Answer:
4
Step-by-step explanation:
Find and classify the global extrema of the following function:
f(x) = -x^3 + 5 x^2 + x
Find the critical points of f(x):
Compute the critical points of -x^3 + 5 x^2 + x
To find all critical points, first compute f'(x):
d/(dx) (-x^3 + 5 x^2 + x) = -3 x^2 + 10 x + 1:
f'(x) = -3 x^2 + 10 x + 1
Solving -3 x^2 + 10 x + 1 = 0 yields x = 1/3 (5 - 2 sqrt(7)) or x = 1/3 (5 + 2 sqrt(7)):
x = 1/3 (5 - 2 sqrt(7)), x = 1/3 (5 + 2 sqrt(7))
f'(x) exists everywhere:
-3 x^2 + 10 x + 1 exists everywhere
The critical points of -x^3 + 5 x^2 + x occur at x = 1/3 (5 - 2 sqrt(7)) and x = 1/3 (5 + 2 sqrt(7)):
x = 1/3 (5 - 2 sqrt(7)), x = 1/3 (5 + 2 sqrt(7))
The domain of -x^3 + 5 x^2 + x is R:
The endpoints of R are x = -∞ and ∞
Evaluate -x^3 + 5 x^2 + x at x = -∞, 1/3 (5 - 2 sqrt(7)), 1/3 (5 + 2 sqrt(7)) and ∞:
The open endpoints of the domain are marked in gray
x | f(x)
-∞ | ∞
1/3 (5 - 2 sqrt(7)) | -0.0490425
1/3 (5 + 2 sqrt(7)) | 21.9009
∞ | -∞
The largest value corresponds to a global maximum, and the smallest value corresponds to a global minimum:
The open endpoints of the domain are marked in gray
x | f(x) | extrema type
-∞ | ∞ | global max
1/3 (5 - 2 sqrt(7)) | -0.0490425 | neither
1/3 (5 + 2 sqrt(7)) | 21.9009 | neither
∞ | -∞ | global min
Remove the points x = -∞ and ∞ from the table
These cannot be global extrema, as the value of f(x) here is never achieved:
x | f(x) | extrema type
1/3 (5 - 2 sqrt(7)) | -0.0490425 | neither
1/3 (5 + 2 sqrt(7)) | 21.9009 | neither
f(x) = -x^3 + 5 x^2 + x has no global extrema:
Answer: -x^3 + 5 x^2 + x has no global extrema
Diction is the way writers arrange words and punctuation to create sentences.
A. True
B. False
Answer:
False
Step-by-step explanation:
determine the test average for your math class after completing test
Considering the numeric value of the function f(x), the test average for your math class after completing test 2 was of 80.8.
How to find the numeric value of a function or of an expression?To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.
For this problem, the function is given by:
f(x) = 79 + 0.9x.
The average after test 2 is represented by the numeric value when x = 2, hence we replace the lone instance of x on the function to find the average as follows:
f(2) = 79 + 0.9(2) = 80.8.
What is the missing information?
The problem asks for the test average for your math class after completing test 2.
The function that gives the average after test x is:
f(x) = 79 + 0.9x.
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t + –9.7 = 0.39
t=___
Answer:
t = 10.09
Step-by-step explanation:
Answer in the picture below!
42. MODELING REAL LIFE The graphs show the weight restrictions w (in tons) for vehicles with (a) axles, (b) axles, and (c) axles traveling on state roads. For each type of vehicle, write and interpret an inequality that represents the weight restriction (in ).
The inequalities that model each situation are given as follows:
a. w ≤ 20, meaning that vehicles with two axles can weight at most 20 tons.
b. w ≤ 30, meaning that vehicles with three axles can weight at most 30 tons.
c. w ≤ 40, meaning that vehicles with four axles can weight at most 40 tons.
Which inequalities models each situation?In each inequality, the plotted numbers are the numbers to the left, with a closed circle, hence:
The numbers to the left means that the numbers less than the value are part of the solution of the inequality.The closed circle means that the bound is a solution to the inequality.In item a, we have that for vehicles with 2 axles, the upper weight limit is of 20 tons, hence the inequality is:
w ≤ 20.
In item b, we have that for vehicles with 3 axles, the upper weight limit is of 30 tons, hence the inequality is:
w ≤ 30.
In item c, we have that for vehicles with 4 axles, the upper weight limit is of 40 tons, hence the inequality is:
w ≤ 40.
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Write the equation for this graph using this format y= a |x-h| +k
The equation of the graph using the format y= a*|x-h|+k is y=|x+4|-5 .
In the question ,
From the graph we can see that the vertex of the graph is (-4,-5) ,
The absolute value equation of the graph is denoted by y=a*|x-h|+k ,
where (h,k) are the vertex of the graph .
Since (-4,-5) is the vertex , So h= -4 and k= -5 ,
Substituting the values of h and in the absolute value equation , we get
y=a*|x-(-4)|+(-5)
y=a*|x+4|-5
Take any point that lies on the graph ,
Selecting the point (1,0) which lie on the graph ,
Substituting the value as x=1 and y=0 , we get
0=a*|1+4|-5
5=a*|1+4|
5=5a
a=1 ,
Substituting the values of a=1 , h= -4 and k=-5 in the absolute value equation , we get y=|x+4|-5
Therefore , the equation of the graph using the format y= a*|x-h|+k is y=|x+4|-5 .
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1. Evaluate f(x) = -4x - 7 for x = -2.
Answer:
1
Step-by-step explanation:
Not sure how to answer it but here's the correct answer i believe
I need help look at the image attached
Answer:
[tex]\dfrac{(x-2)^2}{9}-\dfrac{y^2}{4}=1[/tex]
Step-by-step explanation:
Given points:
(2±3√2, ±2)(5, 0)(-1, 0)Standard equation of a horizontal hyperbola (opening left and right):
[tex]\boxed{\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1}[/tex]
where:
center = (h, k)vertices = (h±a, k)Points (5, 0) and (-1, 0) are the vertices of the hyperbola.
The center (h, k) is midway between the vertices. Therefore:
[tex]\implies h=\dfrac{5-1}{2}=2[/tex]
[tex]\implies k=0[/tex]
Substitute the found values of h and k into the formula:
[tex]\dfrac{(x-2)^2}{a^2}-\dfrac{y^2}{b^2}=1[/tex]
Substitute point (5, 0) and solve for a²:
[tex]\implies \dfrac{(5-2)^2}{a^2}-\dfrac{0^2}{b^2}=1[/tex]
[tex]\implies \dfrac{3^2}{a^2}=1[/tex]
[tex]\implies \dfrac{9}{a^2}=1[/tex]
[tex]\implies 9=a^2[/tex]
Substitute one of the (2±3√2, ±2) points and the found value of a² and solve for b²:
[tex]\implies \dfrac{(2+3\sqrt{2}-2)^2}{9}-\dfrac{2^2}{b^2}=1[/tex]
[tex]\implies \dfrac{(3\sqrt{2})^2}{9}-\dfrac{4}{b^2}=1[/tex]
[tex]\implies \dfrac{18}{9}-\dfrac{4}{b^2}=1[/tex]
[tex]\implies 2-\dfrac{4}{b^2}=1[/tex]
[tex]\implies \dfrac{4}{b^2}=1[/tex]
[tex]\implies 4=b^2[/tex]
Substitute the found values of a² and b², together with the values of h and k, into the formula to create the equation of the hyperbola:
[tex]\dfrac{(x-2)^2}{9}-\dfrac{y^2}{4}=1[/tex]
please answer the question in the photo.
Considering when a triangle is formed given three sides, the code for the puzzle is given as follows:
BBBACC
What is the condition for 3 lengths to represent a triangle?In a triangle, the sum of the lengths of the two smaller sides of the triangle has to be greater than the length of the greater side of the triangle.
For the first letter, we have two sides, hence there are many possible values for the third side x, as long as 2.5 + x > 8, for x < 8 or x < 10.5, for x > 8, hence the first letter of the code is of B.
For the second letter, 4 + 7 < 19, hence no triangle can be formed with these dimensions and the letter is of B.
For the third letter, 2 + 4 > 5, hence one unique triangle can be formed with all the dimensions given and the letter is of B.
For the fourth letter, 6 + 8 > 12, hence one unique triangle can be formed with all the dimensions given and the letter is of A.
For the fifth letter, we have two sides, hence there are many possible values for the third side x, as long as 1 + x > 2.4, for x < 2.4 or x < 3.4, for x > 2.4, hence the letter is of C.
For the sixth letter, 5 + 9 > 13, hence one unique triangle can be formed with all the dimensions given and the letter is of C.
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Why are there two possible solutions to the equation, X² = 100?
Answer:
x could be 10 or -10
Step-by-step explanation:
10 x 10 = 100
and
(-10) x (-10) = 100 A negative times a negative is a positive.
Keaton drew an equilateral triangle on the computer. If the perimeter of the triangle is 29.4 centimeters, the length of a side of the triangle is
centimeters.
2ax-b=cx+b solve for x
The solution for x in the equation is x = 2b/(2a - c)
How to solve for x in the equation?The equation is given as
2ax - b = cx + b
Collect the like terms in the above equation
So, we have the following equation
2ax - cx = b + b
Evaluate the like terms in the above equation
So, we have the following equation
2ax - cx = 2b
Factor out x from the equation
x(2a - c) = 2b
Divide both sides by 2a - c
x = 2b/(2a - c)
Hence, the solution for x is x = 2b/(2a - c)
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Find the derivative: since the function is f(x) = (1-3x)^(1/3), the derivative is f'(x)=1/3(1-3x)^(-2/3) *(-3) =-(1-3x)^(-2/3) =evenutally we get an answer but thats not what im confused about where did the *(-3) come from? what does it mean? it made me get a different answer and i don't understand where it came from? please help asap
The derivative of f(x) = (1 - 3x)^(1/3) is f'(x) = - (1 - 3x)^(-2/3). The *(-3) comes from the derivative of (1 - 3x) with respect to x, due to the chain rule.
Chain rule: dy/dx = dy/du. du/dx
Suppose we have f(g(x)), then its derivative is: f'(g(x)) . g'(x)
In the problem:
f(x) = (1 - 3x)^(1/3)
Let u = 1 - 3x
then f(u) = u^(1/3)
and f'(u) = 1/3 u^(-2/3)
That part only the derivative of f with respect to u. We still need to take the derivative of u with respect to x. That is:
u(x) = 1 - 3x
u'(x) = -3
Hence, the complete derivative is:
f'(x) = f'(u) . u'(x)
= 1/3 u^(-2/3) . (-3)
= - u^(-2/3) ( substitute back u = 1 - 3x )
= - (1 - 3x)^(-2/3)
Hence the *(-3) comes from the derivative of (1 - 3x) with respect to x, due to the chain rule.
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I NEED HELP ASAP PLEASE!!!!!
Based on the discount to be applied by the online store when an order totals below $50 and $50 and above, the correct statement is C. A purchase of 2 pots at $20 each and 1 pan at $35 will be charged at $56.25.
How to find the discounted price?The discount for orders above $50 is 25%.
When a person buys 2 pots for $20 each and then 1 roasting pan for $35, the amount they'll pay normally is:
= (2 x 20) + 35
= 40 + 35
= $75
The amount the person will pay after the 25% discount is applied is:
= 75 x (1 - 25%)
= 75 x 75%
= $56.25
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A baseball team has $1,400 to buy baseball uniforms. Each uniform costs $124. Does the team have enough money to buy 11 baseball uniforms? Use the drop-down menus to explain.
The total cost for 11 uniforms is
Choose...
.
Since
Choose...
is
Choose...
$1,400, the team
Choose...
enough money to buy 11 uniforms.
The team has enough money that will be used to buy 11 baseball uniforms.
How to illustrate the information?The information illustrated that the baseball team has $1,400 to buy baseball uniforms and each uniform costs $124.
It was also stated that the team needs to buy 11 uniforms. In this case, the cost of 11 uniforms will be the multiplication of the coat of each pair of uniform by the number of uniforms that will be bought.
This will be illustrated as:
= Amount of each uniform × Number of uniform
= $124 × 11
= $1364
Therefore, the total amount is $1364. Therefore, since the baseball team has $1400, the amount is enough.
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Translate this sentence into an equation. 67 is the difference of Gail's age and 15. Use the variable g to represent Gail's age.
The algebraic equation that represents the given sentence is:
g - 15 = 67.
Which algebraic equation represents the given sentence?We have to look at the description of the sentence, and then formulate expressions that represent this sentence.
The difference between two numbers x and y is represented by the following expression.
x - y.
Gail's age is represented by the following variable:
g.
Hence the difference of Gail's age and 15 is represented by:
g - 15.
The numeric value of this expression is of 67, hence the equation is:
g - 15 = 67.
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identify if the following statement is a proper interpretation of a 95% confidence interval 95% of the population values will fall within this variable
option a , c and d are the correct statement or is a proper interpretation of a 95% confidence interval 95% of the population values will fall within this variable
What is the 95% confidence interval for a population mean?
It means that for any given number of samples, 95% of them will fall within 2 standard errors of the true mean of the population the sample is derived from.
a. In 95% of all samples, the sample mean will fall within 2 standard errors of the true population mean.
c. In 95% of all samples, the true population mean will be within 2 standard errors of the sample mean.
d. 95% of the population values will lie within 2 standard errors of the sample mean.
therefore option a , c and d are correct
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What is 4 9/16 - 2 1/4
Answer:
Exact Form:
37/16
Decimal Form:
2.3125
Mixed Number Form:
2 5/16
Step-by-step explanation:
Mark raised $405 for his softball team's fundraiser. he wants to raise at least $825. write and solve an inequality to determine how much more money mark must raise to reach his goal. let d represent the amount of money in dollars mark must raise to reach his goal.
Answer: d ≥ 825-405
You're Welcome
72.1 x 1.3 show work
Answer:
93.73
Step-by-step explanation:
72.1
x 1.3
_____
93.73
lucy and her father share the same birthday. When lucy turned fifteen, her father was 3 times her age. On their bday this year, Lucky's father turned exactly twice as old as she turned. How old did lucy turn this year?
Solving a system of equations we can see that Lucy is 30 years old.
How old did lucy turn this year?Let's define the variables:
L = Lucy's age.
F = father's age.
We know that when Lucy turns 15, her father was 3 times her age, so:
if L = 15
then F = 15*3 = 45
So her father is 30 years older than Lucy.
So we can write the linear relation:
F = L + 30
Now we know that this year, her father has exactly twice Lucy's age, then we have the system of equations:
F = L + 30
F = 2*L
Replacing the other equation here we get:
L + 30 = 2*L
30 = 2*L - L = L
30 = L
Lucy is 30 years old.
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What is the prime factorization of 621?
Answer:
[tex]621 = {3}^{3} \times 23[/tex]
Step-by-step explanation:
[tex]621 \div 3 = 207[/tex]
[tex]207 \div 3 = 69[/tex]
[tex]69 \div 3 = 23[/tex]
[tex]621 = 3 \times 3 \times 3 \times 23 = {3}^{3} \times 23[/tex]
i rllly need this one pls help
The slope of the line is 2.
We are given a graph with coordinate axes, namely, the x-axis and the y-axis.The intersection of the coordinate axes is called the origin with coordinates (0, 0).The line is drawn in blue.The line passes through two dots, whose coordinates can be found using the graph.The coordinates of the points are (1, 1) and (-1, -3).The slope "m" of a line passing through points (x1, y1) and (x2, y2) is calculated as :m = (y2-y1)/(x2-x1)The slope of the line shown in the graph is :m = (-3-1)/(-1-1)m = -4/-2m = 2Thus, the slope of the line is 2.To learn more about slope, visit :
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Which of these are like terms? Select all that apply.
3 d
-6 ad
0.75 d
Please help
The likely terms that are the same based on the information include 3/4a³ and 0.75a³.
How to illustrate the information?It should be noted an equation is used to show the relationship between the variables that are given.
In the question, the likely terms that are given include: 3d, 3/4a³, -6ad, and 0.75a³.
It should be noted that the expressions that are the same include 3/4a³ and 0.75a³. This is because 3/4 is the same as 0.75 in decimal.
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What is the area of this face?
20in.
10in.
10in.
5in.
5in.
10in.
10in.
100 in2
200 in2
150 in2
400 in2
Answer:200 in^2
Step-by-step explanation:
Question 1
Solve the inequality.
5a<−35 or a−14>1
Answer:
The answer is
[tex]a < - 7 \: or \: a > 15[/tex]
Find the inverse function in slope-intercept form (mx+b): f(x)=-x-2
Answer:
[tex]f {}^{ - 1} (x) = - x - 2[/tex]
The area of the triangle below is 5.89 square meters. What is the length of the base?
Answer:3.8 square meters
Step-by-step explanation: hope this helps!
4. A bird is flying at 385 feet
above sea level. A fish is
swimming at 197 feet below
sea level. What is the
difference in their
elevation
Answer: their difference in elevation is 188 feet
Step-by-step explanation:
In the last ten games, Jamal made 7/9
of his free throws and Brian made 5/8
of his free throws. Which player has the better record? Explain.
By comparing the fractions, we see that 7/9 is larger than 5/8, thus, Jamal has the better record.
Which player has the better record?We know that Jamal made 7/9 of his free throws while Brian made 5/8 of his free throws.
To see which player has the better record, we need to see which one of the two fractions is larger.
To do so we can write both of the fractions as decimals, we will get:
7/9 = 0.77...
5/8 =0.625
There we can see that 7/9 is larger, thus, we can conclude that Jamal has a better record.
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Given:
A = [ 1 -1 -2 3]
B = [ 1 5 8 -8 ]
C = [ 1 2 3 4 ]
Solve: AX + B = C
Answer:
[-5 3] [-5 6]
Step-by-step explanation:
Answer:
Your answer is on the pic...mate