57. do not use the answer under the line in the explanation itself, only refer to it to make sure of your work. USE DERIVITIVES NOT GRAPHING
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Explanation
Question 57
[tex]\:f\left(x\right)=2x^3-15x^2+24x[/tex]To find the extreme values
[tex]\begin{gathered} \mathrm{Suppose\:that\:}x=c\mathrm{\:is\:a\:critical\:point\:of\:}f\left(x\right)\mathrm{\:then,\:} \\ \mathrm{If\:}f\:'\left(x\right)>0\mathrm{\:to\:the\:left\:of\:}x=c\mathrm{\:and\:}f\:'\left(x\right)<0\mathrm{\:to\:the\:right\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:a\:local\:maximum.} \\ \mathrm{If\:}f\:'\left(x\right)<0\mathrm{\:to\:the\:left\:of\:}x=c\mathrm{\:and\:}f\:'\left(x\right)>\:0\mathrm{\:to\:the\:right\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:a\:local\:minimum.} \\ \mathrm{If\:}f\:'\left(x\right)\mathrm{\:is\:the\:same\:sign\:on\:both\:sides\:of\:}x=c\mathrm{\:then\:}x=c\mathrm{\:is\:neither\:a\:local\:maximum\:nor\:a\:local\:minimum.} \end{gathered}[/tex]So, we will have the steps below
Step 1:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=0\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=0 \\ \mathrm{Minimum}\left(0,\:0\right) \end{gathered}[/tex]Step2:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=1\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=11 \\ \mathrm{Maximum}\left(1,\:11\right) \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=4\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=-16 \\ \mathrm{Minimum}\left(4,\:-16\right) \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} \mathrm{Plug\:the\:extreme\:point}\:x=5\:\mathrm{into}\:2x^3-15x^2+24x\quad \Rightarrow \quad \:y=-5 \\ \mathrm{Maximum}\left(5,\:-5\right) \\ \end{gathered}[/tex]Thus, we will have
[tex]\mathrm{Minimum}\left(0,\:0\right),\:\mathrm{Maximum}\left(1,\:11\right),\:\mathrm{Minimum}\left(4,\:-16\right),\:\mathrm{Maximum}\left(5,\:-5\right)[/tex]Hence, our answer is
[tex]\begin{gathered} \begin{equation*} \mathrm{Minimum}\left(4,\:-16\right) \end{equation*} \\ \begin{equation*} \mathrm{Maximum}\left(1,\:11\right) \end{equation*} \end{gathered}[/tex]Related Questions
Please help by providing answers to these questions.
Answers
Graph of proportional relationship is given y =kx , answer of the following questions are as follow:
1. Based on the information , the constant of proportionality represents the multiplicative relationship between two quantities.
2. Variable represents the constant of proportionality is k.
3. The constant of proportionality is known as the scale factor.
4. The graph of y = kx is a line that passes through the origin.
8. y/x =7 represents the constant of proportionality.
9. Scale factor of the constant of proportionality of figure S to T is 1/4.
As given,
Graph represents proportional relationship is given by:
y = kx
⇒ k = y/x
Represents the multiplicative relationship between the variables y and x.
1. Based on the information , the constant of proportionality represents the multiplicative relationship between two quantities.
'k' is the scale factor represents the constant of proportionality.
2. Variable represents the constant of proportionality is k.
3. k is the scale factor.
4. y =kx
when x=0 ⇒ y =0 represents graph passes through origin.
8. y =kx ⇒y /x =k if k =7 then y/x =7 represents constant of proportionality.
9. 2/8 = 4.5/18= 3/12 =1.5/6 = 1/4
Scale factor of the constant of proportionality of figure S to T is 1/4.
Therefore, graph of proportional relationship is given y =kx , answer of the following questions are as follow:
1. Based on the information , the constant of proportionality represents the multiplicative relationship between two quantities.
2. Variable represents the constant of proportionality is k.
3. The constant of proportionality is known as the scale factor.
4. The graph of y = kx is a line that passes through the origin.
8. y/x =7 represents the constant of proportionality.
9. Scale factor of the constant of proportionality of figure S to T is 1/4.
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The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set.2, 10, 15, 4. 14. 7. 14, 8, 2, 10The range is(Simplify your answer.)The population mean is(Simplify your answer. Round to the nearest tenth as needed.)The population variance is I(Simplify your answer. Round to the nearest tenth as needed.)The population standard deviation is(Simplify your answer. Round to the nearest tenth as needed)Enter your answer in each of the answer boxes.
Answers
The numbers of regular-season wins for 10 football teams in a given season are given below
[tex]2,10,15,4,14,7,14,8,2,10[/tex]We are asked to find the range, mean, variance, and standard deviation of the population data set.
Range:
The range is the difference between the maximum value and the minimum value in a data set.
From the given data set,
Maximum value = 15
Minimum value = 2
[tex]\begin{gathered} \text{Range}=\text{maximum}-\text{minimum} \\ \text{Range}=15-2 \\ \text{Range}=13 \end{gathered}[/tex]Therefore, the range is 13
Mean:
The population mean is given by
[tex]\mu=\frac{\sum^{}_{}X}{N}[/tex]Where X is the terms in the data set and N is the number of terms in the data set.
[tex]\begin{gathered} \mu=\frac{2+10+15+4+14+7+14+8+2+10}{10} \\ \mu=\frac{86}{10} \\ \mu=8.6 \end{gathered}[/tex]Therefore, the population mean is 8.6
Variance:
The population variance is given by
[tex]\sigma^2=\frac{\sum^{}_{}(X-\mu)^2}{N}[/tex]Where X is the terms in the data set, μ is the mean, and N is the number of terms in the data set.
[tex]\begin{gathered} \sigma^2=\frac{\sum^{}_{}(X-\mu)^2}{N} \\ \sigma^2=\frac{(2-8.6)^2+(10-8.6)^2+(15-8.6)^2+(4-8.6)^2+(14-8.6)^2+(7-8.6)^2+(14-8.6)^2+(8-8.6)^2++(2-8.6)^2++(10-8.6)^2}{10} \\ \sigma^2=\frac{214.4}{10} \\ \sigma^2=21.4 \end{gathered}[/tex]Therefore, the population variance is 21.4
Standard deviation:
The population standard deviation is given by
[tex]\begin{gathered} \sigma^{}=\sqrt[]{\frac{\sum^{}_{}(X-\mu)^2}{N}} \\ \sigma=\sqrt[]{\sigma^2} \end{gathered}[/tex]Since we have already find the population variance, we can simply find take the square root of variance.
[tex]\begin{gathered} \sigma=\sqrt[]{\sigma^2} \\ \sigma=\sqrt[]{21.4} \\ \sigma=4.6 \end{gathered}[/tex]Therefore, the population standard deviation is 4.6
how do i find the sale price?if original price is $77.00markdown is 32%
Answers
The markdown price can be calculated as,
[tex]\begin{gathered} \text{Markdown price}=\frac{Markdown\text{ Percent}}{100}\times Original\text{ price} \\ \text{Markdown price}=\frac{32}{100}\times77 \\ \text{Markdown price}=24.64 \end{gathered}[/tex]Now, the sale price is,
[tex]\begin{gathered} \text{Sale price=Original price -markdown price} \\ \text{Sale price=}=77-24.64 \\ \text{Sale price=}52.36 \end{gathered}[/tex]Therefore, the sale price is $52.36.
Find the rule for the following sequence. Then find the 45th term.
Answers
Answer:
[tex]a_{45}=221[/tex]Step-by-step explanation:
Arithmetic sequences are represented by the following equation;
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ where, \\ a_1=\text{ first term} \\ d=\text{ common difference} \\ n=\text{ nth term} \end{gathered}[/tex]The common difference is the difference between the consecutive terms:
[tex]\begin{gathered} d=6-1=5 \\ d=11-6=5 \\ d=16-11=5 \end{gathered}[/tex]Therefore, the equation that represents this sequence:
[tex]a_n=1+5(n-1)[/tex]Now, if we want to find the 45th term, substitute n=45:
[tex]\begin{gathered} a_{45}=1+5(45-1) \\ a_{45}=1+5*(44) \\ a_{45}=1+220 \\ a_{45}=221 \end{gathered}[/tex]as the x increases by 1, what will the rate of change for y in this equation y=-3x+10
Answers
Answer:
Rate of change = -3
Explanation:
Given the equation:
[tex]y=-3x+10[/tex]When x=1
[tex]\begin{gathered} y=-3(1)+10 \\ =-3+10 \\ =7 \end{gathered}[/tex]When x=2
[tex]\begin{gathered} y=-3(2)+10 \\ =-6+10 \\ =4 \end{gathered}[/tex]Observe that the value of y decreases by 3 as the x increases by 1.
Thus, the rate of change is -3.
Alternate Route
Another way is to express and compare the line with the slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ y=-3x+10 \end{gathered}[/tex]The rate of change is the coefficient of x.
Coefficient of x = -3
Thus, the rate of change is -3.
between 1993 and 1996 there were 6545 injured during horse races find the ratio of injured per year
Answers
First, we have to calculate the years passed between 1993 and 1996:
1996-1993 = 3 years
Now divide the number of injured during horse races (6545) by the number of years (3)
6545 /3
2,182 injured per year
16 ftTo the nearest tenth, what is the height of the triangle?A. 9 feetB. 14.4 feetC. 17.5 feetD. 23 feethB7 ftС
Answers
In the right triangle, there is a relation between the 2 legs of the right angle and the hypotenuse (the opposite side to the right angle)
[tex](hypotenuse)^2=(leg1)^2+(leg2)^2[/tex]From the given figure
∵ leg1 = 7 ft
∵ leg2 = h ft
∵ hypotenuse = 16 ft
→ Substitute them in the rule above to find h
[tex](16)^2=(7)^2+h^2[/tex]∵ 16^2 = 256 and 7^2 = 49
[tex]\therefore256=49+h^2[/tex]→ Subtract 49 from both sides
[tex]\begin{gathered} 256-49=49-49+h^2 \\ 207=h^2 \end{gathered}[/tex]→ Take square root for both sides to find h
[tex]\begin{gathered} \therefore\sqrt[]{207}=\sqrt[]{h^2} \\ 14.38749=h \end{gathered}[/tex]→ Round it to the nearest tenth
∴ h = 14.4 feet
The answer is B
Find the rational number halfway between and 1/6 and 3/4
Answers
In order to find the middle number between them we can simply add them together and divide the result by 2 as follows:
[tex]\begin{gathered} \frac{1}{6}+\frac{3}{4}=\frac{11}{12} \\ Now_{\text{ }}divide_{\text{ }}by_{\text{ }}2: \\ \frac{11}{12}\div2=\frac{11}{24} \end{gathered}[/tex]Answer:
11/24
Find the perimeter of each polygon. Assumethat lines which appear to be tangent aretangent.13)7.81118.4
Answers
Answer: We have to find the perimeter of the provided triangle, the perimeter would be the sum of sides, which would be as follows:
[tex]\begin{gathered} P=S_1+S_2+S_3 \\ P=7.8+18.4+11 \\ P=37.2 \end{gathered}[/tex]A media company wants to track the results of its new marketing plan, so the video production manager recorded the number of views for one of the company's online videos. The results of the first 5 weeks are shown in this table. Write an equation to model the relationship between the number of weeks, x, and the number of views, f(x). Enter the correct answer in the box by replacing the values of a and b.
Answers
ANSWER
[tex]f(x)=5120\cdot1.25^x[/tex]EXPLANATION
We want to write an equation that models the relationship between the number of weeks (x) and the number of views, f(x).
From the table, we see that the relationship of the two terms (number of views and number of weeks) is exponential.
The general form of an exponential function is given as:
[tex]f(x)=a\cdot b^x[/tex]where a = initial value
b = exponential factor
We have to find a and b.
We do this by replacing x and f(x) in the function with values from the table.
Let us use the first set of values:
[tex]\begin{gathered} 5120=a\cdot b^0 \\ \Rightarrow5120=a\cdot1 \\ \Rightarrow a=5120 \end{gathered}[/tex]We have found the value of a, now we can find the value of b by using another set of values from the table.
That is:
[tex]\begin{gathered} 6400=5120\cdot b^1 \\ 6400=5120\cdot b \\ \text{Divide both sides by 5120:} \\ b=\frac{6400}{5120} \\ b=1.25 \end{gathered}[/tex]Now, we have found a and b.
Therefore, the equation that models the relationship between number of views and number of weeks is:
[tex]f(x)=5120\cdot1.25^x[/tex]For scenarios of statistical studies are given below decide which study uses a sample statistic
Answers
The sample statistic is defined as any number computed from the sample data. This means that the data must be a sample and not the entire population. Looking at the options,
option D is correct
May you tell me which equation you would choose to solve for one of the variables and explain please.
Answers
This is a simultaneous system of equations, we would need both equations, to solve for the variables.
we have
2x - 3y = 6 - ---i
x +7y = 2------ii
Let's modify equation ii, x +7y = 2 means x = 2 - 7y
Anywhere we see x in equation i, lets put in 2 - 7y instead
2( 2 - 7y) - 3y = 6
4 - 14y - 3y = 6
4 - 17y = 6
-17y = 2
y = -2/17
Lets put this result in equation ii
[tex]undefined[/tex]find the volume of a right circular cone that has a height of 4.3m and a base with a circumference of 17.6. round your answer to the nearest tenth
Answers
Answer:
Explanation:
The volume of a right circular cone can be found using the below formula;
[tex]V=\pi\times r^2\times\frac{h}{3}[/tex]where V = volume of the cone
r = radius of the base
h = height of the cone ne
Which information will prove a quadrilateral is a square?O All 4 sides are congruentO All 4 sides are congruent and all 4 angles are right anglesO All 4 angles are right anglesO Both pairs of opposite sides are parallel
Answers
Answer
All 4 sides are congruent and all 4 angles are right angles
Step-by-step explanation
In a square, all the four sides measure the same (they are congruent). And the four angles are right angles, that is, they measure 90°
Option 1: Piecewise Defined Functions
A t-shirt company is looking to buy t-shirts from a distributor. They are trying to decide which distributor would be best for them when they buy about 80 shirts for their weekly order. Justify your answer with a piece wise function and discuss what you would do if you were in charge. A review on this topic can be found in the Instruction of Piecewise Defiined functions slide 15.
Company 1:
Shirts are $11 a piece for the first 100. After the first 100 each additional shirt is $7.50.
Company 2
$12 a piece for the first 50, $9.50 each additional shirt.
Answers
Answer:
-105$
Step-by-step explanation:
Which situation represents a proportional relationship?
O Renting a movie for $2 per day
O Renting a movie for $2 per day with a coupon for $0.50 off for the first day
O Renting a movie for $2 per day along with paying a $5 membership fee
O Renting a movie for $2 for the first day and $1 for each day after the first day
Answers
As they are in the right ratio, option D, "Renting a movie for $2 for the first day and $1 for each day after the first day," demonstrates a proportionate relationship.
Proportional Relationship
When two variables' ratios are equivalent, proportional relationships between them emerge. The fact that one variable is consistently equal to the constant value of the other in a proportional connection is another way to think of them. This constant is known as the "constant of proportionality."
Ratio
In mathematics, a ratio shows how frequently one number appears in another. For instance, the ratio of apples to mangos in a bowl of fruit would be nine to six if there were nine apples and six mangos. Apples make up 9:15 of the entire fruit, whereas Mangos make up 6:9 of the total fruit.
Option D, "Renting a movie for $2 for the first day and $1 for each day after the first day," illustrates a proportional relationship because the ratio is correct
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cuales son los dos numeros enteros cuyo producto es 294 y cuyo cociente es 6?
Answers
1.- You need two equations
- x*y = 294
- x/y = 6
2.- Solve for x
x = 6y
(6y)y = 294
3.- Simplifying
6y^2 = 294
-Solve for y
y^2 = 294/6
PLS HELP Rewrite the following equation in slope-intercept form.
y + 8 = –3(x + 7)
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Step by step
An equation in the slope-intercept form is written as. y=mx+b.
m is the slope of the line and b is the y-intercept.
y +8 = -3x -21
Subtract 8 from both sides to isolate y
y + 8 - 8 = -3x -21 -8
y = -3x -29
Answer:
[tex] \sf \: y = -3x - 29[/tex]
Step-by-step explanation:
Given equation,
→ y + 8 = -3(x + 7)
The slope-intercept form is,
→ y = mx + b
Let's rewrite the equation,
→ y + 8 = -3(x + 7)
→ y + 8 = -3x - 21
→ y = -3x - 21 - 8
→ [ y = -3x - 29 ]
Thus, answer is y = -3x - 29.
61 less than twice vidy's score
Answers
We are given the following word problem
"61 less than twice Vidy's score"
Let us translate the word problem into an algebraic expression
Let v represents Vidy's score
twice Vidy's score means 2 times v
61 less than means to subtract 61 from 2 times v
So, the algebraic expression becomes
[tex]2v-61[/tex]kName:ID:06/22/1973Time Remaining:00:55:49Teresa KundrataA car costs $14,000. The loan company hasasked for 1/10 of the cost of the car as adown payment what the down payment
Answers
Given:
The cost of the car is $14,000.
Then 1/10 of the cost of the car is
[tex]\frac{1}{10}\times14000=1400[/tex]Hence, the down payment is $1400.
L is the midpoint of JM. K is the midpoint of JL. JL = 15. What is thelength of KM?
Answers
We can draw the situation as:
So, if L is the midpoint of JM, JL is equal to LM and JM is equal to 2 times JL
JL = LM
JL + LM = JM
JL + JL = JM
2JL = JM
We can calculate JM using JL as:
2JL = JM
2*15 = JM
30 = JM
Then, if K is the midpoint of JL, JK is equal to KL and JL is 2 times JK
JL = 2JK
Replacing JL by 15, we get:
15 = 2JK
15/2 = JK
7.5 = JK
Finally, KM can be calculated as:
KM = JM - JK
KM = 30 - 7.5
KM = 22.5
Answer: 22.5
Are all horizontal lines parallel? Explain your reasoning.
Answers
Two lines are parallel if they do not intersect at any point.
Another way of thinking on parallel lines is: two lines are parallel if they have the same slope.
On the other hand, all horizontal lines have the same slope, which is equal to 0.
Since all horizontal lines have a slope equal to 0, this means that all horizontal lines are parallel.
Therefore, the answer is: yes. All horizontal lines are parallel.
Notice: This is only valid in 2D.
4x+10=30
solve it please
Answers
Answer:
x = 5
Step-by-step explanation:
4x + 10 = 30 ( subtract 10 from both sides )
4x = 20 ( divide both sides by 4 )
x = 5
Answer:
x = 5
Step-by-step explanation:
4x + 10 = 30
Step 1:
30 - 10 = 4x
20 = 4x
Step 2:
20/4
x=5
Step 3: Prove your answer correct
4(5) + 10 = 30
20 + 10 = 30
x = 5
The length of a rectangle is 3in longer than its width.If the perimeter of the rectangle is62in , find its length and width.
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We will have the following:
[tex]\begin{gathered} p=2(l+w) \\ \\ and \\ \\ l=w+3 \\ w=w \end{gathered}[/tex]So:
[tex]\begin{gathered} p=2(l+w)\Rightarrow p=2(w+3+w) \\ \\ \Rightarrow p=2(2w+3)\Rightarrow p=4w+6 \end{gathered}[/tex]Then we will have that:
[tex]\begin{gathered} 62=4w+6\Rightarrow4w=56 \\ \\ \Rightarrow w=14 \end{gathered}[/tex]So, the width is 14 inches and the length will then be 17 inches.
please help me it’s do tomorrow 1) Discrete or Cont?
Domain
Range
Function?
Answers
The correct options regarding each function are as follows:
1.
Continuous.Domain: {-3, 2}.Range: (-∞,∞).Function: No.2.
Continuous.Domain: (-5,5]Range: [-2,2]Function: Yes.3.
Continuous.Domain: (-∞,∞).Range: (-∞,∞).Function: Yes.4.
Continuous.Domain: (-∞,∞).Range: {3}Function: Yes.5.
Discrete.Domain: {-5, -4, 1, 2, 5}.Range: {-5,0,1,4}.Function: Yes.6.
Continuous.Domain: (-∞,4].Range: [0,∞).Function: Yes.Continuous and discreteThe graph is classified as continuous or discrete as follows:
Continuous: solid line.Discrete: set of points.Hence only function 5 is discrete, the other are all continuous.
Domain and range:In the graph of a function, the domain and the range are given as follows:
Domain: values of x -> set of input values.Range: values of y -> set of output values.Hence the domain and the range for the functions in this problem are given as follows:
1.
Domain: {-3, 2}. -> two vertical lines, one at x = -3 and the other at x = 2.Range: (-∞,∞).2.
Domain: (-5,5] -> open interval due to the open circle at x = -5.Range: [-2,2]3.
Domain: (-∞,∞).Range: (-∞,∞).4.
Domain: (-∞,∞).Range: {3} -> constant function at y = 3.5.
Domain: {-5, -4, 1, 2, 5}. -> discrete function, hence both the domain and the range contain only those exact values, not an interval.Range: {-5,0,1,4}.6.
Domain: (-∞,4].Range: [0,∞).When does a graph represent a function?A graph represents a function if it has no vertically aligned points, that is, each input is mapped to only one output.
Hence only item 1 is not a function, as the two inputs x = -3 and x = 2 are mapped to multiple outputs.
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Minnesota fell from 48 degrees to -12 degrees over a 24 hour period. what was the average temperature change per hour?
Answers
We have to calculate the average temperature change per hour.
We know that the temperature drops from 48 degrees to -12 degrees in 24 hours.
To calculate the average change, in degrees per hour, we calculate the ratio between the variation of the temperature and the interval of time.
We can expres this as:
[tex]v=\frac{\Delta T}{t}=\frac{T_f-T_i}{t}=\frac{-12-48}{24}=\frac{-60}{24}=-2.5[/tex]Answer: The average change in temperature is -2.5 degrees per hour.
Pls help & also give an easy explanation thank youuuuu
Answers
Given
A digital picture frame with a border of 3 cm. The actual length of the frame is x
Answer
a) The actual side of the picture is x-3
Area of picture
[tex]=(side)^2=(x-3)^2[/tex]b) Area of frame
[tex]x^2[/tex]c) Area of border = Area of frame - area of picture
[tex]x^2-(x-3)^2[/tex]If 25% of your math class received an A, how many students were in your math class if 9students earned an A for the semester?
Answers
Answer:36
Step-by-step explanation:
Assume the total number of students to be x
According to the question
25% of x =9
⇒x=900/25=36
Estimate. Then find the quotient. Round to the nearest thousandth.24.752:6Estimate=Quotient =
Answers
Estimate = 4.13
Quotient = 4.12533333
To the nearest thousand 4.12533
A governor has been working to decrease the unemployment rate but it has gone up by 3%. In an effort to undermine the governor, a media outlet releases a bar graph comparing the unemployment rate before and after the governor took office.Which of the following tactics did the media outlet use to create this graph?A. Comparison chartsB. SizingC. Missing informationD. Axis and scaling manipulation
Answers
From the given graph, let's determine the tactics which the media outlet used to create the graph.
From the graph, we can see that the scaling of the y-axis was manipulated.
The numbers in the y-axis starts from 8%, while a normal graph is suposed to start from 0%.
Although the graph is correct, but the scaling of the y-axis is misleading. This is because when you look at the graph, you will think there is a major difference between unnemployment before and unemployment after.
Therefore, the tactics the media outlet used to create this graph can be said to be Axis and Scaling manipulation.
Axis and scaling manipulation is a method used in producing misleading graphs to make the data look worse or better than it actually is. This method leads to incorrect conclusions,
ANSWER:
D. Axis and Scaling manipulation.