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chegg find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative f(x)
Answers
The derivative and domain of the function f(x) = x²-2x³ is :[tex](-\infty, \infty)[/tex].
What is derivative of the function (differentiation)?The slope of a function's graph or, more precisely, the slope of the tangent line at a point can be used to interpret a function's derivative.
Its computation actually stems from the slope formula for a straight line, with the exception that curves require the employment of a limiting procedure.
Calculation for the derivative:
Step 1: Use the definition of the derivative. Remember that f(x+h) means plug (x+h) into everywhere there is an "x" in f(x).
[tex]\begin{aligned}f^{\prime}(x) &=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \\&=\lim _{h \rightarrow 0} \frac{(x+h)^{2}-2(x+h)^{3}-\left(x^{2}-2 x^{3}\right)}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(x^{2}+2 h x+h^{2}\right)-2(x+h)(x+h)^{2}-x^{2}+2 x^{3}}{h} \quad \text { cancel } x^{2}\end{aligned}[/tex]
[tex]\begin{aligned}&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2(x+h)\left(x^{2}+2 h x+h^{2}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2\left(x^{3}+2 h x^{2}+h^{2} x+h x^{2}+2 h^{2} x+h^{3}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-2 x^{3}-4 h x^{2}-2 h^{2} x-2 h x^{2}-4 h^{2} x-2 h^{3}+2 x^{3}}{h}\end{aligned}[/tex]
[tex]=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-6 h x^{2}-6 h^{2} x-2 h^{3}}{h}[/tex]
Step 2: Cancel out a factor of h from each term in the numerator with the h in the denominator. Then direct substitute h=0.
[tex]\begin{aligned}&=\lim _{h \rightarrow 0}\left(2 x+h-6 x^{2}-6 h x-2 h^{2}\right) \\&=2 x+0-6 x^{2}-6(0) x-2(0)^{2} \\&=2 x-6 x^{2}\end{aligned}[/tex]
f and f' are polynomials, so their domains are all real numbers.
Therefore, for f(x) = x²-2x³ domain of f and f' :[tex](-\infty, \infty)[/tex].
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The complete question is -
Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative f(x) = x²-2x³.
If you register a 0. 08 bac or refuse to take a breath test, your license will be automatically suspended for.
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If you register a 0. 08 bac or refuse to take a breath test, your license will be automatically suspended for 12 months.
What is bac test?The amount of alcohol in your blood is determined via a blood alcohol(bac)test. The breathalyzer test, which police officers frequently administer to people they suspect of driving while intoxicated, is more widely known. While breathalyzers provide quick findings, they are not as precise as bac tests that measure alcohol in the blood.
The same 0.08 bac limit applies to adults in all 50 states who are 21 years of age or older, who are driving while intoxicated and breaching the law.
No amount of alcohol is safe when you are driving, even if your bac is below the legal limit. Don't drive after drinking, please!
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Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem?
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction = StartFraction R T Over V T EndFraction
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction and angle S is-congruent-to angle U
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction = StartFraction R T Over V T EndFraction
Answers
The statement that can be concluded from the triangle is A. RS/VU=ST/UT and ∠S≅∠U.
How to illustrate the information?The Side-Angle-Side Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
In this problem the included angle is ∠S≅∠U, therefore side RS must be proportional to side VU and side ST must be proportional to side UT
Hence, RS/VU=ST/UT.
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The 3 stages representing the hierarchy of fluency progression including Automaticity, are embedded into which strand of the B.E.S.T. mathematics standards
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The three stages that have to do with fluency, progression and automaticity are found in the Number Sense and Operations .
What is the number sense and operation strand of mathematics?This is the part of mathematics that is known to teach the student basic ways to carry out number operations in mathematics. This has to do with representation of numbers as well as solving for the existing relationships in these numbers.
Having a sense of numbers is a very important ability skill that has to be developed early is students to enable them progress in the subject.
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Write an equivalent expression by distributing the "-−" sign outside the parentheses: -(-8r-9.8s)+8.1
Answers
Answer: 8r + 9.8s + 8.1
Step-by-step explanation:
Given:
-(-8r-9.8s)+8.1
Distribute:
↳ A - times a - becomes a +, a -times a + stays a -
8r + 9.8s + 8.1
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As part of your retirement planning, you purchase an annuity that pays 5.75% annual interest compounded quarterly If you make quarterly payments of $1600 how much will you have saved in 5 years? Instead, if you make quarterly payments of $800, how much will you have saved in 10 years?
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Jasmine wants to buy a car marked at $5200 at a second hand car dealer. The deposit is two-fifth of the price of the car
for the next weck's delivery. Jasmine's father helped her in the deposit by paying 30% of the price. Will jasmine have
enough for her car deposit? If not, how much more does she need to add to get the deposit?
Answers
Jasmine will not have enough for the car. The amount more that she needs is $520.
Will Jasmine have enough for the car?
The first step is to convert the fraction that represents the amount needed as a deposit to percentage.
(2/5) x 100 = 40%
Difference in the deposit and the amount Jasmine's father deposited: 40% - 30% = 10%
Amount more that she needs : 10% x 5200 = $520
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all numbers less than 7 and greater than 7
Answers
Step-by-step explanation:
123456 less then 7
unlimited greater then 7
The numbers from negative infinity to 7, excluding 7."are less than 7 and "all numbers from 7 to positive infinity, excluding 7" are more than 7.
The combination of positive, negative numbers including 0 are called as integers.
The numbers less than 7 are:
This set includes all real numbers that are strictly less than 7.
It can be denoted as (-∞, 7), which means "all numbers from negative infinity to 7, excluding 7."
The numbers greater than 7 are:
This set includes all real numbers that are strictly greater than 7. It can be denoted as (7, +∞), which means "all numbers from 7 to positive infinity, excluding 7."
Thus, there are infinite numbers which are less than 7 and more than 7.
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The total value of a collection of nickels can be described by this sequence: 5, 10, 15, 20, 25, 30, ...
Type of sequence:
Explicit formula:
Recursive formula:
Answers
Type of sequence: arithmetic progression
Explicit formula: 5n
Recursive formula: [tex]5_{n-1}[/tex] + 5
What does the word Sequence mean ?A Sequence is a series of numbers in a regular pattern of increment. A sequence can be arithmetic or geometric in nature.
Given that a total value of a collection of nickels can be described by this sequence: 5, 10, 15, 20, 25, 30, .....
The difference in the sequence above is 10 - 5 = 5. There is an increment of 5 in each term.
Therefore, the type of sequence is arithmetic progression
The difference d = 5 and the first term is also 5
An explicit formula will be
a + (n - 1)d
substitute a and d into the formula
5 + (n - 1)5
5 + 5n - 5
5n
Therefore, 5n gives the value of a specific term based on the position
A recursive formula will be
[tex]a_{n-1}[/tex] + d
substitute a and d into the formula
[tex]5_{n-1}[/tex] + 5
Therefore, [tex]5_{n-1}[/tex] + 5 gives the value of a specific term based on the previous term
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a nickel has 5 grams what is the mass of a nickel in milligrams
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The mass of the same nickel which is 5 grams in milligrams is 5,000 milligram.
Weight1 gram = 1000 milligramWeight of a nickel = 5 gram
Weight of same nickel in milligram = 5 grams × 1000
= 5,000 milligram
Therefore, the mass of the same nickel is 5,000 milligram
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7,
24*
nswer:
What is the total probability of rolling a single die twice, and having it land on 3 the
first roll, and a number greater than 3 the second roll?
Answers
Answer:
1/12
Step-by-step explanation:
the chances of rolling a 3 is 1/6
there are 3 numbers more than 3 on a number die, 4,5, and 6
which is 3/6 or 1/2 if you decide to simplify
to find the probability you want you have to multiply the fractions by each other
1/6x1/2=1/12
can someone please help me
answer choices:
A - sin(0°)
B - cos(0°)
C - sin(180°)
D - cos(180°)
E - sin(270°)
F - cos(270°)
Answers
Answer:
B
Step-by-step explanation:
Cos(0)=1
since the diagram shows x as (1,0)
F.IF.3 Jim is starting a new company and decides to send a promotional e-mail offering a free sample of his product to anyone who receives the e-mail. His plan is to send the promotional e-mail to 128 contacts with a request to forward the e-mail to 3 different people. Suppose that Jim sends the initial e-mail to 128 contacts on day 1. On day 2, each recipient sends the e-mail to 3 different people. On day 2, each of the new recipients sends the e-mail to 3 different people. If the process continues, how many emails will be sent on day 7? * 1 point A. 93,312 B. 279,936 C. 2,304 D. 49,152
Answers
Using a geometric sequence, the number of emails sent on day 7 is given as follows:
A. 93,312.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
This situation can be modeled by a geometric sequence with first term and common ratio given as follows:
[tex]a_1 = 128, q = 3[/tex]
Hence the number of people that receive the email on day n is:
[tex]a_n = 128(3)^{n-1}[/tex]
On day 7, the amount is:
[tex]a_7 = 128(3)^{7-1} = 93,312[/tex]
Hence option A is correct.
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Solve for x. − 15 = 22 x + 7
Answers
Answer:
x = - 1
Step-by-step explanation:
- 15 = 22x + 7 ( subtract 7 from both sides )
- 22 = 22x ( divide both sides by 22 )
- 1 = x
Which numbers are integers? Check all that apply.
4
Negative 1 and one-third
-10
2.5
-4
0.ModifyingAbove 13 with Bar
YOOOO QUICK I REALLY NEED THIS PLEASEEE
Answers
The numbers : 4,-10 and -4 are integers.
A number without a decimal or fractional element is known as an integer, which can be both positive and negative, including zero.
The Latin word "integer" signifies "whole" or "intact." Thus, fractions and decimals are not included in integers.
All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.
"Negative 1 and one-third" includes a fractional part, so it is not an integer.
"2.5" and "0.ModifyingAbove 13 with Bar" contain a decimal, so it is also not an integer.
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A credit card company uses these rules to calculate the minimum amount owed: • For a bill of less than $100, the entire amount is due. • For a bill of at least $100 but less than $500, the minimum due is $100. • For a bill of at least $500 but less than $1,000, the minimum due is $300. • For a bill of $1,000 or more, the minimum due is $500. Which graph shows the minimum amount due for a credit amount of × (given that the credit limit is $2,000). O A. graph A O B. graph B O C. graph C O D. graph D
Answers
The graph that shows the minimum amount due for a credit amount of x given that the credit limit is $2,000 is graph B.
How to illustrate the information?Let x represent the credit amount and y represent the minimum amount due.
For a bill of less than $100, the entire amount is due. That is for 0 ≤ x < $100, y = x
For a bill of at least $100 but less than $500, the minimum due is $100. That is for $100 ≤ x < $500, y = 100
For a bill of at least $500 but less than $1,000, the minimum due is $300. That is for $500 ≤ x < $1000, y = $300
For a bill of $1,000 or more, the minimum due is $500. But the credit limit is $2000. That is For $1000 ≤ x < $2000, y = $500
The graph that shows the minimum amount due for a credit amount of x is graph B.
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The length of your school building is shown as 40 cm in a map. If the scale
is taken as 1 cm=Im to draw a map then what is the actual length of the school ?
Answers
The school building's actual length is 40 m.
How to estimate the actual length of the school building?Length exists as a measure of distance. In the International System of Quantities, length exists as a quantity with dimension distance. In most systems of measure a base unit for length is selected, from which all other units exist derived. In the International System of Units system, the base unit for length exists as the meter.
Given: School building length is given 40 cm on the map
scale used is 1 cm = 1 m
The scale utilized exists 1 cm = 1 m
1 cm in map = 1 m in actual
⇒ 40 cm in map = 40 m in actual
School building length in map = 40 cm
⇒ Actual Length of the school building is 40 m
Therefore, the school building's actual length is 40 m.
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In the following diagram, BC is parallel to DE.
What is x?
Answers
Answer:
21
Step-by-step explanation:
Using alternate interior angles, we can conclude that angle C is equal to X (the 3rd, unmarked angle in the center triangle)
To find that 3rd angle, we can do 180 - 105 - 54. This is because all angles in a triangle must equal 180. Using this, we find that angle C is equal to 21. By the law, X must also equal 21.
Answer:
x is 21
Step-by-step explanation:
add 54 and 105, then subtract it by 180 and you get 21.
The measures of the angles of a triangle
are shown in the figure below. Solve for x.
60°
(4x+3)°
(2x+9)⁰
Answers
Answer:
x = 18
Step-by-step explanation:
In order for a triangle to be a triangle, all angles must add up to 180.
This means that we can create an equation to solve for x, using the angles given.
180 = 60 + (4x+3) + (2x+9) --> remove brackets and combine like terms
180 = 60 + 6x + 12
180 = 72 + 6x
108 = 6x
18 = x
Brittany and four of her friends want to join a softball league. The league requires teams to have at least nine players, but teams cannot have more than eighteen players. In interval notation, how many more people can join Brittany's team?
Answers
The additional number of people is [4, 13]
How to determine the number of people?Brittany and four of her friends are five people.
So, we have:
n = 5
The conditions are given as
At least = 9At most = 18Let the additional number of people be x
So, we have the following inequalities
x + 5 ≥ 9 and x + 5 ≤ 18
Subtract 5 from both sides
x ≥ 4 and x ≤ 13
Express as interval notation
[4, 13]
Hence, the additional number of people is [4, 13]
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Which of the following segments is a diameter of o
Answers
Answer:
Segment UF
Step-by-step explanation:
Diameter is a line that passes through the center and meets the circumference at opposite ends.
Segments OF and WO are radii, and segment WM is a chord.
If p= the motorcycle's original price in dollars, which algebraic expression
represents the reduced price?
A. 275-p
B. 275p
C. 275+ p
D. p - 275
Answers
Answer: D
Step-by-step explanation:
If the original price was p, a price reduction would be p- the amount. Per the given answers, $275 is used for the reduction amount.
What is the perimeter of the given quadrilateral?
y
0000
20 units
10 units
50 units
25 units
A
D
B
C
Answers
Answer:
20 units
Step-by-step explanation:
As you know that the quadrilateral is a square, you’ll just have to find the length of one side and multiply it by four. We can count and see that one side is 5 units.
5 * 4 = 20 units
You can also add the length of each of the four sides.
5 + 5 + 5 + 5 = 20
Hope that helps you! Please let me know if you need more help with this question. Have a great day!
find the mod points of line AB where point A and B have coordinate (2,3) and (4,5)
Answers
Answer:
( 3 , 4 )
Step-by-step explanation:
Midpoint Formula: ( (x1+x2)/2 , (y1+y2)/2 )
Distance Formula: d = √[(x1-x2)^2 + (y1-y2)^2]
Gradient (Slope) Formula: (y2-y1) / (x2-x1)
Midpoint Formula:
( (x1+x2)/2 , (y1+y2)/2 )
(2,3) and (4,5)
( (2+4)/2 , (3+5)/2 )
( (6)/2 , (8)/2 )
( 3 , 4 )
wyzant sean w
The average height of students at UH from an SRS of 14 students gave a standard deviation of 2.5 feet. Construct a 95% confidence interval for the standard deviation of the height of students at UH. Assume normality for the data.
Answers
The 95% confidence interval for the standard deviation of the height of students at UH is given by; CI = (1.81, 4.03)
How to find the confidence interval for standard deviation?
The formula for the confidence interval for the standard deviation is given by the formula;
CI = √[(n - 1)s²/(χ²ₙ ₋ ₁, α/2)], √[(n - 1)s²/(χ²ₙ ₋ ₁, (1 - α)/2)]
We are given;
Sample size; n = 14
D F = n - 1 = 14 - 1 = 13
Standard Deviation; s = 2.5
Confidence Level; CL = 95% = 0.95
Significance level; α = 1 - 0.95 = 0.05
Thus, using Chi-square distribution table online we have;
χ²₁₃, ₀.₀₂₅ = 24.736
(χ²₁₃, ₀.₉₇₅) = 5.01
Now, the 95% confidence interval for the standard deviation of the height of students at UH is given by :-
CI = √[(13 * 2.5²/(24.736)], √[(13 * 2.5²/(5.01)]
CI = (1.81, 4.03)
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3) A normal distribution has a mean of 75 and a standard deviation of 15. Determine the z-score for the data value of 85.
Answers
Step-by-step explanation:
z = (specific score - mean) / standard deviation
in our case
z = (85 - 75)/15 = 10/15 = 2/3 = 0.666666... ≈ 0.67
as z-tables usually round the z-score to hundredths.
The z-score for the data value of 85 is 0.67.
How to Calculate Z-Score?A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score. A value that is one standard deviation from the mean would have a Z-score of 1.0. Z-scores can be either positive or negative, with a positive number signifying a score above the mean and a negative value signifying a score below the mean.
To find the z-score, you simply need to apply the following formula:
z = (x - μ) / σ
μ=75
σ=15
x=85
z =85-75/15
z=10/15
=2/3
=0,66666....=0.67
Therefore, the z-score for the data value of 85 is 0.67.
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Given: AD is parallel to BC
Prove: DC = 6 units
Which step is missing?
Answers
To prove DC = 6 units the missing step is ΔDAC ≅ ΔBCA by ASA.
Option C is the correct answer.
What is triangle congruency?There are ways to prove that two triangles are congruent.
- Side-Side-Side (SSS) Congruence.
The three sides of one triangle are equal to the corresponding three sides of another triangle.
- Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
- Angle-Side-Angle (ASA) Congruence.
The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
- Angle-Angle-Side (AAS) Congruence.
We have,
AD is parallel to BC
From the figure and the given information,
We have,
∠DAC ≅ ∠BCA
AC ≅ AC∠DCA ≅∠BACThis means,
Angle-Side-Angle (ASA) Congruence
ΔDAC ≅ ΔBCA
Thus,
To prove DC = 6 units the missing step is ΔDAC ≅ ΔBCA by ASA.
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Identify the perimeter of a rectangle in which h = 8 ft and a = 144x ft^2. please help asap
Answers
Here, Given
h= 8ft
a=144 * ft^2
then,
A=L*H
144=L*8 or 144/8 =L
L=18
now, P=2(L+H)
P=2(18+8)
P=52m
Perimeter and area are two important and basic mathematical subjects. They help quantify the physical space and also provide a more advanced foundation of mathematics in algebra, trigonometry, and calculus. Perimeter is a measure of the distance around a shape, and area indicates how much area the shape covers.
The perimeter of a 2D shape is the distance around the shape. You can imagine wrapping a string around a triangle. The length of this cord is around the triangle. Or, if you're traveling outside the park, take a route that goes around the edge of the park.
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What is the fuction for the graph?
Answers
The piecewise defined function is formed by the following three functions: y = 40, for 0 ≤ x < 15, y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65 and y = 0.4 · x - 6, for x ≥ 65.
What is the piecewise defined function behind the graph?
In this problem we have a piecewise defined function formed by three functions: (i) Linear equation, (ii) Quadratic equation, (iii) Linear equation. The first function is y = 40, for 0 ≤ x < 15.
The second function can be found based on the knowledge of three points:
y = a · x² + b · x + c
(x₁, y₁) = (15, 40)
40 = 225 · a + 15 · b + c
(x₂, y₂) = (45, 2.5)
2.5 = 2025 · a + 45 · b + c
(x₃, y₃) = (65, 20)
20 = 4225 · a + 65 · b + c
And the quadratic equation is y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65.
And the latter linear equation is:
y = m · x + b
m = (30 - 20)/(90 - 65)
m = 0.4
And the x-intercept is:
b = y - m · x
b = 20 - 0.4 · 65
b = - 6
The linear equation is y = 0.4 · x - 6, for x ≥ 65.
The piecewise defined function is formed by the following three functions: y = 40, for 0 ≤ x < 15, y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65 and y = 0.4 · x - 6, for x ≥ 65.
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Which type of bacterial pneumonia is most often seen in children and young adults, is characterized by a persistent cough and low-grade fever, and is usually treated with tetracycline
Answers
The type of bacterial pneumonia is most often seen in children and young adults is; Pneumococcal infection.
What is the Type of Bacteria?The correct type of Bacterial pneumonia that is most often seen in children and young adult is called Pneumococcal infection. This is because it is a name for any infection caused by bacteria called Streptococcus pneumoniae, or pneumococcus.
Thus, we can conclude that the type of Bacterial pneumonia here is called Pneumococcal infection.
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