Find f'(x) and find the values(s) of x where f'(x) = 0. f(x)= (2x - 27)(x² +24) f(x) 6x2 = 54x + 48 x=1 (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
Answers
The derivative of f(x) is f'(x) = 6x³ - 142x² - 27x + 648, and the value of x where f'(x) = 0 is x = -4/3, 0, or 9.
To find the derivative of f(x), we can use the product rule, which states that the derivative of a product of two functions u(x) and v(x) is u'(x)v(x) + u(x)v'(x). Applying the product rule, we get:
f'(x) = (2x - 27)(2x² + 48) + (x² + 24)(4x - 27)
Simplifying, we get:
f'(x) = 6x³ - 142x² - 27x + 648
To find the values of x where f'(x) = 0, we can set the derivative equal to zero and solve for x:
6x³ - 142x² - 27x + 648 = 0
We can factor this expression by first factoring out a common factor of 3:
3(2x - 27)(x² - 8x - 24) = 0
Using the zero product property, we get:
2x - 27 = 0 or x² - 8x - 24 = 0
Solving for x, we get:
x = 27/2 or x = (-(-8) ± √((-8)² - 4(1)(-24))) / 2(1)
x = 27/2 or x = (-8 ± 10) / 2
x = 27/2 or x = -4/3 or x = 9
Therefore, the values of x where f'(x) = 0 are x = -4/3, 0, or 9.
For more questions like Derivative click the link below:
https://brainly.com/question/25324584
#SPJ11
Related Questions
What is the slope of the line that passes through the points (-4, 4)(−4,4) and (-6, 6) ?(−6,6)? Write your answer in simplest form.
Answers
if u =( 20 +i, i, 3-1) v = (1+i, 2, 41) Find the imaginary part of u.v ? (Round off the answer upto 2 decimal places)
Answers
The given vectors are: u = (20 + i, i, 2)v = (1 + i, 2, 41)The dot product of u and v is:u.v = (20 + i)(1 + i) + (i)(2) + (2)(41 - 1)= 20 + 20i + i + i² + 2i + 80= 101 + 22i
To find the imaginary part of u.v, we can simply extract the coefficient of i, which is 22. Hence, the imaginary part of u.v is 22. Therefore, the answer is rounded off to 22.00.
A quantity or phenomenon with two distinct properties is known as a vector. magnitude and course. The mathematical or geometrical representation of such a quantity is also referred to by this term. In nature, velocity, momentum, force, electromagnetic fields, and weight are all examples of vectors.
A movement from one point to another is described by a vector. Direction and magnitude (size) are both properties of a vector quantity. A scalar amount has just greatness. An arrow-labeled line segment can be used to represent a vector. The following describes a vector between two points A and B: A B → , or .
Learn more about vectors:
https://brainly.com/question/24256726
#SPJ11
Equation of a parabola y = (x + 5)(x - 7)
What are the coordinates of the x-axis intercepts?
A. (5, 0) and (7, 0)
B. (-5, 0) and (7, 0)
C. (5, 0) and (-7, 0)
D. (-5, 0) and (-7, 0)
Answers
Answer:
B. (-5, 0) and (7, 0)
Step-by-step explanation:
Here are the steps to find the x-axis intercepts of the parabola with the equation y = (x + 5)(x - 7):
Set y equal to zero: y = 0.
Substitute y with 0 in the equation: 0 = (x + 5)(x - 7).
Set each factor equal to zero: (x + 5) = 0 and (x - 7) = 0.
Solve the first equation: x + 5 = 0. Subtract 5 from both sides: x = -5.
Solve the second equation: x - 7 = 0. Add 7 to both sides: x = 7.
Therefore, the x-axis intercepts are x = -5 and x = 7, which correspond to the points (-5, 0) and (7, 0) on the coordinate plane.
Find the profit margin on ladders that were purchased for $65.00 each, and now sell
for $105.99 each. Round to nearest hundredths. (Hint: This is a two-step problem.)
Answers
105.99 - 65.00 / 105.99
profit = 40.99
40.99 / 105.99 = 0.38673
profit margin = 38.673%
HELLLLPPPPP PLZZZZZZZ ITS TIMED An 8” candle burns at a rate of one-third of an inch per hour and an 11” candle burns at 1” per hour. How long will it be until they are the same height?
Answers
HELP ASAP PLSSSS HELP!!
Answers
Answer:
c. vertical and horizontal
Step-by-step explanation:
Answer:
Horizontal for bottom and top are simmatrical and its not faced verticle because veticle is Upwards becuase this is sideways
its horizotal!
Rewrite 12-(5+6m) without parenthesizes
Answers
7 + 6m is solution of parenthesizes equation .
What is parentheses in maths ?
These are also referred to as round brackets and are represented by the following symbols: ( ). The most typical brackets are those mentioned above.
They are utilized to combine several numbers and formulae. In an equation, terms are grouped together or the order of operations is stated using parentheses or "round brackets."
Rewrite 12-(5+6m)
= 12 - 5 + 6m
= 7 + 6m
Learn more about parentheses
brainly.com/question/28146414
#SPJ1
The continuous random variable V has a probability density function given by: 6 f(v) = for 3 ≤ ≤7,0 otherwise. 24 What is the expected value of V? Number
Answers
The expected value of the continuous random variable V is 5. The expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.
To calculate the expected value of a continuous random variable V with a given probability density function (PDF), we integrate the product of V and the PDF over its entire range.
The PDF of V is defined as:
f(v) = 6/24 = 0.25 for 3 ≤ v ≤ 7, and 0 otherwise.
The expected value of V, denoted as E(V), can be calculated as:
E(V) = ∫v * f(v) dv
To find the expected value, we integrate v * f(v) over the range where the PDF is non-zero, which is 3 to 7.
E(V) = ∫v * (0.25) dv, with the limits of integration from 3 to 7.
E(V) = (0.25) * ∫v dv, with the limits of integration from 3 to 7.
E(V) = (0.25) * [(v^2) / 2] evaluated from 3 to 7.
E(V) = (0.25) * [(7^2 / 2) - (3^2 / 2)].
E(V) = (0.25) * [(49 / 2) - (9 / 2)].
E(V) = (0.25) * (40 / 2).
E(V) = (0.25) * 20.
E(V) = 5.
Therefore, the expected value of the continuous random variable V is 5.
The expected value represents the average value or mean of the random variable V. It is the weighted average of all possible values of V, with each value weighted by its corresponding probability. In this case, the expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.
Learn more about random variable here
https://brainly.com/question/17217746
#SPJ11
Of the total school population of 800 students, 200 live outside the student limits. What percentage of students live outside the city limits?
Answers
Answer:
1/4 population
Step-by-step explanation:
Answer: 25%
Step-by-step explanation: 200/800=0.25
Move the decimal places of 0.25 two spaces to the right so is 25.
when cutting carrots into small pieces, you are deciding whether to use a knife and cutting board or a food processor. Each carrot chopped by hand takes 45 seconds. each carrot chopped in a food processor takes 12 seconds. it takes 25 seconds to clean off the knife and board. It takes 6 minutes to clean the food processor. What is the minimum number of carrots to cut up for which it will be faster to use a food processor than the knife and cutting board? (factor in both the cutting time and the cleaning time, Your final answer should be an integer
Answers
The minimum number of carrots to cut up for which it will be faster to use a food processor than the knife and cutting board is 11.
In order to find the minimum number of carrots to cut up for which it will be faster to use a food processor than the knife and cutting board, we need to calculate the time taken by each method and then compare it. Let's say the minimum number of carrots is x.
Here's how we can calculate the time taken to chop x carrots:
Time taken using knife and cutting board = 45x + 25 (25 is added for the time taken to clean the knife and board)
Time taken using food processor = 12x + 360 (360 is added for the time taken to clean the food processor)
Now, we need to find the value of x for which the time taken using the food processor is less than the time taken using the knife and cutting board.
So,12x + 360 < 45x + 2512x - 45x < 25 - 360-33x < -335x > 10.15
Therefore, the minimum number of carrots to cut up for which it will be faster to use a food processor than the knife and cutting board is 11.
Thus, the minimum number of carrots to cut up for which it will be faster to use a food processor than the knife and cutting board is 11.
To know more about time taken visit:
brainly.com/question/24258354
#SPJ11
what is the number of distinct proper subsets of a set with n elements is
Answers
A number of Appropriate Subsets of the Set: There are 2n - 1 appropriate subsets of the set for every n element in the set.
What are sets?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets.
A set is a mathematical model for a collection of various things.
A set with a single element is a singleton, while a set with no elements is an empty set.
A set can either be infinite or have a finite number of elements.
If all of the elements in two sets are identical, then the sets are equal.
The number of subsets of a set is 2n if the set has 'n' items.
A number of Appropriate Subsets of the Set: If a set has 'n' items, then 2n - 1 is the number of appropriate subsets of the set.
Therefore, a number of Appropriate Subsets of the Set: There are 2n - 1 appropriate subset of the set for every n element in the set.
Know more about sets here:
https://brainly.com/question/13458417
#SPJ4
Correct question:
The number of distinct proper subsets of a set with n elements is ____.
Please Please prioritize the last part
A mistake was made in mixing the lemonade for the concession stand, but you can fix it!
The lemonade comes in 100% juice concentrate, but you only serve it as 70% solution. Unfortunately, one batch got overwatered, so you have 4 quarts of 50% solution.
How much 100% concentrate do you need to add in order to get the 70% solution?
How much of the 70% solution will you have?
Set up a system of equations and then show each step to solve it.
Answers
The total is 6 and 2/3 quarts of 70%
How to solveGiven the data:
0.5(4)+1x=(x+4)0.7
2+x=0.7x+2.8
minus 0.7x both sides
2+0.3x=2.8
minus 2 from both sides
0.3x=0.8
divide both sides by 0.3
x=8/3
adds 8/3 quarts or 2 and 2/3 quarts
total is 4+ 2 and 2/3 or 6 and 2/3
adds 2 and 2/3 quarts of 100%
total is 6 and 2/3 quarts of 70%
Read more about percentage here:
https://brainly.com/question/24877689
#SPJ1
Simplify.
6a2−4b2+4abc−9b2−4a2+8abc
Answers
Answer:
\(\huge\boxed{\sf 2a^2-13b^2+12abc}\)
Step-by-step explanation:
Given expression:\(=6a^2-4b^2+4abc-9b^2-4a^2+8abc\\\\Combine \ like \ terms\\\\=6a^2-4a^2-4b^2-9b^2+8abc+4abc\\\\=2a^2-13b^2+12abc\\\\\rule[225]{225}{2}\)
Answer:
Hello! The answer is: \(2a^2 - 13b^2 + 12abc\)
Step-by-step explanation:
\(6a^2 - 4b^2 + 4abc - 9b^2 - 4a^2 + 8abc\)
Rearrange to combine like terms:
\(6a^2 - 4a^2 - 4b^2 - 9b^2 + 4abc + 8abc\)
Combine like terms:
\(2a^2 - 13b^2 + 12abc\)
What is 166.6789 to the nearest hundredth
Answers
Answer:
166.68
Step by Step:
166.678
The bolded number is greater than 5 meaning you have to round up.
so 166.678 is rounded to 166.68.
Hope this helped.
A motorist drives north for 35.0 minutes at 70.5 km/h and then stops for 15.0 minutes. He then continues north, traveling 130 km in. 1.90. h. (a) What is his total displacement? x Your response is within 10 ss of the correct value. This may be due to roundoff emor, of you could have a mistake in yoar calcufation. Carry out all intermediate result to atleast four-digit accuracy to minimize roundoff error. km (b) What is his average velocity? Your response is within.10\% of the conrect vatue. This may be due to roundoff erro, or you could have a misrake in your calcutation. Carry out alf intermediate results to at least four-digit acouracy to minimize roundoff erroc. km/h
Answers
The total displacement is approximately 171.049 km. The average velocity is approximately 68.940 km/h.
- Time of the first leg: 35.0 minutes
- Speed of the first leg: 70.5 km/h
- Time of the second leg: 1.90 hours
- Distance of the second leg: 130 km
(a) Total DisplacementTo find the total displacement, we need to calculate the distance traveled in each leg and sum them up. Since the motorist is traveling north on both legs, we can consider north as the positive direction.
Distance of the first leg = Speed * Time = 70.5 km/h * (35.0 minutes / 60 minutes)
Distance of the second leg = 130 km
Total Displacement = Distance of the first leg + Distance of the second leg
35.0 minutes = 35.0 minutes / 60 minutes = 0.5833 hours
Distance of the first leg = 70.5 km/h * 0.5833 hours
Total Displacement = (70.5 km/h * 0.5833 hours) + 130 km
Distance of the first leg = 41.04865 km (rounded to 5 decimal places)
Total Displacement = 41.04865 km + 130 km
Total Displacement = 171.04865 km
Therefore, the total displacement is approximately 171.049 km.
(b) Average VelocityTo find the average velocity, we need to divide the total displacement by the total time taken.
Total Time = Time of the first leg + Time of the second leg
Time of the first leg = 35.0 minutes / 60 minutes = 0.5833 hours
Time of the second leg = 1.90 hours
Total Time = 0.5833 hours + 1.90 hours
Average Velocity = Total Displacement / Total Time
Average Velocity = 171.04865 km / (0.5833 hours + 1.90 hours)
Average Velocity = 171.04865 km / 2.4833 hours
Average Velocity ≈ 68.940 km/h (rounded to three decimal places)
Therefore, the average velocity is approximately 68.940 km/h.
Learn more about Average Velocity here:
https://brainly.com/question/28512079
#SPJ11
a ton of recycled paper will save 17 trees. if one bag weighs 2 oz, how many bags are needed to save 68 trees?
Answers
Answer:8
Step-by-step explanation:divide 136 with 17 to see how many tons needed
I need to find the area please help
Answers
Answer:
It is trapizium so the area can be calculated as
\( \frac{1}{2} (6ft + 8ft) \times 5ft \\ = {35ft}^{2} \)
u can solve area of trapizium by
1/2(a+b)h
and when you solve it u get the answer 35ft^2
Of the following sets, which represents a function?
Situation A = {student's name, all the colors that the student likes}
Situation B = {student's name, names of all of the student's teachers}
Only A
Only B
Both A and B
Neither A nor B
Answers
Answer:
the second one only b or it could be neither of a nor b
Answer:
D
Step-by-step explanation:
It is neither A nor B because:
You would get so many different responses for Situation A and the same goes for Situation B!
perry and chelsea each improved their yards by planting daylilies and ivy they bought their supplies from the same store perry spent $132 on 12 daylilies and 6 post of ivy . chelsea spent $159 on 3 daylilies and 12 pots of ivy . what is the cost of one daylily and the cost of one pot of ivy ?
Answers
The cost of one lily is 5 and cost of one ivy is 12.
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. Every mathematical equation begins with L.H.S = R.H.S.
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:
Perry store perry spent $132 on 12 daylilies and 6 post of ivy .
chelsea spent $159 on 3 daylilies and 12 pots of ivy.
let the number of daylilies sold be x.
let the number of ivy sold be y.
So, the equation is
12x+ 6y = 132
2x + y = 22......(1)
3x + 12y = 159
x + 4y = 53....(2)
Now solving (1) and (2)
x= 5
y= 12
hence, cost of one lily is 5 and cost of one ivy is 12.
Learn more about equation here:
https://brainly.com/question/10413253
#SPJ1
Anyone understand this ?? Please help, I literally dont understand math at all.
Answers
Answer:
A
Step-by-step explanation:
The entire frame is 42 x 23 in, but for each dimension there are two lengths of x inches that are included in the entire dimension but not that of the actual picture. Thus, the correct equation is (42 - 2x)(23 - 2x) = 700 which is choice A.
Find the amount of periodic payment necessary for the deposit to a sinking fund. (Round your answer to the nearest cent.)
$ X
Amount Needed Frequency Rate Time
A n r t
————————————————————————
$85,000 quaterly 1,4 % 5 yr
Answers
The amount of the periodic payment necessary for the deposit to a sinking fund is approximately $18,065.19.
To find the amount of the periodic payment necessary for the deposit to a sinking fund, we can use the formula for the future value of an ordinary annuity. The formula is:
X = A * (1 + r)^nt / [(1 + r)^nt - 1]
Where:
X is the amount needed
A is the periodic payment
r is the interest rate per period
n is the number of compounding periods per year
t is the total number of years
Given the information:
Amount Needed (X) = $85,000
Frequency: Quarterly
Rate (r) = 1.4% (or 0.014 as a decimal)
Time (t) = 5 years
Since the frequency is quarterly, the number of compounding periods per year (n) is 4.
Substituting the values into the formula:
$85,000 = A * (1 + 0.014)^(4*5) / [(1 + 0.014)^(4*5) - 1]
Simplifying the equation:
$85,000 = A * (1.014)^20 / [(1.014)^20 - 1]
To find the value of A, we can rearrange the equation:
A = $85,000 * [(1.014)^20 - 1] / (1.014)^20
Using a calculator or spreadsheet, we can calculate the value of A.
A ≈ $85,000 * 0.298 / 1.350
A ≈ $18,065.19
Learn more about Frequency at: brainly.com/question/29739263
#SPJ11
An item is regularly priced at $70. It is on sale for 20% off the regular price. How much (in dollars) is discounted from the regular price?
Answers
Answer:
14 is the discount
56 is discounted price.
(Q2) The set of line segments _____ meet the requirements to form a triangle.8 cm4 cm3 cm
Answers
To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.
We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.
In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.
In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.
learn more about the inequality theorem here: brainly.com/question/1163433
#SPJ11
Mrs. Santos baked 25 cookies. 3 fifths of the cookies were oatmeal. How many oatmeal cookies did Mrs. Santos bake?
Answers
Answer: 15 oatmeal cookies.
Step-by-step explanation:
There were 25 cookies baked.
Out of these, 3/5 are oatmeal cookies.
The amount of actual oatmeal cookies is:
= fraction of oatmeal cookies * total number of cookies
= 3/5 * 25
= 75 / 5
= 15 oatmeal cookies.
find the yy -component of vector a⃗ a→ = (5.0 m/s2m/s2 , −y−y -direction).
Answers
The yy-component of vector a a is -y-direction, which is equal to 0 m/s2.the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.
Given a vector, a⃗ a→ = (5.0 m/s2, −y−direction)Find the yy -component of the given vector a⃗ a→.Solution: The yy-component of the given vector a⃗ a→ = -y-directionTo find the yy-component of the given vector a⃗ a→, we have to take the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.Therefore, the yy-component of vector a⃗ a→ is :a_yy = -y-direction = (-1)(0) = 0 m/s² Answer: 0 m/s².
To know more about Vector Visit:
https://brainly.com/question/24256726
#SPJ11
The yy-component of vector a⃗ a→ is -y-direction.
Explanation:The yy-component of a vector represents the magnitude of the vector in the y-direction.
In this case, the vector a⃗ a→ is given as (5.0 m/s2, −y-direction).
Since the yy-component is the magnitude in the y-direction, the yy-component of the vector a⃗ a→ is -y-direction.
Learn more about Vector Components here:https://brainly.com/question/31400182
#SPJ12
How do I simplify fractions ?
Answers
Write down the factors for the numerator and the denominator.
Determine the largest factor that is common between the two.
Divide the numerator and denominator by the greatest common factor.
Write down the reduced fraction.
(1 + 2 × 3)² + 7
please helppppooppppppppp
Answers
Answer:
56
Step-by-step explanation:
(1+2*3)^2+7
(1+6)^2+7
7^2+7
49+7
56
Answer:
Step-by-step explanation:
Using PEMDAS, first find the product of the parentheses. 2*3=6. 1+6=7. 7² is 49. 49+7=56.
The length of a rectangular room is 8 feet more than twice the width. If takes perimeter of the room is 124 feet, what are its dimensions?
Answers
Hey there! I'm happy to help!
Let's call the length and width L and W respectively.
L=2W+8
2W+2L=124
We plug our value of L into the second equation and solve for W.
2W+2(2W+8)=124
We undo the parentheses with the distributive property.
2W+4W+16=124
Combine like terms.
6W+16=124
Subtract 16 from both sides.
6W=108
Divide both sides by 6.
W=18
We plug this W value into the first equation to solve for L.
L=2(18)+8
L=36+8
L=44
So, the length is 44 feet and the width is 18 feet.
Have a wonderful day! :D
Plssss help due tomorrow!!
Answers
Answer:
y = -1/3x +1
Step-by-step explanation:
You want the slope-intercept form equation of the line through the points (-3, 2) and (-9, 4).
SlopeThe slope is given by the formula ...
m = (y2 -y1)/(x2 -x)
m = (4 -2)/(-9 -(-3)) = 2/-6 = -1/3
Y-interceptThe y-intercept is given by the formula ...
b = y1 -m(x1)
b = 2 - (-1/3)(-3) = 1
Slope-intercept equationThe slope-intercept equation of the line is ...
y = mx +b
y = -1/3x +1
solve each question -15=7n+8n=
Answers
Answer:
-15 = 7n + 8n
-15 = 15n
n = -1
plz brainlist me I need it
n = - 1
Step-by-step explanation:- 15 = 7n + 8n
15n = - 15
n = - 15 : 15
n = - 1