Determine the intervals where the function f(x)=x^3-6x^2 is increasing and decreasing. Also determine the local maximum and minimum values for the function. Sketch a graph of the function showing these maximum and minimum points on your graph.
Answers
For the function f(x) = x³ - 6x², we have that:
The function is increasing on these following intervals: (-∞, 0) U (4, ∞).The function is decreasing on the interval (0,4).The local maximum value for the function is at point (0,0).The local minimum value for the function is at point (-4,32).When a function is increasing and when it is decreasing, looking at it's graph?Considering the graph of the function, it is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when x increases, y increases.Then, it is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when x increases, y decreases.In the context of this function, we have that it is increasing to the left of x = 0 and to the right of x = 4, hence the interval is given by:
(-∞, 0) U (4, ∞).
On the remaining interval, that is, (0,4), the function is decreasing.
The critical points are given as follows:
At x = 0, the function changes from increasing to decreasing, hence there is a local maximum at point (0,0).At x = 4, the function changes from decreasing to increasing, hence there is a local minimum at point (4,32).More can be learned about functions at https://brainly.com/question/24808124
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Related Questions
on a certain hot summer day 629 people use the public swimming pool The daily prices are $1.25 for children and $2.50 for adults The receptionist for admission totaled $1,200 how many children and how many adults swim at the public pool that day
Answers
Let the number of children be "c" and the number of adults be "a".
There are a total of 629 adults and children.
Thus, we can write an equation:
[tex]c+a=629[/tex]Price of each children admit is 1.25 and each child admit is 2.50 for a total of $1200.
Thus, we can write an equation to represent this information as:
[tex]1.25c+2.50a=1200[/tex]We can solve the system of 2 equations we got and find out the values of "a" and "c".
Solving the first equation for c:
[tex]\begin{gathered} c+a=629 \\ c=629-a \end{gathered}[/tex]We substitute it into second equation and figure out a:
[tex]\begin{gathered} 1.25c+2.50a=1200 \\ 1.25(629-a)+2.50a=1200 \\ 786.25-1.25a+2.50a=1200 \\ 1.25a=1200-768.25 \\ 1.25a=413.75 \\ a=\frac{413.75}{1.25} \\ a=331 \end{gathered}[/tex]Now, we simply find out c:
[tex]\begin{gathered} c=629-a \\ c=629-331 \\ c=298 \end{gathered}[/tex]Answer:
Children = 298Adults = 331Health and Fitness Masha is training for a marathon. She is doing
tempo runs to increase her speed. In tempo runs, a runner varies
their pace during the run. Masha jogs 1 mile, then runs at a fast pace
for 11 miles. She finishes by walking 2 miles to cool down. Write a
numerical expression to model the number of miles Masha runs,
walks, or jogs.
Answers
The numerical expression to model the number of miles Masha runs, walks, or jogs is 14.
What is meant by numerical expression?Mathematical operations like addition, subtraction, multiplication, and division can be used to mix integers and numbers to create a numerical expression.
The rule should state something along the lines of: "When simplifying, parentheses must be simplified first, followed by all exponents, all multiplication, and ultimately, all addition."
Based on the given conditions, formulate: 2 + 1 + 11
Calculate the sum or difference: 3 + 11
Calculate the sum or difference: 14
Therefore, the numerical expression to model the number of miles Masha runs, walks, or jogs is 14.
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) Anita prepared 28 kilograms of
dough after working 4 hours. How
much dough did Anita prepare if she
worked for 5 hours? Solve using unit
rates.
Answers
Answer: should be around 35 kilos dont got an explaination just used meh brain
Step-by-step explanation:
Greg graduated in the bottom 9% of his class. If the mean was 585 and the standard deviation was 134, and the distribution was normal, what was Greg's raw score?
Answers
Greg's raw score in the test is 405
How to determine the raw score of the test?The given parameters are
Mean = 585Standard deviation = 134Proportion, p = bottom 9%The above implies that
z = P(p < 0.09)
From z tables of probabilities, we have
z = -1.34
The z-score of the data value is calculated using the following formula
z = (raw score - mean value)/standard deviation
Substitute the given parameters in the above equation
-1.34 = (raw score - 585)/134
This gives
-180 = raw score - 585
So, we have
raw score = 585 - 180
Evaluate
raw score = 405
Hence, the raw score is 405
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
its 5
Step-by-step explanation:
f
dddd
A firecracker sends a small pebble vertically upward from a height of 35 feet above a
pool of water. The starting speed of the pebble is 85 feet per second. Its distance in
feet, d, above the water is given by the equation:
d=35+85t-16t2, where t is the time in seconds after the launch.
Drag statements to the table to show what each coordinate labeled on the graph
represents in this problem situation.
Answers
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included.It also goes by the name quadratic equations.The quadratic equation has the general form ax2 + bx + c = 0.where a, b, and c are numerical coefficients and x is an unknown variable.
Solve the quadratic equation?
d=35+85t-16t²
35+85-16t²-d
35+85t-16t²-d=0
35-d+85t-d=0
16t²-85t-35+d=0
t=85±√[tex]\sqrt{x}[/tex]-(85)²-4×16(-35+d)/2×16
t=85±√(-85)²-4×16(-35+d)/32
-(85)²-4×16(-35+d)
=7225-64(-35+d)
=7225-64(-35+d)
7225+2240-64d
=9465-64d
=-9401
t=85+√9465-64d/32
t=85+97
t = 182
t=85-√9465-64d/32
t=85-97
t = -12
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Graph the solution set l 2x + 4l + 2 <= 8
Answers
ANSWER :
EXPLANATION :
From the problem, we have :
[tex]\begin{gathered} \lvert{2x+4}\rvert+2\le8 \\ \text{ which can be simplified as :} \\ \lvert{2x+4}\rvert\le6 \end{gathered}[/tex]Note that in solving absolute values, the terms inside the absolute value sign can have inverse signs.
Case 1 : Positive
[tex]\begin{gathered} 2x+4\le6 \\ 2x\le2 \\ x\le\frac{2}{2} \\ \\ x\le1 \end{gathered}[/tex]Case 2 : Negative, the symbol will change since we are multiplying a negative number
[tex]\begin{gathered} -(2x+4)\ge6 \\ -2x-4\ge6 \\ -2x\ge10 \\ x\ge\frac{10}{-2} \\ \\ x\ge-5 \end{gathered}[/tex]So the solution is :
[tex]\begin{gathered} x\le1\quad and\quad x\ge-5 \\ \text{ when written together :} \\ -5\le x\le1 \end{gathered}[/tex]or in interval notation :
[-5, 1]
The graph of it will be :
What is the greatest common factor of this expression?
12m + 18m2
A.
2m
B.
6m
C.
6
D.
2
Answers
Answer:
I think the answer is B because when you check the factors, you get 6 then you add your unit
Lena prepared 4.3 kilograms of dough after working 2 hours. How many hours did Lena work if she prepared 10.75 kilograms of dough? Assume the relationship is directly proportional.
Answers
Lena worked for 5 hours if she prepared 10.75 kilograms of dough assuming 4.3 directly proportional 2.
What is proportional?A comparison of two numbers mathematically is called a proportion. Two sets of given numbers are said to be directly proportional to one another if they increase or decrease in the same ratio, according to the law of proportion. The symbols "::" or "=" are used to indicate proportions.
We have given that 4.3 ∝ 2
where 4.3 kilograms is completed in 2 hours
If 4.3 ∝ 2, the constant k is
4.3 = k2
k = 4.3/2
k = 2.15
We have asked to find how many hours did Lena work if she prepared 10.75 kilograms of dough.
Let hours she took be x, Thus
10.75 ∝ x
We already have the contestant, so this gives us
10.75 = kx
10.75 = 2.15x
x = 10.75/2.15
x = 5 hours
Thus, Lena worked for 5 hours if she prepared 10.75 kilograms of dough assuming 4.3 ∝ 2.
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Figure W was ___ to create W’. Figure W’ was dia lates by a scale factor of ___ fromThe origin to create w”
Answers
Transformations
One of the rigid transformations is reflection. When a figure is reflected across some line, it maps to the very same shape but inverted as if the line was a mirror.
Right between figures W and W' the y-axis separates two identical images as if the y-axis was a mirror, thus:
Figure W was reflected over the y-axis to create figure W'
A Dilation from the origin maps an object to another such that its vertices are all multiplied by a common factor (scale factor).
For example, the upper-right vertex of W' is located at (2-2). The upper-right vertex of W'' is at (4,-4). The scale factor is 2.
The bottom-left vertex of W' is at (4,-4) and the bottom-left vertex of W'' is at (8,-8). We find the same scale factor of 2. If we tested all of the vertices, we'll obtain the same scale factor of 2, thus:
Figure W' was dilated by a scale factor of 2 from the origin to create figure W''
after two years $900 deposited in a savings account with simple interest had earned $18 in interest. what was the interest rate
Answers
The expression for Simple Interest is :
[tex]\text{Simple Interest = }\frac{\text{ Principal AMount}\times Time\text{ }\times Rate\text{ of Interest}}{100}[/tex]Given that Principal amount = $900
Time period = 2 years
Simple Interest = $18
Substitute the value and solve for RAte of interest
[tex]\begin{gathered} \text{Simple Interest = }\frac{\text{ Principal AMount}\times Time\text{ }\times Rate\text{ of Interest}}{100} \\ 18=\frac{900\times2\times R}{100} \\ R=\frac{18\times100}{900\times2} \\ R=1 \\ \text{ Rate of interest = 1 percent} \end{gathered}[/tex]Answer : Interest Rate = 1%
4x3 − 6x2 − 28x Is this a special product?
Answers
ANSWER:
It is not a special product
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]4x^3-6x^2-28x[/tex]Among the special products we have:
The sum and difference of same terms
The square of a binomial
The cube of a binomial
Let's factor the expression to determine if it satisfies any of the above:
[tex]\begin{gathered} 2x\cdot\left(2x^2-3x-14\right? \\ 2x^{2}-3x-14 \\ -3x=4x-7x \\ 2x^2+4x-7x-14 \\ 2x\left(x+2\right?-7\left(x+2\right? \\ 2x\cdot\left(x+2\right)\cdot\left(2x-7\right) \end{gathered}[/tex]Therefore, we can determine that it does not belong to the group of special products.
Find the lateral area of a right cylinder with a diameter of 6.4 yards and a height of 16.2 yards. Round to the nearest tenth.
Answers
You can use the following formula in order to calculate the Lateral area of the right cylinder given in the exercise:
[tex]LA=2\pi rh[/tex]Where "LA" is the lateral area of the cylinder, "r" is the radius and "h" is the height.
In this case you know that its diameter is:
[tex]d=6.4yd[/tex]Since the diameter of a circle is twice the radius:
[tex]2r=6.4yd[/tex]Knowing that the height of the cylinder is:
[tex]h=16.2yd[/tex]You can substitute values into the formula and then evaluate, in order to find the lateral area:
[tex]\begin{gathered} LA=\pi(6.4yd)(16.2yd) \\ LA\approx325.7yd^2 \end{gathered}[/tex]Then, the answer is:
[tex]LA\approx325.7yd^2[/tex]It takes you 6 hours to row 12 miles, how long will it take you to row 32 miles.
Answers
Answer:16
Step-by-step explanation:
1 hour=2miles
Construct an appropriate triangle to find the missing values
Answers
This can be solved using trigonometry.
What is trigonometry?
Trigonometry is a field of mathematics that examines correlations between triangle side lengths and angles (from the Ancient Greek words "trigonon" and "metron"). The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. While Indian mathematicians produced the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine, the Greeks concentrated on chord computation. Trigonometry has been used historically in fields including geodesy, surveying, celestial mechanics, and navigation. Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric similarities are frequently employed to rewrite trigonometrical statements.
Using trigonometric relations,
cos 30° = cos π/6 rad = √3/2
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A rabbit runs 35 miles per hour. A fox can run 21 miles in half an hour. Which animal is faster, and by how much?
Answers
Answer:
The fox can run faster by a factor of 7 miles per hour
Step-by-step explanation:
If the fox runs 21 miles in half of an hour, that means that by multiplying the fraction 21miles/0.5hours by 2/2 you can find that the fox runs 42 miles per hour, 7 miles per hour faster than the rabbit.
Answer:
The Fox, by 7 Miles per hour
Step-by-step explanation:
The rabbit runs 35 Miles per hour
The Fox runs 21 in half an hour
1 hour - 30 minutes = 30 minutes meaning we have to double the foxes miles
21 x 2 = 42
42>32
To find out by how much do 42-32 and we get 7 Miles per hour.
1:
Jerrod brought 48 cupcakes to school. At school, he gave 3 cupcakes to
each student in his class. He has 6 cupcakes remaining. How many
students are in Jerrod's class? Variable,equation and answer
Answers
42/3 = 14
14 students are in his class
Answer:
There were eight studentsin jerrods class
Patricia O'Malley purchased fifty $1,000 bonds having a quoted price of 99.75. She paid a 6.5% brokerage fee of the selling price). What was the total cost of the bond sale(to the nearest whole cent)?$53,116.88$54,024.65$55,346.77$58,021.99None of these choices are correct.
Answers
It is given that 50 bonds were bought with a cost of $1000 each.
6.5% brokerage was paid.
The total price of the share without brokerage is:
[tex]C=50\times1000\times\frac{99.75}{100}=49875[/tex]The brokerage is given by:
[tex]B=49875\times\frac{6.5}{100}=3241.88[/tex]Hence the total cost of the sale is given by:
[tex]\begin{gathered} T=C+B \\ T=49875+3241.88 \\ T=53116.88 \end{gathered}[/tex]Hence the total cost of sale is $53116.88.
Lety = tan(3x + 3) . Find the differential dy when x = 5 and dx = 0.4
Answers
Applying the derivative of the trigonometric functions, the derivative of tan x is sec²x.
Hence, the derivative of tan (3x + 3 ) is sec² (3x + 3) times the derivative of 3x - 3 which is 3.
[tex]\begin{gathered} y=tan(3x+3) \\ dy=3sec^2(3x+3)dx \end{gathered}[/tex]To find the differential dy when x = 5 and dx = 0.4, simply replace the x and dx in the dy function with their given values.
[tex]dy=\lbrace3sec^2[(3(5)+3)]\rbrace(0.4)[/tex]Then, simplify.
[tex]dy=[3sec^2(18)](0.4)[/tex][tex]dy=3.3167(0.4)[/tex][tex]dy=1.32668\approx1.33[/tex]Hence, at x = 5 and dx = 0.4, the differential dy is approximately equal to 1.33.
For x = 5 and dx = 0.8, we do the same process above but this time, multiply the derivative by 0.8.
[tex]dy=[3sec^2(18)](0.8)[/tex][tex]dy=3.3167(0.8)[/tex][tex]dy=2.6534\approx2.65[/tex]Hence, at x = 5 and dx = 0.8, the differential dy is approximately equal to 2.65.
Raymond places four colored blocks in a bag. The colors are red, blue, yellow and green. Without looking, he reaches into the bag andpulls one block out.What is the probability that the block he pulls out will be yellow?A. 1/4. B.1/3. C.3/1. D.4/1
Answers
Given:
Total number of colored blocks in the bag = 4
Given that Raymond picks one block out without looking(randomly), let's find the probability it is a yellow block.
Probablity can be said to be the likelihood of the occurence of an event.
Given:
Number of yellow blocks = 1
To find the probability that the blocks he pulls out will be a yellow block, apply the formula below:
[tex]P(\text{yellow)}=\frac{\text{Number of yellow blocks}}{Total\text{ number of blocks}}[/tex]Thus, we have:
[tex]P(\text{yellow)}=\frac{1}{4}[/tex]Therefore, the probability thatvthe block he pulls out will be yellow is ¼
ANSWER:
[tex]A\text{. }\frac{1}{4}[/tex]How do i find the x intercept using the slope intercept form, graphing the y intercept, then using the slope to step to the x intercept. How do i know to go left or right for run?
Answers
How do i find the x intercept using the slope intercept form, graphing the y intercept, then using the slope to step to the x intercept.
slope intercept form is: y = mx + b where m = slope and b = y-intercept
Once you have your slope intercept equation, solve for m.
How do i know to go left or right for run?
slope = rise/run
if the number is negative, you will go left.
Please comment if you have further questions.
Helen borrowed $2,500 for home repairs. She paid back 24 payments of$115 each. How much did she pay in interest on the loan?a. $108.96b. $4.79c. $2,760d. $260
Answers
To solve this problem, we will compute the total amount Helen paid back and we will subtract $2,500 from it.
To determine the total amount she paid back we multiply the number of payments by the amount of each payment:
[tex]T=24\times115\text{dollars}=2760\text{ dollars.}[/tex]Subtracting $2,500 from the above result we get:
[tex]2760-2500=260\text{dollars.}[/tex]Answer: Option d.
In general, the value of a car decreases with age. Provide an estimate that could show the correlation between the age and value of a car. Provide numerical response rounded to the nearest tenths
Answers
Answer:
in general, the value of a car decreases with age what would ne the correlation between the age and values of all cars -1, 0.7, 1, -0.7
Greg Losier put $26,500 down on a $92,500 home.
How much did he have to mortgage?
Answers
Using mathematical operations we conclude that Greg has to mortgage the amount of $66,000.
What are mathematical operations?An operation, also known as an "operand" or "argument," is a function in mathematics that converts zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the operations that are most frequently studied. The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out by the arithmetic operators.So, the mortgage will be:
$92,500 - $26,500Solve this expression as follows:
$92,500 - $26,500$66,000Therefore, using mathematical operations we conclude that Greg has to mortgage the amount of $66,000.
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5÷4=
what is the quotient
Answers
help pleaseeee. I need it quick
Answers
x: -3 -2 -1 0 1 2 3 4
y: 6 0 -4 -6 -6 -4 0 6
You plug in x into the equation and you get the value of y. Then graph the points: (-3, 6) (-2, 0) (-1, -4) (0, -6) (1, -6) (2, -4) (3, 0) (4, 6).
Hope it helps! :D
Studying for a test, need some help solving this question
Answers
Solution
Part A
To find C
[tex]_{\angle\text{ C+}\angle A+\angle B=180^0(Sum\text{ of angles in a triangle\rparen}}[/tex][tex]\begin{gathered} \angle C+33.84+19.32=180 \\ \angle C+53.16=180 \\ \angle C=180-53.16 \\ \angle C=126.84^0 \\ \end{gathered}[/tex]Part B
To find a
Using sine rule
[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex][tex]\begin{gathered} \frac{sin33.84}{a}=\frac{sin126.84}{13.95} \\ cross\text{ multiply} \\ asin126.84=13.95sin33.84 \\ divide\text{ both side by sin126.84} \\ \\ a=9.70672 \end{gathered}[/tex]Part C
To find b
Using sine rule
[tex]\begin{gathered} \frac{sin33.84}{9.70672}=\frac{sin19.32}{b} \\ \\ \\ b=5.76683 \end{gathered}[/tex]<
Which of the following statements are true?
Choose all answers that apply:
The equation represents a proportional relationship.
The unit rate of change of y with respect to a is
7
2
The slope of the ne is
2
A change of 7 units in a results in a change of 2 units in y.
A change of 6 units in a results in a change of 21 units in y.
Answers
Based on the function given of y = 2.5x, the true statements are:
The equation represents a proportional relationship.The slope of the line is 2.5.A change of 2 units in x results in a change of 5 units in y.What is proportional relationship?
When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the name of this constant.The equation y = 2.5x is a proportional relationship because y increases by a certain amount when x increases. That amount is shown by the slope of the line which is 2.5.
For instance, if there is a change of 2 in x, the change in y would be:
= 2.5 × x
= 2.5 x 2
= 5
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PointProduction chocolate barsProduction cans of colaA 0 100B 10 90C 20 70D 30 40E 40 0The above table shows production points on Sweet-Tooth Land's production possibilities frontier. Which of the following statements is TRUE?A.Producing 0 chocolate bars and 100 cans of cola is both attainable and efficient.B.Producing 20 chocolate bars and 80 cans of cola is attainable but inefficientC.Producing 30 chocolate bars and 38 cans of cola is both attainable, with an inefficientD.Producing 40 chocolate bars and 0 cans of cola is both attainable and inefficient
Answers
First look and see if each of the values are true (attainable) before looking at efficiency
A.Producing 0 chocolate bars and 100 cans of cola is both attainable and efficient.
This is attainable
B.Producing 20 chocolate bars and 80 cans of cola is attainable but inefficient
This is not attainable
C.Producing 30 chocolate bars and 38 cans of cola is both attainable, with an inefficient
This is attainable
D.Producing 40 chocolate bars and 0 cans of cola is both attainable and inefficient
This is attainable
Now lets looks at efficiency
efficient when it is producing at the lowest point on the graph
Inefficient is below the graph
D should be efficient
A should be efficient
I am not sure why C is wrong
help mee pleasee!!
thank you <3
Answers
The equation of the line passing through points (-2, 1) and (1, -4) is f(x) = (-5/4)x - 3/2
In this question we have been given two points.
We need to find an equation of the line passing through points (-2, 1) and (1, -4)
Using the two-point form of equation of line.
(y - y1)/(y2 - y1) = (x - x1) / (x2 - x1)
(y - 1) / (-4 - 1) = (x - (-2)) / (1 - (-2))
(y - 1) / (-5) = (x + 2) / (1 + 3)
y - 1 / (-5) = (x + 2) / 4
y - 1 = (-5/4)(x + 2)
y = -5x/4 - 10/4 + 1
y = (-5/4)x - 3/2
Let y = f(x)
so, equation of line is f(x) = (-5/4)x - 3/2
Therefore, the equation of line passing through points (-2, 1) and (1, -4) is f(x) = (-5/4)x - 3/2
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