81x^6-(y+1)^2 what are the U and V

According to the Second-Derivative Test for Local Extrema, f(x,y) has a critical point if f x(a,b) = 0 and f y(a,b) = 0, and all second-order partial derivatives of f(x,y) exist in some circular region containing (a,b) as center.

The Second-Derivative Test is as follows:

Case 1: If AC - B2 > 0 and A < 0, then f(x,y) has a local maximum at (a,b).

Case 2: If AC - B2 > 0 and A > 0, then f(x,y) has a local minimum at (a,b).

Case 3: If AC - B2 < 0, then f(x,y) has a saddle point at (a,b).

Case 4: The test fails if AC - B2 = 0. The steps to apply the Second-Derivative Test for Local Extrema are as follows:

Find the critical point of f(x,y). Calculate A, B, and C using second-order partial derivatives of f(x,y). Evaluate AC - B2 and A.

Using the above cases, determine whether f(x,y) has a local maximum, minimum, or a saddle point.

Thus, we need to apply the Second-Derivative Test for Local Extrema to find the local extrema of the function f(x,y). The Second-Derivative Test can be used to determine whether a function has a local minimum, a local maximum, or a saddle point, which can help solve optimization problems in various fields.

To know more about the Second-Derivative Test, visit:

brainly.com/question/30404403

#SPJ11

Answer: The correct answer is Yes, the relationship between x and y is a non-linear function.

I hope this helps.

Step-by-step explanation:

Given the table

Edge Length, x            Surface Area, y

1                                             6

2                                            24

3                                            54

4                                             96

The table values clearly represent a function, because each input value has one and only one output value. i.e. there is no repetition of x values.

Also from the table values and the graph, it is clear that the function is not a linear function, because the graph is not a straight line. Also, In a cubic function, the highest power over the x variable(s) is 3. So, it is not a linear function.

Hence, we conclude that Yes, the relationship between x and y is a non-linear function.

Therefore, the 'last option' is correct.

Answer:

\(2*y^{2}\)

Step-by-step explanation:

The product of 2 is multiplication and the second power of y is just y squared

The answer is true. The curve of t-distribution has thicker tails than the curve of the standard normal distribution.

The t-distribution is also called as Student's t-distribution which is a type of probability distribution with a bell shape which is similar to  normal distribution but has thicker tails. It is used to estimate population parameters when sample sizes are small or variances are unknown. T-distributions have a higher probability of extreme values more than normal distributions which results in thicker tails.

Tail thickness is determined by a t-distribution parameter called degrees of freedom, with lower values resulting in heavier tails and higher values resulting in the t-distribution resembles standard normal distribution with a  standard deviation of 1and mean of 0.

Thus, t-distribution has thicker tails than the normal distribution.

To learn more about t-distribution refer here

https://brainly.com/question/13574945

#SPJ4

it is not possible for det A to equal 3 if the entries of both A and A^-1 are integers.

The determinant of a matrix and its inverse are multiplicative inverses of each other, meaning that det(A)det(A^-1) = 1. If det A = 3, then det(A^-1) = 1/3. However, since the entries of both A and A^-1 are integers, this is a contradiction, as the determinant of a matrix with integer entries must also be an integer. Therefore, it is impossible for det A to equal 3 in this scenario.

it explains the reasoning behind the solution and provides a deeper understanding of the concept of determinants.

To know more about matrix visit:

https://brainly.com/question/29995229

#SPJ11

Take the square root of each side.

\(\sf \sqrt{x^{2} } =\sqrt{25} \\\\\\ x=\± 5\)

The probability that a data value is between 56 and 64 is 62.5%. Option D is the correct answer.

The given normal distribution has the following parameters:

Mean = 62

Standard deviation = 4

To find the probability that a data value is between 56 and 64, we need to find the z-scores corresponding to these values. Using the z-score formula, $$z=\frac{x-\mu}{\sigma}$$

Where x is the data value, µ is the mean, and σ is the standard deviation. Substituting the given values, we get:

For x = 56,$$z=\frac{56-62}{4}=-1.5$$For x = 64,$$z=\frac{64-62}{4}=0.5$$

Now we need to find the probability that a data value is between these z-scores using the standard normal distribution table. The table gives the area under the curve to the left of a given z-score. To find the area between two z-scores, we need to find the difference between the areas to the left of the two z-scores.

Using the standard normal distribution table, we find:

Area to the left of z = -1.5 is 0.0668

Area to the left of z = 0.5 is 0.6915

Therefore, the area between z = -1.5 and z = 0.5 is:0.6915 - 0.0668 = 0.6247

Rounding off to the nearest tenth of a percent, we get 62.5%. Hence, the correct option is D.

You can learn more about probability at: brainly.com/question/31828911

#SPJ11

The expressions 2nd and 3rd are correct.

Proceed LHS 1st given expression,

6\(c^{5}\)(9\(c^{3}\)) = 54\(c^{15}\)

LHS, 6\(c^{5}\)(9\(c^{3}\))  = 54\(c^{5+3}\)

                      =  54\(c^{8}\) not equal to RHS

Hence this is incorrect.

Proceed LHS of 2nd given expression,

8\(z^{7}\)(3\(z^{4}\))

= 24\(z^{7+4}\)

= 24\(z^{11}\) =RHS

Hence this expression is correct.

Proceed LHS of 3rd given expression,

9\(a^{5}\)(-3\(a^{2}\))

= -27\(a^{7}\) = RHS

Hence this expression is correct.

Proceed LHS of 3rd given expression,

4\(x^{3}\)(-5\(x^{2}\))

= -20\(x^{5}\) is not equal to RHS

Hence this is incorrect.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Equation 8z⁷(3z⁴)=24z¹¹ is true. Therefore, option (2) and (3) are correct answers.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

Given that,

1) 6c⁵(9c³)=54c¹⁵

6c⁵(9c³)

= 6×9×c⁵×c³

= 54c⁸

Therefore, the given equation is not true.

2) 8z⁷(3z⁴)=24z¹¹

8×3×z⁷×z⁴

= 24z¹¹

Therefore, the given equation is true.

3) 9a⁵(-3a²)=-27a⁷

9×(-3)×a⁵×a²

= -27a⁷

Therefore, the given equation is true.

4) 4x³(-5x²)=-20x⁶

4x³(-5x²)

= 4×(-5)×x³×x²

= -20x⁵

Therefore, the given equation is not true.

Therefore, option (2) and (3) are correct answers.

To learn more about an exponents visit:

https://brainly.com/question/15993626.

#SPJ1

21 is the value of function f(3) .

What is function?

f(x) = 5x + 6

f(3) = 5(3) + 6 = 15 + 6 = 21

Learn more about function

brainly.com/question/12431044

#SPJ9

Solution:

Multiply either numerator or denominator such that one of the terms is 30.

And:

Hoped this helped!

The stationing of the end of the excavation is Station 2+080.

The volume of fill by end area method is 1440 cubic meters.

The volume of excavation by end area is 1080 cubic meters.

We have,

The stationing of the end of excavation can be determined by adding the given sections to the starting station.

Assuming the starting station is Station 2+020, the end of excavation would be at Station 2+080 (given as Station 2+020 + 60 meters).

To find the volume of fill by end area method, we need to calculate the area of the end section and multiply it by the distance between the start and end stations.

Given that the base for fill is 12 meters and the sideslope for fill is 2:1, the area of the end section can be calculated as follows:

Area of end section = (Base for fill) * (Sideslope for fill)

Area of end section = 12 * (2/1) = 24 square meters

Now, multiply the area of the end section by the distance between the start and end stations (60 meters) to find the volume of fill:

Volume of fill = Area of end section * Distance

Volume of fill = 24 * 60 = 1440 cubic meters

Therefore, the volume of fill by end area method is 1440 cubic meters.

Similarly, to compute the volume of excavation by end area, we calculate the area of the end section (base for cut * sideslope for cut) and multiply it by the distance between the start and end stations. Given that the base for cut is 12 meters and the sideslope for cut is 1.5:1, the area of the end section can be calculated as follows:

Area of end section = (Base for cut) * (Sideslope for cut)

Area of end section = 12 * (1.5/1) = 18 square meters

Multiply the area of the end section by the distance between the start and end stations (60 meters) to find the volume of excavation:

Volume of excavation = Area of end section * Distance

Volume of excavation = 18 * 60 = 1080 cubic meters

Therefore, the volume of excavation by end area is 1080 cubic meters.

Thus,

The stationing of the end of the excavation is Station 2+080.

The volume of fill by end area method is 1440 cubic meters.

The volume of excavation by end area is 1080 cubic meters.

Learn mroe about earthwork constructions here:

https://brainly.com/question/25749167

#SPJ4

Ans: The value of f(t) is 10t/π.

The given signal is x(t)=3cos(−10t²+π/5)+4cos(10t²−π/7)

Let's use the following formula to convert x(t) into the standard sinusoidal form.

Acos(ωt2+φ).Acos(ωt2+φ)=Acosφcos(ωt2)−Asinφsin(ωt2)x(t)=3cos(−10t²+π/5)+4cos(10t²−π/7)x(t)=3cos(−10t²)cos(π/5)+3sin(−10t²)sin(π/5)+4cos(10t²)cos(π/7)−4sin(10t²)sin(π/7)x(t)=3cos(−10t²)cos(π/5)−3sin(10t²)sin(π/5)+4cos(10t²)cos(π/7)−4sin(10t²)sin(π/7)x(t)=(3cos(π/5))cos(10t²)+(−4sin(π/7))sin(10t²)+(−3sin(π/5))sin(10t²)+(4cos(π/7))cos(10t²)x(t) =3/2cos(10t²)+ 1/2cos(10t²−2π/7) −1/2cos(10t²+2π/5)+2sin(10t²−π/7)

Let's convert

x(t) into the standard sinusoidal form.

Acos(ωt2+φ).Here, A= 2√(13), φ=−π/7ω= 10Hzx(t)=3/2cos(10t²)+1/2cos(10t²−2π/7)−1/2cos(10t²+2π/5)+2sin(10t²−π/7)A= 2√(13)x(t)=2√(13)cos(10t²−π/7+π/2)x(t)=2√(13)cos(10t²−π/7)cos(π/2)−2√(13)sin(10t²−π/7)sin(π/2)x(t)=2√(13)sin(10t²−π/7)

Now, let's find the instantaneous frequency in Hz. An instantaneous frequency in Hz can be defined as the derivative of the phase φ with respect to time t.f(t)=1/2π dφ(t)/dtx(t)=Acos(ωt²+φ).

The derivative of the phase φ with respect to time t is given bydφ(t)/dt= 2ωtTherefore, the instantaneous frequency in Hz is given byf(t)=1/2π dφ(t)/dt=1/2π (2ωt)f(t)=ωt/πNow, let's substitute the value of ω and get the value of f(t).ω = 10 Hzf(t) = ωt/π = 10t/π

Learn more about value

https://brainly.com/question/7440937

#SPJ11

Answer:

Step-by-step explanation:

9+x ≥ 0

x ≥ -9

Step-by-step expTo calculate the impedance of the load in a balanced three-phase system, we need to know the line current (Ia) and the line-to-line voltage (Vbc).

However, in the given question, the line current (Ia) is given as 10 A, but the line-to-line voltage (Vbc) is not provided. Without the value of Vbc, we cannot calculate the impedance accurately.

The impedance of a load in a three-phase system is calculated using the formula Z = V / I, where Z is the impedance, V is the voltage, and I is the current. However, since we only have the value of Ia and not Vbc, it is not possible to calculate the impedance accurately.

Please provide the value of the line-to-line voltage (Vbc) so that we can calculate the impedance of the load for the given cases.

To learn more about Impedance - brainly.com/question/30475674

#SPJ11

Let \(n=0\). Then \(0^3 = 0\) but 0 > 0 is a false statement.

Question 1a

To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:

Annual Depreciation = (Cost - Salvage Value) / Useful Life

Substituting the given values, we get:

Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year

This means that the tractor will depreciate by $18,000 each year for the next 10 years.

To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:

Depreciation Expense for Year 1 = $18,000

Therefore, the book value of the tractor at the end of the first year will be:

Book Value = Cost - Depreciation Expense for Year 1

= $200,000 - $18,000

= $182,000

So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D

Question 1(b)

To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:

Calculate the total current liabilities using the current ratio:

Current Ratio = Current Assets / Current Liabilities

2 = $80,000 / Current Liabilities

Current Liabilities = $80,000 / 2

Current Liabilities = $40,000

Calculate the total liabilities using the debt/equity ratio:

Debt/Equity Ratio = Total Liabilities / Owner Equity

1.0 = Total Liabilities / $100,000

Total Liabilities = $100,000 * 1.0

Total Liabilities = $100,000

Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:

Noncurrent Liabilities = Total Liabilities - Current Liabilities

Noncurrent Liabilities = $100,000 - $40,000

Noncurrent Liabilities = $60,000

Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.

Based on the information, we can say that 45% proportion of the customers in the sample expressed satisfaction with the bookstore.

To assess what the sample data tells us about the bookstore's claim, we can calculate the proportion of customers who expressed satisfaction based on the sample.

The proportion is calculated by dividing the number of customers who expressed satisfaction by the total,

Proportion of customers satisfied = Number of satisfied customers / Total sample size

In this case, the number of satisfied customers is given as 270, and the total sample size is 600:

Proportion of customers satisfied = 270 / 600 = 0.45

The proportion of customers satisfied in the sample is 0.45 or 45%.

These factors help determine the level of confidence

we can have in extending the sample results to the entire population.

Learn more about Proportion here:

https://brainly.com/question/33460130

#SPJ11

Step-by-step explanation:

You want to demonstrate the identity ...

  (1-tan⁴(A))·cos⁴(A) = 1 -2·sin²(A)

Working with the left side, we have ...

  \((1-\tan^4(A))\cos^4(A)=1-2\sin^2(A)\\\\(1-\dfrac{\sin^4(A)}{\cos^4(A)})\cos^4(A)=1-2\sin^2(A)\qquad\text{use tangent identity}\\\\\cos^4(A)-\sin^4(A)=1-2\sin^2(A)\qquad\text{multiply it out}\\\\(\cos^2(A) +\sin^2(A))(\cos^2(A)-\sin^2(A))=1-2\sin^2(A)\qquad\text{factor}\\\\1((1-\sin^2(A))-\sin^2(A)) = 1-2\sin^2(A)\qquad\text{use $\cos^2$ identity}\\\\1-2\sin^2(A)=1-2\sin^2(A)\qquad\text{Q.E.D.}\)

__

Additional comment

The referenced identities are ...

  tan = sin/cos

  cos² = 1 -sin²

and the factorization of the difference of squares:

  a² -b² = (a +b)(a -b).

The statement "All seasons had the same level of variability in game scores" must be false.

To determine which statement must be true based on the mean game scores and standard deviations of four seasons of a football team, we need to analyze the data provided.

Given:

Season 2005: Mean = 193.5, Standard Deviation = 0

Season 2006: Mean = 212.8, Standard Deviation = 0

Season 2007: Mean = 121.0, Standard Deviation = 0

Season 2008: Mean = 94.0, Standard Deviation = 0

From the given data, we observe that all the standard deviations are zero. This indicates that there is no variation or spread in the game scores within each season. However, it is highly unlikely for a football team to have zero variation in game scores across multiple seasons.

Therefore, the statement "All seasons had the same level of variability in game scores" must be false.

Learn more about standard deviations here:

https://brainly.com/question/29115611

#SPJ11

The volume of the remaining piece of ice cube is 6911.5 cubic cm

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have

Radius, r = 20/2  = 10 cm

Height, h = 33 cm

The volume of the remaining piece is calculated is

V = 2/3πr²h

Substitute the known values in the above equation, so, we have the following representation

V = 2/3 * 22/7 * 10² * 33

Evaluate

V = 6911.5

Hence, the volume of the remaining piece is 6911.5 cubic cm

Read more about volume at

https://brainly.com/question/30849227

#SPJ1

The initial concentration of the solution in the tank is 0.03 kg/L. After 1.5 hours, the amount of salt in the tank is 60.135 kg. As time approaches infinity, the concentration of salt in the tank will stabilize at 0.015 kg/L, which is the concentration of the entering solution.

In the given problem, initially, the tank contains 60 kg of salt and 2000 L of water. The solution entering the tank has a concentration of 0.015 kg of salt per liter, and it enters and drains from the tank at a rate of 6 L/min. We need to find the initial concentration of the solution in the tank, the amount of salt in the tank after 1.5 hours, and the concentration of salt in the solution as time approaches infinity.

(a) The initial concentration of the solution in the tank can be calculated by dividing the total mass of salt (60 kg) by the total volume of the mixture (2000 L of water). Therefore, the initial concentration is 60 kg / 2000 L = 0.03 kg/L.

(b) To find the amount of salt in the tank after 1.5 hours, we need to consider the rate at which the solution enters and drains from the tank. In 1.5 hours, the total volume of solution entering and draining from the tank is (1.5 hours) * (6 L/min) = 9 L. Since the concentration of the solution is 0.015 kg/L, the amount of salt added to the tank is (9 L) * (0.015 kg/L) = 0.135 kg. Therefore, the amount of salt in the tank after 1.5 hours is 60 kg + 0.135 kg = 60.135 kg.

(c) As time approaches infinity, the concentration of salt in the solution in the tank will reach a steady state. Since the solution enters and drains from the tank at the same rate, the concentration of salt in the tank will eventually become equal to the concentration of the entering solution, which is 0.015 kg/L.

Learn more about infinity here:

https://brainly.com/question/17714945

#SPJ11

Answer:

x is equal to 5 ± i√21

Step-by-step explanation:

x² -10x + 4 = 0

x²- 10x -25 = -21

(x - 5)² = -21

x - 5 = √(-21)

x = 5 ± √(-21)

x = 5 ± i√21

There are 120 people in a theatre. 72 are female and 48 are male. 12 females purchase an ice cream and 31 males purchase an ice cream.

Frequency trees display the real frequency of certain events. They can display the same data as a two-way table, but frequency trees are more readable since they illustrate the frequency hierarchy. Probability trees depict the likelihood of a series of occurrences.

Solution:

From the question, we can see the there are 120 people in the theatre.

Since, there are 72 females in the theatre we can find the total number of males by 120-72 = 48

Also, the male who purchased Ice Cream were 36 therefore, the males who did not purchased Ice Cream are 48-36 = 12

And, the females who purchased Ice Cream are 41. So, the female who did not purchased Ice Cream are 72 - 41 = 31

To learn more about Frequency Tree from the given link

brainly.com/question/20433037

#SPJ1

complete question"

there are 120 people in a theatre 72 are female of these 41 purchase an ice cream 36 males purchase and ice cream use this information to compete the frequency tree

When looking at sides AC and CB, the included angle is angle ABC. The included angle is the angle between two given sides. In this particular question, we are given the sides AC and CB.

Here, we have a triangle ABC, and we are interested in the angle between sides AC and CB. This angle is opposite to the side AB. Therefore, this included angle is angle ABC. We can summarize this as follows: When we have two sides of a triangle, we can determine the included angle by finding the angle that lies between them. In the case of sides AC and CB, the included angle is the angle that is opposite to the third side of the triangle, AB.

Therefore, the included angle in this case is angle ABC.

To know more about Included angle visit-

https://brainly.com/question/12798845

#SPJ11

(Question is incomplete i answered what is included angle)

The first four terms of the Taylor series for the function (2x) about the point (a=1) are (2x + 2x - 2).

To find the first four terms of the Taylor series for the function (2x) about the point (a = 1), we can use the general formula for the Taylor series expansion:

\(\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \ldots\]\)

Let's calculate the first four terms:

Starting with the first term, we substitute

\(\(f(a) = f(1) = 2(1) = 2x\)\)

For the second term, we differentiate (2x) with respect to (x) to get (2), and multiply it by (x-1) to obtain (2(x-1)=2x-2).

\(\(f'(a) = \frac{d}{dx}(2x) = 2\)\)

\(\(f'(a)(x-a) = 2(x-1) = 2x - 2\)\)

Third term: \(\(f''(a) = \frac{d^2}{dx^2}(2x) = 0\)\)

Since the second derivative is zero, the third term is zero.

Fourth term:\(\(f'''(a) = \frac{d^3}{dx^3}(2x) = 0\)\)

Similarly, the fourth term is also zero.

Therefore, the first four terms of the Taylor series for the function (2x) about the point (a = 1) are:

(2x + 2x - 2)

Learn more about taylor series

brainly.com/question/31140778

#SPJ11

Answer:

the answer is 55

Step-by-step explanation:

if you have a straight line each side equals 180 degrees so take 60+65 which equals 125 then do 180-125 and you get 55

A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.

A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.

A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.

Read more about multipliers:

brainly.com/question/15883095

7 + 7 + 7 + 7 + 7​ means 7 is added 5 times

It could be written as

5(7)

7 x 5 and

7 . 5

But it can not be written as 7^5 because 7^5 means 7 x 7 x 7 x 7 x 7

Hence, 7^5 does not represent the expression 7 + 7 + 7 + 7 + 7​

This makes the correct option to be the third option. That is 7^5

Answer:

I would think d for the answer