Find any critical numbers for f and then use the second derivative test to decide whether the critical number(s) lead to relative maxima or relative minima. If f''(C) = 0 or f''(c) does not exist for a critical number c, then the second derivative test gives no information. In this case, use the first derivative test instead. f(x) = 4x^3 - 16x^2 +5
Answers
To find the critical numbers of f(x) = 4x^3 - 16x^2 + 5, we need to find where the derivative of f(x) is equal to zero or does not exist.
f'(x) = 12x^2 - 32x = 4x(3x - 8)
Setting f'(x) = 0, we get:
4x(3x - 8) = 0
Solving for x, we get:
x = 0 or x = 8/3
These are the critical numbers of f(x). To determine whether they correspond to relative maxima or minima, we need to use the second derivative test.
f''(x) = 24x - 32
f''(0) = -32 < 0, so f(x) has a relative maximum at x = 0.
f''(8/3) = 8 > 0, so f(x) has a relative minimum at x = 8/3.
Therefore, the critical number x = 0 corresponds to a relative maximum, and the critical number x = 8/3 corresponds to a relative minimum.
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Related Questions
a town is 61km north of 23km east of town B.bCalculate the bearing of A from B
Answers
Answer:
20.7°
Step-by-step explanation:
Bearing angle is measured clockwise from north. The geometry can be modeled by a right triangle with the sides equal to the distances north and east of town B. The tangent relation can be used to find the angle.
__
The attachment shows the geometry. The relevant angle relation is ...
Tan = Opposite/Adjacent
tanIβ) = 23/61 . . . . . where β is the bearing angle
The angle value can be found using the arctangent function.
β = arctan(23/61) ≈ 20.659°
The bearing of A from B is about 20.7°.
if a cube 4 centimeters on each edge, what is the volume of the cube?
Answers
Answer:
Volume of cube =a3=43=64 cm3.
Step-by-step explanation:
Answer is 64 cm3
44% of the books are fairy tales. What fraction of the books are fairy tales (Give your answer in simplest form e.g. 10/11)
Answers
Answer:
\(\frac{11}{25}\)
Step-by-step explanation:
44% can also be written as a fraction: \(\frac{44}{100}\)
To simplify this fraction, let's divide the numerator and the denominator by 4:
44/4 = 11
100/4 = 25
The simplest form of the fraction of books that are fairytales is \(\frac{11}{25}\)
Which expression uses the associative property to make it easier to evaluate 6(3/2 * 1/5)?
A. (6 * 3/2)1/5
B. (3/2 * 1/5)6
C. 6(3/2 * 1/5)
D. 6(1/5 * 3/2)
Answers
Answer:
A. (6*3/2)1/5
Step-by-step explanation:
A-P-E-X
3.6.2 CST
how to find the scale factor of 10 cm=5m
Answers
The scale factor of 10cm to 5m is 50.
What is scale factor?The scale factor is a measure for similar figures, who look the same but have different scales or measures.
For example ,if a length of 5cm is doubled and it gives a length 10cm, the scale factor is 10/5 = 2. This means that we can express scale factor with a formula;
scale factor = new dimension / old dimension
Here, the old dimension is 10cm and the new dimension is 5m. We need to convert the 5m into cm
therefore 5m = 5× 100 = 500cm
therefore scale factor = 500/10 = 50
This means the scale factor of 10cm = 5m is 50
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a company had 80 employees whose salaries are summarized in the frequency distribution below. find the standard deviation.
Answers
The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.
The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).
By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.
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if 5 apples cost 0.60 then how much does 6 apples cost
Answers
Answer:
$0.72 for 6 apples
Step-by-step explanation:
0.60 / 5 = 0.12
0.12 * 6 = 0.72James takes out a loan of 9000 euros which keeps on charging simple interest at a rate of 3% of the original amount per annum until it is cleared. James pays of 770 euros each year to reduce the loan. After how many years will James have fully cleared the loan?
Answers
James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.
To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.
The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.
In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.
In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.
This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.
Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.
Combining like terms, we have 9000 + 270 = 1.04x.
Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.
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Please help I need this really quick I will name brainliest to whoever can answer this quickly please!!!
Answers
Answer:
180 degree rotation around the origin
Step-by-step explanation:
Both points are on exactly opposite sides of the graph
A system of two linear equations is graphed on a coordinate grid. The lines intersect at one point. Which statement about the system of equations is True or False (; I will Give you the Brainliest.
Answers
do any of y'all know how to do this I'm so confused and I need help
Answers
Answer:
x=28 bottom left angle is 60, bottom right is 70
Step-by-step explanation:
the angles add up to 180
lets set up an equation
x+32+x+42+50=180
2x+124=180
2x=56
x=28
Write a unit rate: Bob drove 240 miles in 4 hours.
Answers
————. ———. = —- or 60
Minutes 4. Divided by 4. 1
how many miles are in acre
Answers
There is 0.0015625 miles in 1 acre.
The acre is basically considered to be one of the oldest units of measurement commonly used for value in imperialism, and the unit of measurement is used all over the world to measure units of land. increase. In other words, an acre is defined as an area 4 rods wide.
Various types of shapes such as squares, pentagons, and circles can be used to easily measure national units to acres. An acre of land can be measured in any length or width as long as the total acre does not exceed 43,560 square feet.
For example, 1 acre of land is the total of 16 tennis courts that can be built into that land.
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difference between disguised and seasonal unemployment
Answers
Answer:
I don't know.
Step-by-step explanation:
Disguised unemployment and seasonal unemployment are the same thing lol.
Answer:
Seasonal unemployment occurs as demands shift from one season to the next. This category can include any workers whose jobs are dependent on a particular season. Official unemployment statistics will often be adjusted or smoothed, to account for seasonal unemployment.
A disguise can be anything which conceals or changes a person's physical appearance, including a wig, glasses, makeup, fake moustache, costume or other items. Camouflage is a type of disguise for people, animals and objects. Hats, glasses, changes.
Hey y’all can u please give me the correct answer.
Answers
Step-by-step explanation:
-8 - 6x < 1
Bringing like terms on one side
-6x < 1 + 8
-6x < 9
x < 9/-6
x < 3/-2
I think the correct answer is none
5- ܫ ܐx
.9
Use square roots
Answers
what is the probability that a 2-card hand (drawn from a standard deck of 52) has two queens, two kings, or one of each?
Answers
2/221 is the probability that a 2-card hand has two queens, two kings, or one of each.
What is probability?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or the probability that a statement is true.Probability varies between zero and 1, wherein zero approaches are not possible and 1 approach is certain.Now, calculate the probability as follows:
There are 4 kings and 4 queens in a deck of cards.Then, it can be either KK or QQ.
Select 2 kings from 4 king cards that can be done in 4c₂=6 ways.Select 2 queens from 4 queen cards that can be done in c₂ = 6 ways.Total ways = 52c₂ = 1326So required probability = 2king or 2 queen
= 6/1326 + 6/1326= 12/1326= 2/221Therefore, the probability that a 2-card hand (drawn from a standard deck of 52) has two queens, two kings, or one of each is 2/221.
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Triangle SAM is congruent to Triangle REN. Find x and y.
Answers
\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)
HELP HELP HELP HELP HELPPPPPPPPPPPPP
Answers
Answer:
The ratio of x-values to y-values in the table is 2:3
Step-by-step explanation:
8 / 12 = 2/3
10 / 15 = 2/3
12 / 18 = 2/3
Each has a ratio of 2 to 3.
1/3 (1632 + x) = 726 solve for x
pLS help please i beg i plea plssss
Answers
\( \frac{1}{3} (1632 + x) = 726\)
\( \frac{1}{3} (x + 1632) = 726\)
\( \frac{1(x + 1632)}{3} = 726\)
\( \frac{x + 1632}{3} = 726\)
\(3· \frac{x + 1632}{3} = 3·726\)
\(x + 1632 = 3·726\)
\(x + 1632 = 2178\)
\(x + 1632 - 1632 = 2178 - 1632\)
\(x =546\)
So, the value of x is 546.
can some help me out im just a bit confused, thank you!
Answers
\(Hey\) \(there!\)
The best and most correct answer among the choices provided is D, because if you did that it would completely cancel out the \(y\)'s and leave you with \(x\).
Hope it helps and have a great day!
In a recent election, 63% of all registered voters participated in voting. In a survey of 275 retired voters, 162 participated in voting. Which is higher, the population proportion who participated or the sample proportion from this survey?
Answers
The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).
To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.
The population proportion who participated in voting is given as 63% of all registered voters.
This means that out of every 100 registered voters, 63 participated in voting.
In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.
Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .
Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).
Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.
It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.
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If 45% of a number is 99 and 35% of the same number is 77, find 80% of that number.
Answers
Answer:
176 = 80% Extra: If you need 100% its, 220
Step-by-step explanation:
99+ 77 is 176
45% + 35% = 80%
which of the following is not influenced by stream velocity? discharge suspended load dissolved load abrasion bed load
Answers
The stream velocity has no influence on the amount of dissolved load it contains. The amount of dissolved material depends on erosion and deposition carried out in the watercourse. These are affected by factors such as the slope of the land, the resistance of the material to erosion, the size of the sediments transported, etc.
Which of the following is not influenced by stream velocity?Dissolved loadStream velocity plays an important role in the transport of sediments and dissolved loads in a watercourse. It affects the erosion and deposition processes that occur in the watercourse, which in turn affect the amount of sediment and dissolved load that is carried by the stream. For example, faster stream velocities can cause more erosion of the stream bed, leading to more material being carried in the water.
Sediment is any particulate matter that is transported by a fluid, and it can come in many different forms. The three main types of sediment are:
The suspended load is made up of small particles that are carried along in the water column. The bed load consists of larger particles that are moved along the bottom of the streambed. And the dissolved load is made up of particles that are carried in solution.Learn more about Erosion: https://brainly.com/question/17905503
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4 quarts per day. Express this rate of flow in liters per week.
Answers
Answer:
26.49787 or about 26.50 liters.
Step-by-step explanation:
4 quarts = 3.78541 liters
For the week = 3.78541 x 7 = 26.49787
Ben deposits $7,000 now into an account that earns 6 percent interest compounded annually. He then deposits $1,000 acr veat at the end of the first and second years. How much will the account contain 10 years after the initial deposit? \$ Round entry to the nearest dollar. Tolerance is ±4. Adriana wishes to accumulate $2,020,000 in 35 years. If 35 end-of-year deposits are made into an account that pays interest at a rate of 7% compounded annually, what size deposit is required each year to meet Adriana's stated objective? $ Use Time Value of Money Table factor values rounded to 5 decimals. Round entry to the nearest dollar. Tolerance is ±12. You deposit $1,000 in a fund at the end of each year for 11 years. The fund pays 7% compounded annually. How much money is available to withdraw immediately after your last deposit?\$ Round entry to the nearest dollar. Tolerance is ±4. In planning for your retirement, you would like to withdraw $45.000 per year for 20 years. The first withdrawal will occur 20 years from today. Click here to access the TVM Factor Table Calculator Part at What amount must you invest today if your return is 10% per year?\$ Round entry to the nearest dollar. Tolerance is ±4.
Answers
1. Ben's deposits over 10 years:
- Initial deposit: $7,000
- Annual deposit at the end of the first and second years: $1,000
- Interest rate: 6% compounded annually
To calculate the total amount after 10 years, we can use the Future Value (FV) formula:
FV = Initial deposit * (1 + interest rate)^number of years + Annual deposit * [(1 + interest rate)^number of years - 1] / interest rate
Substitute the values into the formula to find the total amount.
2. Adriana's goal in 35 years:
- Desired accumulated amount: $2,020,000
- Number of years: 35
- Interest rate: 7% compounded annually
To calculate the required annual deposit, we can use the Present Value of an Annuity (PVA) formula:
PVA = Desired accumulated amount / [(1 - (1 + interest rate)^(-number of years)) / interest rate]
Substitute the values into the formula to find the required annual deposit.
3. Deposits of $1,000 for 11 years:
- Annual deposit: $1,000
- Interest rate: 7% compounded annually
To calculate the amount available to withdraw immediately after the last deposit, we can use the Future Value (FV) formula:
FV = Annual deposit * [(1 + interest rate)^number of years - 1] / interest rate
Substitute the values into the formula to find the total amount.
4. Retirement withdrawal of $45,000 per year for 20 years:
- Annual withdrawal amount: $45,000
- Number of years: 20
- Interest rate: 10% per year
To calculate the required initial investment, we can use the Present Value of an Annuity (PVA) formula:
PVA = Annual withdrawal amount * [(1 - (1 + interest rate)^(-number of years)) / interest rate]
Substitute the values into the formula to find the required initial investment.
Please provide specific values for interest rates, and if any additional information is available, so that I can provide the calculations for each scenario.
PLSS Help I'm desperate
Answers
Answer:
20 -> 5
Step-by-step explanation:
20 / 4 = 5
40 -> 10
160 -> 40
Answer:
so the answer should 20 because
if you divide 20/4 you would get 5
so basically all you are looking for is what number times what = that number
Step-by-step explanation:
A 3-yard roll of butcher paper costs $8.55. What is the price per foot?
Answers
Answer:
$2.85
Step-by-step explanation:
8.55/3
Answer:
$2.85 per foot
Step-by-step explanation:
all u gotta do is 8.55/3
A side view of a desk telephone is shown below.
9.5 cm
11 cm
Answer choices
A 2 cm
B 10 cm
C 20 cm
D 6 cm
Answer D
Answers
Answer:
I'm guessing it's D
Step-by-step explanation:
It says D is the answer
what is outlier math definition
Answers
Answer:
In statistics, an outlier is a data point that differs significantly from other observations.
Step-by-step explanation: