Let f(x)=x^3-6x+3 i. find the domain of the function and f’(x) in the domain.
Answers
Domain of a any cubic function [tex]f(x)=ax^3+bx^2+cx+d[/tex] is defined to be always [tex]\mathbb{R}[/tex].
The derivative with respect to x of your cubic function is,
[tex]\dfrac{d}{dx}f(x)=f'(x)[/tex]
to find the derivative of a polynomial function, simply take a derivative of each factor and sum them up,
[tex]\dfrac{d}{dx}x^3=3x^2[/tex] by the rule [tex]\dfrac{d}{dx}x^m=mx^{m-1}[/tex] where [tex]m\in\mathbb{R}[/tex]
[tex]\dfrac{d}{dx}-6x=-6[/tex]
[tex]\dfrac{d}{dx}3=0[/tex]
So the derivative is,
[tex]f'(x)=3x^2-6[/tex]
both derivative and the original function have equal domain.
Hope this helps :)
Step-by-step explanation:
[tex]thank \: you[/tex]
Related Questions
33. The population of Canada, y (in millions), can be approximated by the relation y=
0.146x + 31, where x represents the number of years since 2000.
a. Approximate the population of Canada in the year 2006.
b. In what year did the population of Canada reach approximately 32,752,000?
Answers
Answer:x=6573/500,x=13(73/500
Step-by-step explanation:
It will takes 12 years to reach approximately 32,752,000.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
y = 0.146x + 31
where x represents the number of years since 2000.
a) The population of Canada in the year 2006
x= 6
y= 0.146 x 6 + 31
y = 31.876
b) The population of Canada reach approximately 32,752,000 in
y = 32.752
0.146x + 31= 32.752
0.146x = 1.752
x= 1.752/0.146
x= 12
Hence, it will takes 12 years to reach approximately 32,752,000.
Learn more about Equation here:
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During a test period, an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emissions of 667 pounds per 1000 miles, with a standard deviation of 20 pounds. A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds. At α = 0.05, in a left-tailed test (assuming equal variances) the test statistic is:______.
A. 1.321.
B. -2.508.
C. -2.074.
D. -1.717.
Answers
Answer:
-1.683
Step-by-step explanation:
Given :
Group 1 :
x1 = 667 ; n1 = 10 ; s1 = 20
Group 2 :
x2 = 679 ; n2 = 14 ; s2 = 15
The test statistic assuming equal variance :
x1 - x2 / √[Sp² * (1/n1 + 1/n2)]
sp² = [(n1 - 1)*s1² + (n2 - 1)*s2²] ÷ (n1 + n2 - 2)
Sp² = [(10 - 1)*20² + (14 - 1)*15²] = 296.59
Test statistic =
(667 - 679)/ √[296.59 * (1/10 + 1/14)]
-12 / 7.1304978
Test statistic = - 1.682
Jessica works 5 days a week at a factory 7.5 miles from her home.
She travels to and from work in her car which has a fuel consumption of 30 miles per gallon.
Fuel costs £1.14 per litre and there are 4.55 litres in a gallon.
It costs £2.50 to park her car each day.
Rounded to the nearest £1, how much does it cost Jessica to travel to work in her car for a week?
Answers
Answer:
£25
Step-by-step explanation:
total distance travelled per week = 2 * 7.5 * 5 = 75
amount of fuel used = 75/30 = 2.5 gallons = 11.375 litre
cost of fuel = 11.375 * 1.14 = 12.9675
total cost = 5(2.5) + 12.9675 = 25.4675 ~~ 25
Find the numerical value of the area under the normal curve given the following information:
to the right of z = 2.28
enter your answer as a decimal (NOT percentage) and lead with a zero...for example: 0.1234
Answers
Answer:
1 - 0.9887 = 0.0113
Step-by-step explanation:
A (5,3) and B (2,-1) are two verticles of a square ABCD and D is on the x axis. Find the coordinate of C and D
Answers
Answer:
1) D(1,0), C(-2,-4) or 2) D(9,0), C(6,-4)
Step-by-step explanation:
The vector AB is (2-5, -1-3)= (-3,-4)
The modul of the vector is equal to sqrt (3squared+4squared)=5 (the length of the side AB of square)
Explore the point D (the coordinates of the point is (x,0), y=o, because it is an axis x). AD (x-5, -3)
The modul of AD is sqrt ((x-5)^2+(-3)^2)= sqrt (x^2-10x+25+9), it is equal to the side AD which is equal to AB
sqrt(x^2-10x+34)= 5
x^2-10x+34=25
x^2-10x+9=0
x=1, x=9
D is (1,0) or D is (9,0),
find C, (for D1(1,0))
Find the midpoint of BD (O)
xo= (2+1)/2= 1.5
y0=(-1+0)/2= -0.5
It is the midpoint of Ac too
x0= (xa+xc)/2 1.5 = (5+xc)/2 xc= -2
y0=(ya+yc)/2 -0.5= (3+yc)/2 yc=-4
c(-2,-4)
Find C2 (for D(9,0))
Find the midpoint of BD (O)
x0= (2+9)/2=5.5
y0= (-1+0)/2=-0.5
o(5.5, -0.5)
It is the midpoint of Ac too
x0= (xa+xc)/2 5.5= (5+x)/2 x=6
y0=(ya+yc)/2 -0.5= (3+x)/2 y=-4
number
5. Thesum of a two-digit number a
(CBSE 2002]
Find the numbers.
If the two digits differ by 2, find the number. I
6. The sum of two numbers is 1000 and the difference between their squares is 256000.
7. The sum of a two digit number and the number obtained by reversing the order of its
digits is 99. If the digits differ by 3, find the number.
8. A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits
are reversed. Find the number.
(CBSE 2001C]
[CBSE 2001C]
9. A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the
(CBSE 2001C]
number, the digits are reversed. Find the number.
10. A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from
the number, the digits are reversed. Find the number.
11. A two-digit number is 4 times the sum of its digits and twice the product of the digits.
[CBSE 2005]
Find the number.
[CBSE 2005]
12. A two-digit number is such that the product of its digits is 20. If 9 is added to the number,
the digits interchange their places. Find the number.
13. The difference between two numbers is 26 and one number is three times the other. Find
them.
14. The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the
Answers
Let the numbers are x and y
According to the question
⇒x+y=1000.....eq1⇒x 2 −y 2
=256000∵x 2 −y 2
=(x+y)(x−y)
⇒1000∗(x−y)=256000
⇒x−y=256.....eq2
Adding eq1 and eq2
⇒2x=1256⇒x=628
Put the value of x in eq1
⇒628+y=1000⇒y=372
The numbers are 628 and 372
Hi I'm From PHILIPPINES
I'm here to help USA users like you
At the Olympic games, many events have several rounds of competition. One of these events is the men's 100100100-meter backstroke. The upper dot plot shows the times (in seconds) of the top 888 finishers in the semifinal round at the 201220122012 Olympics. The lower dot plot shows the times of the same 888 swimmers in the final round. A dot plot is divided into 2 parts labeled, Semifinal Round and Final Round. The horizontal axis is labeled, Time, in seconds, from 52 to 54, in increments of 0.10 second. The portion of the dot plot dedicated to Final Round has dots above the following points; 52.2, 52.3, 52.8, 53.1, 53.2, 53.3, 53.5, and 53.8. The portion of the dot plot dedicated to Semifinal Round has dots above the following points; 52.7, 53, 53.3, 53.3, 53.5, 53.5, 53.5, and 53.7. Which pieces of information can be gathered from these dot plots? (Remember that lower swim times are faster.)
Answers
Answer: None of the above.
Step-by-step explanation:
I got it right on khan. I’ll explain a little though. Semifinals median=47.05. Finals median=53.05. Therefore A is not and option and B is DEFINITLEY not an option. Sorry I’m not good at explaining
Answer:
None of the above
Step-by-step explanation:
Got it right on test
Find the simple interest. The rate is an annual rate unless otherwise noted. Assume 365 days in a year and 30 days per month Round to the nearest cent $600 at 3% for 1 year
Answers
9514 1404 393
Answer:
$18
Step-by-step explanation:
The interest is computed using the formula ...
I = Prt
where P is the principal, r is the annual rate, and t is the number of years. The interest is ...
I = $600×0.03×1 = $18
Solve for x.
A. 1
B. 5
C. 3
D. 12
Answers
9514 1404 393
Answer:
A. 1
Step-by-step explanation:
Arc AB is twice the measure of the angle ABC. The sum of the arc measures around the circle is 360°.
2(43x)° +(272x +2)° = 360°
358x +2 = 360 . . . . . . . . . . . . divide by °, collect terms
358x = 358 . . . . . . . . subtract 2
x = 1 . . . . . . . . . . divide by 358
a road rises 16 feet for every 50 feet of horizontal distance covered. in percent what is the grade of the road?
Answers
Answer:
32%
Step-by-step explanation:
The slope of the road is measured as
slope = [tex]\frac{rise}{run}[/tex] = [tex]\frac{16}{50}[/tex]
To express as a percentage multiply the fraction y 100% , that is
slope = [tex]\frac{16}{50}[/tex] × 100% = 16 × 2 = 32%
Solve for the length of the unknown side in the following right triangle. (Side AC is the hypotenuse.)
Round your answer to two places, where applicable.
Side AB 3 Side BC 4 Side AC ?
Answers
Answer:
side AC is 5
Step-by-step explanation:
by using th pythagorean theorm you would square both sides add them together and the square root the sum to get you answer.
AB =3 BC=4
9+16=25
25 square root is 5
makeing AC=5
A car dealership is advertising a car for $16,299.99. If the sales tax rate is 6.5 percent, what
is the total tax paid for the car?
A. S993 34
B. $1.000.00
CS1.059 50
DS1.359.19
Answers
Answer:
C. 1059.50
Step-by-step explanation:
Sales price x sales tax rate = sales tax
16299.99 x .065 (6.5%) = 1059.50
evaluate (-1)^6-4^0+(3/7)^0
Answers
Answer:
The answer is 1
.............
please mark this answer as brainlist
An advertising firm wanting to target people with strong desires for success conducted a study to see if such people differed in the types of television shows they watched. Randomly selected participants recorded the shows they watched for a week, then their desire for success was assessed, and finally they were divided into two groups. Low Success seekers watched 8 comedies, 15 romances, 6 documentaries, 13 dramas, and 3 news shows. High Success seekers watched 3 comedies, 3 romances, 9 documentaries, 7 dramas, and 8 news shows.
1. Use the five steps of hypothesis testing.
2. Sketch the chi-square distribution. Be sure your sketch gives a rough indication of its shape and shows the cutoff score and the sample's score.
3. Explain the logic of what you have done to a person who is familiar with the logic and steps of hypothesis testing for the t test and analysis of variance, but who knows nothing about chi-square tests.
4. Figure a measure of effect size and indicate whether it is small, medium, or large.
Answers
Answer:
Blablabla
Step-by-step explanation:
Bababa
if x=2 and y=3. What is x*y/xy+x*y
Answers
Answer
its uhhhhh i dont know
Step-by-step explanation:
If a < 0 and b > 0, then which of the following is true?
Select one:
a. a + b > 0
b. a + b < 0
c.
a + b = 0
d.
The relationship between a and b cannot be determined.
Answers
Answer:
d. The relationship between a and b cannot be determined.
Step-by-step explanation:
Given
[tex]a < 0[/tex]
[tex]b > 0[/tex]
Required
Which is true
To do this, we test each of the options using assumed values
[tex]a + b > 0[/tex]
Let:
[tex]a = -5[/tex] [tex]b= 1[/tex]
So:
[tex]-5 + 1 > 0[/tex]
[tex]-4 > 0[/tex] --- false
[tex]a + b < 0[/tex]
Let:
[tex]a = -5[/tex] [tex]b= 7[/tex]
So:
[tex]-5 + 7 < 0[/tex]
[tex]2 < 0[/tex] --- false
[tex]a + b = 0[/tex]
Let:
[tex]a = -5[/tex] [tex]b= 7[/tex]
So:
[tex]-5 + 7 = 0[/tex]
[tex]2 = 0[/tex] --- false
Hence, the relationship is not specific and cannot be determined
WORTH 30 POINTS PLEASE HELP!!!!! WILL GIVE POINTS
Answers
Answer:
2/3 and 4/6
Step-by-step explanation:
This is because if we take 2/3 and multiply each number by 2, we get 4/6. Therefore, they are equal.
Are the ratios 6:3 and 2:1 equivalent?
Answers
is 3 so it would be equivalent
How does sample size affect determinations of statistical significance? The smaller the sample size, the more confident one can be in one's decision to reject or retain the null hypothesis. The smaller the sample size, the greater the probability that the variable has an effect. The larger the sample size, the more accurate the estimation of the true population value. The larger the sample size, the greater the probability that the variable has an effect.
Answers
Answer:
The larger the sample size, the more accurate the estimation of the true population value.
Step-by-step explanation:
As large will be the sample size more data will be shown and more are the c c changes of it being an estimate of a true population. The sample size can be determined on the basis of use of experience, target variance, confidence level, and target for power.what should be the rate of simpe interest such that the interest is double of the sun at 10 years
Answers
Answer:
you never showed the chocies
Step-by-step explanation:
I need help please guys thank you
Answers
Answer:
Option A, the parent function has been translated up
Option B, the parent function has been compressed
Option C, the parent function has been translated to the right
Solve the following system of equations for x to the nearest hundredth : y + 2x + 1 = 0; 4y - 4x ^ 2 - 12x = - 7
Answers
Answer:
+3.464; -3.464
Step-by-step explanation:
call A = y + 2x + 1 = 0 => y = (1 - 2x)
call B: 4y - 4(x^2) - 12x = -7
=> replace y from A to B =>
4(1 - 2x) - 4(x^2) - 12x = -74 - 8x - 4(x ^ 2) - 12x = -7-8x - 4(x ^ 2) - 12x = -7 - 4 = -11-4(x^2) - (8x - 12x) = -11-4(x^2) + 4x = -11-4(x^2) + 4x + 11 = 0=> get delta Δ = (-4^2) - 4*(-4 * 11) = 192
=> Δ > 0 => got 2 No
=> x1 = [tex]\frac{-4 + \sqrt{192} }{2 * -4}[/tex] = [tex]\frac{1 - 2\sqrt{3} }{2}[/tex] = -1.232
=> x2 = [tex]\frac{-4 - \sqrt{192} }{2 * -4}[/tex]=[tex]\frac{1 + 2\sqrt{3} }{2}[/tex]= 2.232
=> replace x from B into A
=> y1 = (1 - 2x) = (1 - 2 * -1.232) = 3.464
=> y2 = (1 - 2x) = (1 - 2 * 2.232) = - 3.464
Which of the following rational functions is graphed below?
10
- 10
10
tho
A. F(x) =
3
X-7
B. F(x) = x + 3
X-7
C. F(x) =
(x+3)(x-7)
(x+3)(x-7)
D. F(X)
1
(x + 7(x-3)
7\x-
Check the picture out and please help me lol
Answers
Vertical asymptote:
A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;
In a graphic, these vertical asymptotes are given by dashed vertical lines.
An example is a value of x for which the denominator of the function is 0.
In this graphic:
Dashed vertical lines at: [tex]x = -3, x = 7[/tex], thus, for [tex]x - (-3) = x+3[/tex] and [tex]x - 7[/tex] the denominator is zero.
Thus, the function graphed is:
[tex]F(x) = \frac{1}{(x+3)(x-7)}[/tex]
And the correct answer is given by option C.
To take a look at a problem with asymptote, you can check this item https://brainly.com/question/4084552.
The graph is for the rational function f(x) = 1/(x + 3)(x - 7).
Option C is the correct answer.
We have,
To understand the graph of the function f(x) = 1/((x + 3)(x - 7)).
Vertical Asymptotes:
The function has vertical asymptotes at the values of x for which the denominator becomes zero.
The denominator is (x + 3)(x - 7), so the vertical asymptotes occur at
x = -3 and x = 7.
Horizontal Asymptote:
The highest power of x in the denominator is x², and there is no x² term in the numerator, the function approaches 0 as x goes to positive or negative infinity.
The horizontal asymptote is y = 0.
x-Intercept:
To find the x-intercept, we set y = 0 and solve for x:
0 = 1/((x + 3)(x - 7))
Since the numerator can never be zero, the only way the fraction can be zero is if the denominator is zero:
(x + 3)(x - 7) = 0
Solving for x:
x + 3 = 0
x = -3
x - 7 = 0
x = 7
So, the x-intercepts are (-3, 0) and (7, 0).
y-Intercept:
To find the y-intercept, we set x = 0:
f(0) = 1/((0 + 3)(0 - 7)) = 1/(-3 * -7) = 1/21
The y-intercept is (0, 1/21).
Thus,
The graph is for the rational function f(x) = 1/(x + 3)(x - 7).
Learn more about functions here:
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Solve this inequality: 14 <-7x
Answers
Answer:
-2 > x
Step-by-step explanation:
14 <-7x
Divide each side by -7, remembering to flip the inequality
14/ -7 > -7x/-7
-2 > x
if 405 is to be divided among three persons A, B, C in the ratio of 3:5:7, how much money does each one get? Express them in percentages.
Answers
Step-by-step explanation:
Pls Mark me
Brainliest!!!!Percent decrease from 20 to 11
Answers
Answer:
45 percent
Step-by-step explanation:
20-11=9
9 divided by 20= 0.45
0.45 x 100= 45%
find area of a square garden having a length 45m
Answers
Answer:
A = 2025 ft^2
Step-by-step explanation:
The area of a square is given by
A = s^2 where s is the side length
A = 45^2
A = 2025 ft^2
Answer:
Step-by-step explanation:
The area of any square is s^2
s in this case is 45
Area = s^2
Area = 45 * 45
Area = 2025 m^2
Question 13 plz show ALL STEPS
Answers
Step-by-step explanation:
Here are some of the graphs:
Blue is g(x) and Green is f(x). The 2nd graph is for the 13b. It shows our graph after 1 transformation. The 3rd graph is after both transformations.
13a. Let use the following values in
[tex]f(x) = \frac{2}{x} [/tex]
We know by definition of rational function x cannot be zero.
Let find some values across interval 2 through 4.
[tex]f(2) = \frac{2}{2} = 1[/tex]
[tex]f(3) = \frac{2}{3} [/tex]
[tex]f(4) = \frac{2}{4} = \frac{1}{2} [/tex]
Let use the following values in
[tex]g(x) = \frac{3x - 1}{x - 1} [/tex]
By definition of rational function, x cannot be 1 because it will make the denominator zero. Let use some values across the interval 0 through 4.
[tex]g(0) = \frac{0 - 1}{0 - 1} = 1[/tex]
[tex]g(2) = \frac{3(2) - 1}{2 - 1} = {5} [/tex]
[tex]g(3) = \frac{8}{2} = 4[/tex]
[tex]g(4) = \frac{11}{3} [/tex]
So graph this in a table of values. I'll post a picture of the table of values on the top.
13b. We need to write g(x) as a transformation of f(x). If we look at the graphs, g(x) has a asymptote at x=1 while f(x) has a asymptote of 0. This means that we need to move f(x) to the right one unit or move (x-1) units.
We will upgrade the graph.
Now we can just add 3 to f(x) to get to g(x).
In the 3rd graph, notice how both graphs coincide. Our transformations is complete.
The answer is
[tex]g(x) = f(x - 1) + 3[/tex]
13c. We can say this as we move f(x) to the right 1 unit and shift f(x) up 3 units.
(-1)×(-1)×(-1)×(2m+1) times where m is a natural number,is equal to?
1. 1
2.-1
3.1 or-1
4.None
Answers
Answer:
(2). -1
Step-by-step explanation:
The given parameter can be represented as:
[tex](-1)^{2m + 1}[/tex]
See comment for correct question
Required
The end result
From the question, we understand that m is a natural number
This means that:
[tex]2m + 1 \to[/tex] odd number
So:
[tex](-1)^{2m + 1} = -1[/tex] --- i.e. -1 to the power of an odd number will give -1
Hence; (2) is correct
What are Julie’s taxable wages as a data-entry operator if her withholding allowances total $1,500 and her annual gross pay is $24,500?
Answers
Julie's Taxable Wages:
Julie's taxable wages as a data-entry operator is:
= $23,000.
Data and Calculations:
a) Annual gross pay = $24,500
Total withholding allowances = 1,500
Taxable wages (income) = $23,000 ($24,500 - $1,500)
b) Julie's total withholding allowance of $1,500 is the total exemption that reduces how much income tax her employer can deduct from Julie's paycheck. This means that $1,500 will be deducted from $24,500, the gross pay, before arriving at her taxable income.
Thus, Julie's taxable wages represent the difference between her annual gross pay and her total withholding allowances.
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