)
from first principles, as the definition of the derivative is:
f
'
(
x
)
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
This is the function we had in [1], so as we take the limit as
h
→
0
we get the derivative
f
'
(
x
)
for any
x
, This:
f
'
(
x
)
=
h
→
0
4
x
+
2
h
=
4
x
this is a example
The following graphs have no scales assigned to them. Which of them couldbe density curves for a continuous random variable if they were provided withthe right scale?Check all that apply.A. Graph AB. Graph BC. Graph CD. Graph DE Graph E
Given that:
- The graphs have no scales assigned to them.
- You have to identify the ones that could be density curves for a continuous random variable assuming that they have the right scale.
Then, in order to solve this exercise, you need to remember the following:
1. A Probability Density Function is useful to define the probability of a random variable within a distinct range of values.
2. It is also known as PDF.
3. The Probability Density Function is always positive in all its Domain.
4. The total enclosed area under the curve of the function is:
[tex]A=1[/tex]Knowing all these concepts, you can identify that:
- In graph B the area under the curve is 0. Therefore, this cannot be the graph asked in the exercise.
- In Graph C, the function is not positive in its Domain. Therefore, this does not satisfy the properties mentioned before.
Hence, the answers are:
- Option A.
- Option D.
- Option E.
Layla skated x kilometers around the rink. Lamel skated 5/2 less than Layla.
Now write an equivalent equation to show how many kilometers Lamel skated around the rink.
An equivalent equation to show how many kilometers Lamel skated around the rink is x - 5/2.
Linear equations in one variable
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
For example, 2x+3=8 is a linear equation having a single variable in it.
Given that Layla skated x kilometers around the rink, Lamel skated 5/2 less than Layla.
Therefore Lamen skated x - 5/2 kilometers, as Lamen skated 5/2 less than the kilometers skated by Layla
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Find The Measurement Of <6
The measure of ∠6 from the given figure is 45°.
From the given figure, the measure of angle is 135°.
What are Co-interior angles?Co-interior angles occur in between two parallel lines when they are intersected by a transversal. The two angles that occur on the same side of the transversal always add up to 180°.
From the given figure,
135° + ∠6 = 180° (Co-interior angles adds upto 180°°)
⇒ ∠6 = 180°-135°
⇒ ∠6 = 45°
Therefore, the measure of ∠6 from the given figure is 45°.
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2. Stephanie will be sending 2 parcels of personal items to her niece. The big parcel weighs 12
lbs 11 oz and the smaller parcel is 3 lbs 1 oz lighter than the big parcel. What is the combined
weight of the two parcels?
Weight of the two parcels 22lbs 5oz.
What is Weight?
The force exerted on an object by gravity is known as its weight. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.
Given,
The weight of big parcel = 12lbs 11oz
The weight of small parcel = 12lbs 11oz - 3lbs 1oz
= 9lbs 10oz
The weight of total parcel = big parcel + small parcel
= 12lbs 11oz + 9lbs 10oz
= 21lbs 21oz = 22lbs 5oz
Hence, The weight of the 2 parcels is 22lbs 5oz.
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In XYZ, XY=14, YZ=22, and XZ=28. What is the measure of angle Z to the nearest degree? *Law of Cosines
Solution
Draw the diagram
So using cosine rule
[tex]\begin{gathered} z^2=x^2+y^2-2xycosZ \\ \\ cosZ=\frac{x^2+y^2-z^2}{2xy} \\ \\ cosZ=\frac{22^2+28^2-14^2}{2(22)(28)} \\ \\ cosZ=\frac{67}{77} \\ \\ Z=30\degree\text{ \lparen to the nearest degree\rparen} \end{gathered}[/tex]When you translate, (x-4,y) will move
With the translation rule given by (x,y) -> (x - 4, y), the function will move 4 units left.
TranslationA translation is one of the many transformations that can be applied to the vertices of a figure. Other examples are stretch, compression, rotation, reflection, dilation and so on.
Each of these transformations has their respective characteristics regarding what they change on the transformed figure. For a translation, the figure will move either left, right, up or down(may be more than one of those), keeping it's orientation and congruence.
In the context of this problem, the rule for the translation is given by:
(x,y) -> (x - 4, y)
Hence the meaning is given as follows:
x -> x - 4 means that the figure moves 4 units left.y -> y means that the figure keeps the same vertical position.More can be learned about translations at https://brainly.com/question/28174785
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Lillian país sixty one dollars and thirty nine venta for groceries . The digit 3 in this number has a value of a.(3×10) dollarsb.(3×1) dollarsc.(3×0.01) dollard.(3×0.1) dollar
Given in the scenario:
a.) One Dollar and Thirty Nine, in digit, is equal to $1.39.
The digit 3 in $1.39 is in the Tenth (0.1) decimal place.
Therefore, the digit has a value of 3 x 0.1 dollars which is equal to $0.3.
The answer is letter D.
Use slope formula to find the slope of the line between the points (5,3) and (7,0)
The formula for calculating the slope of a line is
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ Where(x_1,y_1)=(5,3)and_{} \\ (x_2,y_2)\text{ = (7, 0)} \end{gathered}[/tex][tex]\begin{gathered} \text{Substituting the values of }(x_1,y_1)\text{ and }(x_2,y_2),\text{ we have } \\ m=\frac{0-3}{7-5} \\ m=\frac{-3}{2} \end{gathered}[/tex]Hence, the slope of the line is -3/2 or -1.5
What do I need to know?
[tex]-2f(x)\implies -2[\log_2(x)]\implies \log_2\left( x^{-2} \right)\implies \log_2\left( \cfrac{1}{x^2} \right)=g(x) \\\\[-0.35em] ~\dotfill\\\\ f(x-2)\implies \log_2(x-2)=j(x) \\\\[-0.35em] ~\dotfill\\\\ f(x)+2\implies \log_2(x)+2=h(x)[/tex]
What is the rate of change in the graph below?
Answer
Rate change = 1
Step-by-step explanation:
Rate change means the slope on the graph
Slope = rise / run
Rise = y2 - y1
Run = x2 - x1
Slope = y2 - y1 / x2 - x1
From the graph, Given the picked points
(5, 5) and (-5, -5)
x1 = 5, y1 = 5, x2 = -5, and y2 = -5
Slope = -5 - 5 / -5 -5
Slope = -10 / -10
Slope = 1
Hence, the rate change is 1
find the measure of arc GM if KP=PL and GM=36ft.
Given:
KP = PL
GH = 36 ft
Let's find the measure of arc GM.
Apply the angle arc relationship to find the measure of angle KGL:
[tex]KG\text{L}=\frac{HJ}{2}[/tex][tex]KGL=\frac{52}{2}=26\text{ degre}es[/tex]GKP + GLP + KGL + KGP = 360 degrees
90 + 90 + 26 + KPL = 360
206 + KPL = 360
Subtract 206 from both sides:
206 - 206 + KPL = 360 - 206
KPL = 154 degrees
To find the measure of arc GM, we have:
[tex]\begin{gathered} arcGM=\frac{KPL}{2} \\ \\ arcGM=\frac{154}{2} \\ \\ \text{arcGM}=77\text{ degre}es \end{gathered}[/tex]Therefore, the length of arc GM is 77 degrees
ANSWER:
77°
or = to compare ž, 1.75, and -0.75. ThenHaru was asked to compare and order threerational numbers. Show how he can use <, >,23order these numbers from least to greatest.+-2-101NHelppppo
It's important to know that proper fractions like 2/3 are between 0 and 1, specifically, 2/3 is equal to 0.67.
Now, we have three numbers, 0.67, 1.75, and -0.75. If we organize the numbers from least to greatest we have -0.75, 0.67, and 1.75. Then, we use the inequality symbols to express this order.
[tex]-0.75<\frac{2}{3}<1.75[/tex]The symbols are telling us that -0.75 is less than 2/3, and 2/3 is less than 1.75.
Now, let's graph this relation between the three numbers.
In a certain Algebra 2 class of 30 students, 8 of them play basketball and 10 of them
play baseball. There are 18 students who play neither sport. What is the probability
that a student chosen randomly from the class plays both basketball and baseball?
The probability that a classmate picked at random will participate in both basketball and baseball is 0.2.
What in mathematics is a probability?The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.
Given: In a particular Algebra 2 class of 30 students, 8 play basketball and 10 play baseball. There are 18 students who participate in neither sport.
Let n denote the number of students who participate in basketball and baseball.
The number of students that play both games: 30 = 18 - n + 8 - n + 10 + n
30 = n + 36
n = 36 - 30 = 6
Probability = 6/30 = 0.2
Therefore, the probability that a student chosen at random from the class will play both basketball and baseball is 0.2.
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What are the five theorems / rules used to prove that two triangles are congruent?
Answer:
The first of the congruency theorems is
1) SSS :
Side-Side-Side or SSS is a kind of triangle congruence rule where it states that if all three sides of one triangle are equal to all three corresponding sides of another triangle, the two triangles are considered to be congruent. Two or more triangles are said to be congruent when the measurements of the corresponding sides and the corresponding angles are equal.
2) SAS:
SAS congruence is the term which is also known as Side Angle Side congruence, which is used to describe the relation of two figures that are congruent. Let's discuss the SAS congruence of triangles in detail to understand the meaning of SAS
Consider the two tringles blelow
Under this criterion, if the two sides of a triangle are equal to the two sides of another triangle, and the angle formed by these sides in the two triangles are equal, then these two triangles are congruent. The SAS Criterion stands for the 'Side-Angle-Side' triangle congruence theorem.
3) AAS:
The AAS Theorem says: If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. Notice how it says "non-included side," meaning you take two consecutive angles and then move on to the next side (in either direction).
4) ASA:
The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
5)HL:
The HL Theorem states; If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
Please I need help please I need help
The number of groups of 1/9 in 2 are 18.
The value of 2 ÷ (4/9) = 9/2.
We can see a number line with equal intervals of 1/9.
We have to find the number of groups of 1/9 in 2 and the value of 2 ÷ (4/9) .
As we can see in the number line,
2 is two intervals after 16/9 , hence,
2 = 16/9 + 1/9 + 1/9 = 16/9 + 2/9 = 18/9
We can write it as,
(1/9)*18
Hence, there are 18 groups of 1/9 in 2.
The value of 2 ÷ (4/9) = 2*(9/4) = 18/4 = 9/2.
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Help 50 points please show your work
DUE TODAY
Answer:
3. 72 questions
4. 180 students
5. 120 students
6. 9 puzzles
Step-by-step explanation:
Question 3[tex]\begin{aligned}\implies \rm 80\% \;of \; 90 \; questions & =80\% \times 90\\&= \dfrac{80}{100} \times 90\\& = \dfrac{7200}{100}\\& = 72\end{aligned}[/tex]
Therefore, a student must answer 72 questions correctly to pass the test.
Question 4[tex]\begin{aligned}\implies \rm 40\%\; of\; 450\; students & = 40\% \times 450\\& = \dfrac{40}{100} \times 450\\& = \dfrac{18000}{100}\\& = 180\end{aligned}[/tex]
Therefore, at least 180 students must plan to attend in order for the school to have the festival.
Question 5[tex]\begin{aligned}\implies \rm 40\% \; of \; 300 \; students & = 40\% \times 300\\& = \dfrac{40}{100} \times 300\\& = \dfrac{12000}{100}\\& = 120\end{aligned}[/tex]
Therefore, 120 students chose recycling.
Question 6If 55% of 20 puzzles are completed, then 45% of 20 puzzles are left to complete, since 100% - 55% = 45%.
[tex]\begin{aligned}\implies \rm 55\% \; of \; 20 \; puzzles & = 45\% \times 20\\& = \dfrac{45}{100} \times 20\\& = \dfrac{900}{100}\\& = 9\end{aligned}[/tex]
Therefore, Magdalena has 9 puzzles left to complete.
a line passes through the point (-8, -7) and has a slope of 3/2. write an equation in slope-intercept form for this line.
Answer:
y=(3/2)x+5
Explanation:
Given a line with a slope of 3/2 that passes through the point (-8, -7).
To determine the equation of the line, we first use the point-slope form below.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ m=\frac{3}{2} \\ (x_1,y_1)=(-8,-7) \end{gathered}[/tex]Substituting, we have:
[tex]\begin{gathered} y-(-7)=\frac{3}{2}(x-(-8)) \\ y+7=\frac{3}{2}(x+8) \end{gathered}[/tex]Next, we express the line in the slope-intercept form (y=mx+b).
[tex]\begin{gathered} y+7=\frac{3}{2}x+12 \\ y=\frac{3}{2}x+12-7 \\ y=\frac{3}{2}x+5 \end{gathered}[/tex]The equation of the line in slope-intercept form is:
[tex]y=\frac{3}{2}x+5[/tex]Please help me with both I’ll mark you brainly
Answer:
See picture below
Step-by-step explanation:
It took a long time for my picture to show up.
help meeeeeeeeeeeeeeeeeeeeeee
thank you
Answer:
x = -2
Step-by-step explanation:
x is represented by the horizontal axis, so read up from the given point to find where it would lie on the x axis.
I need some help please do this
The coefficient of z² is 25 and the constant term is 28. The product of 25 and 28 is 700. The factors of 700 which sum to -55 are -20 and -35, so:
[tex]\begin{gathered} 25z^2-55z+28=(5z-4)(5z-7) \\ so\colon \\ z=\frac{4}{5} \\ and \\ z=\frac{7}{5} \end{gathered}[/tex]For every 7 questions Anthony answers correctly he typically answers 3 incorrectly there are 30 questions on a test how many questions woild Anthony be expected to answer incorrectlyA.9 QuestionsB.10 QuestionsC.21 QuestionsD.27 Questions
Given the information, we can see that anthony has 7 correct answers and 3 incorrect in 10 questions, therefore, we can calculate the direct proportion solving for x:
[tex]\begin{gathered} \frac{3}{10}=\frac{x}{30} \\ \Rightarrow x=\frac{3\cdot30}{10}=3\cdot3=9 \\ x=9 \end{gathered}[/tex]Therefore, Anthony would be expected to answer incorrectly 9 questions
The coaches of a school football team want to know how many families from the school plan to attend this week's game. Each coach takes a different approach to obtain this information. Which sampling method would provide a good representation of the population? F Call all the parents of the football players to ask if their families will attend the game. G Stop every fifth car that enters the school parking lot one morning to ask if their families will attend the game. H Ask all the students in the last period PE class if their families will attend the game. J Choose every fourth student from an alphabetical list of the entire student body and ask if their families will attend the game
The option that takes samples putting the entire families of the students into account is the last option.
Option J is the correct answer
How are the coordinates of the extreme value and the equation from part B in the form y=(x - h)² - Crelated? extreme value is at (1, -8)
The coordinates of the extreme value or the vertex of the parabola is the (h, -c) of the equation form y = (x - h)² - c.
please tell me someone knows this
The vertex of the given graph is (0,5).
The axis of symmetry is y = 5x.
The number of zeroes are 3.
The x intercepts are 0 and -5.
the y intercepts are (-3,0) and 0,-3).
What is a parabola?A quadratic function's graph is called a parabola. According to Pascal, a parabola is a circle's projection. Galileo explained that projectiles falling under the influence of homogeneous gravity have a path known as a parabolic path. Many bodily movements have a curvilinear course with the shape of a parabola. In mathematics, a parabola is any mirror-symmetrical plane curve that typically has the shape of a U. Here, our goal is to comprehend the origin of the parabola's standard formula, its several standard forms, and its characteristics. A parabola is an equation of a curve where a point on the curve is equally far from a fixed point.
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Lalile vatte... Student: Login Students and Famili... ReadWorks C Clever | Portal Madison White - Su... XL for School: Practice & Problem Solving https://useast2-ww... 7.5.PS-18 Question Help Zari folds the net shown into a model of a solid figure. How many edges, faces, and vertices does the model have? The model has edges, faces, and vertices. Enter your answer in the edit fields and then click Check Answer: All parts showing Clear All Check Answer Review
Looking at the figure, the faces of the solid figure will be made from each small triangle in the 2D figure, so since we have 4 small triangles, the solid figure will have 4 faces.
Also, the central small triangle will be the base of the solid figure, and there we have 3 vertex. Each vertex of the bigger triangle will unite and become only one vertex in the solid figure, so in total we will have 4 vertices.
Then, for the number of edges, we have the 3 edges of the base of the solid figure, and we have more 3 edges, each one going from one vertex of the base into the fourth vertex of the solid figure. So in total we have 6 edges.
It's easier to see and count this amount of faces, vertices and edges when we fold the 2D figure and create the solid figure:
what is the greatest common factor of the numbers 2835 and 8960
35
Step-by-step explanation:
3x3x3x3x5x7
hope it helps have a nice day with apples
help mee pleasee!!
thank you <3
An equation that models the number of people employed in some country as medical assistant in the last year x is y = 359 + 14.35x
In this question, we have been given the number of people employed in some country as medical assistant.
We need to write an equation that models the number of people employed in some country as medical assistant in the last year x.
the number of people employed in some country as medical assistant:
in 2004 = 359 thousand
and by 2014 this number is expected to be 560 thousand.
We find the rate of employment.
Consider (x1, y1) = (0, 359) and (x2, y2) = (14, 560)
m = (560 - 359)/(14 - 0)
m = 201/14
m = 14.35
We have been given the line must pass through points (0, 359) and (14, 560)
And, we get the y-intercept c = 359
with slope m = 14.35 and y-intercept c = 359, the equation of the line would be,
y = 14.35x + 359
Therefore, an equation that models the number of people employed in some country as medical assistant in the last year x is y = 359 + 14.35x
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pefume discounted 25% on sale for 27$
PROBLEM #2A package contains 56 cups of oatmeal. A batch ofcookies requires 2 34 cups of oatmeal. Is thereenough oatmeal to make 21 batches of cookies?Explain. Show your work to prove your answer.
First, calculate the total amount of cups of oatmeal required to make 21 batches of cookies by multiplying 21 times 2 3/4:
[tex]21\times2\frac{3}{4}=21\times2+21\times\frac{3}{4}[/tex]Simplify that fraction:
[tex]\begin{gathered} =42+\frac{21\times3}{4} \\ =42+\frac{63}{4} \\ =42+\frac{60+3}{4} \\ =42+\frac{60}{4}+\frac{3}{4} \\ =42+15+\frac{3}{4} \\ =57+\frac{3}{4} \\ =57\frac{3}{4} \end{gathered}[/tex]Since a total of 57 3/4 cups of oatmeal are needed to make 21 batches of cookies, but a package contains only 56 cups of oatmeal, therefore, there is not enough oatmeal to make 21 batches of cookies.
Find
152.87+35.4
. Express your answer in decimal form.
