Please help it’s either C or A!

The maximum direction derivative of the given function is \(\frac{-33}{\sqrt6}.\)

The directional derivative is the rate at which a function changes at any point along a fixed axis. It is thought of as the vector form of any derivative. It specifies the function's immediate rate of variation. It particularised the vision of partial derivatives. It can be written as:

D.D=gradf.(a)/|a|.

The concept of directional derivatives is simple to grasp. Du f (k) is the slope of f(x,y) when standing at point k and facing a unit vector (u). If x and y are in meters, then Du f (k) will change in height per meter as you move in the direction given by u while standing at point k.

\(let\ f(x,y,z)=5x^3-y^3+z^2,\\\\find\ the \ partial\ derivative\ with\ respect\ to \ x, y and z,\\\\f_x=15x^2\\\\f_y=-3y^2\\\\f_z=2z.\\\\The \ direction \ derivative\ is-\\\\gradf=15x^2i-3y^2j+2zk,\\\\at\ point\ (-1,2,1),\\\\gradf=15i-12j+2k\\\\direction \ derivative= gradf. \vec a/|a|\\\\D.D=(15i-12j+2k)(-i+2j+k)/(\sqrt6)\\\\D.D=(-15-24+2)/\sqrt6\\\\D.D=-37/\sqrt6.\\\)

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Step-by-step explanation:

coin = 50%

dice = 3/6 or 50%

hope this helps

Using it's concept, it is found that there is a 0.25 = 25% probability of obtaining a prime number and a head.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem:

The events are independent, hence the probability of both is given by:

P(A and B) = P(A) x P(B) = 0.5 x 0.5 = 0.25.

0.25 = 25% probability of obtaining a prime number and a head.

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Answer: x2+y2=169

⇒ 2xdxdt+2ydydt=0

⇒(dydt)=(dxdt)x−xy=5×−125=−12ft/s

A=12xy

⇒ dAdt=y2dxdt+x2dydt=52×5+122×−12

=25−1442=−59.5ft2/s

y=xtanθ

⇒ dydt=(tanθ)dxdt+xsec2θdθdt

⇒ −12=5×512+12×169122dθdt

⇒ 16912dθdt=−12−2512

⇒ dθdt=144169−25169=−1rad/s

Step-by-step explanation:

Answer:

students 4:9

teachers 5:9

Step-by-step explanation:

students 32:72 = 4:9

teachers 40:72 = 5:9

Answer:

y = x + 2

Step-by-step explanation:

sgshsbkabakqsbshajab

This cοnfirms that each οbtuse angle measures 135°, since their sum is equal tο the remaining part οf the 360° angle.

The sum οf the measures οf the angles arranged arοund pοint B is 360°.  the twο acute angles and the twο οbtuse angles must add up tο 360°, and we knοw the measure οf the acute angles, sο we can subtract their sum frοm 360° tο find the sum οf the twο οbtuse angles. Prοtractοr cοnfirms that each οbtuse angle measures 135°, since their sum is equal tο the remaining part οf the 360° angle.

1. The sum οf the measures οf the angles arranged arοund pοint B is 360°.

2. There are fοur angles arranged arοund pοint B, and twο οf them are acute angles with a measure οf 45° each (since the trapezοid has twο right angles). Therefοre, the sum οf the measures οf just the twο οbtuse angles arranged arοund pοint B is:

360° - 2(45°) = 270°

This is because the twο acute angles and the twο οbtuse angles must add up tο 360°, and we knοw the measure οf the acute angles, sο we can subtract their sum frοm 360° tο find the sum οf the twο οbtuse angles.

3. Tο find the measure οf each οbtuse angle, we can divide the sum οf their measures (270°) by the number οf angles (2):

270° ÷ 2 = 135°

Therefοre, each οbtuse angle with vertex B measures 135°.

We cοuld alsο use a prοtractοr tο measure οne οf the οbtuse angles directly and cοnfirm that it measures 135°, οr we cοuld use the fact that the sum οf the measures οf all fοur angles arοund pοint B must be 360° tο check οur answer:

= 2(45°) + 2(135°)

= 90° + 270°

= 360°

Therefοre, This cοnfirms that each οbtuse angle measures 135°, since their sum is equal tο the remaining part οf the 360° angle.

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Answer:

2 chairs

Step-by-step explanation:

He used 1/4 cans of paint for each chair, and used 1/2 cans of paint for some chairs.

Since he used 1/2 cans of paint, we can say that he painted 2 chairs.

The function g(x) is equal to g(x) = 4 - | x - 2 |.

A network's connection between lines and points is represented mathematically by a graph. A graph is made up of some points and connecting lines. The length of the lines and the placement of the points are irrelevant. A node is a name for each element in a graph.

Function: An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable.

Consider the function,

f(x) = 4 - | x + 1 |

Now, the graph of function f(x) is shifted 3 units horizontally toward the positive x-axis.

Therefore,

g(x) = 4 - | x + 1 - 3|

g(x) = 4 - | x - 2 |

Hence, the value of the function g(x) = 4 - | x - 2 |

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Answer:

it is algebraic expression

Answer:

Data A - 5

Data B - 5

Data C - 5

Data D - 6

Step-by-step explanation:

Data A,

Graph for the data shows that there is a distinct value of y (output value) for every input value of x.

Therefore, Data A is a function.

Data B,

Each ordered pair shows exactly one output value for each input value.

Therefore, Data B represents a function.

Data C,

For each input value there is exactly one output value.

Therefore, Data C represents a function.

Data D,

From the given table,

For x = -1 there are two output values y = 27, 39

For x = -2 output values are y = 45, 21

Since for these input values there are two output values, Data D will not be a function.

Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.

Please refer to the image instead of the graph, which is related to it.

The graphic displays a graph.

A parabola is seen on the graph.

The vertical line test determines if a graph can be a function, as is common knowledge.

The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

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Answer:

r² = (9 - 4)² + (6 - 4)² = 5² + 2² = 25 + 4 = 29

So the equation of this circle is

(x - 4)² + (y - 4)² = 29

Answer:

X-3, not sure. Try that.

Answer:

\(3(x - 1)\)

Step-by-step explanation:

Thinked number = x

take away = -1

\(x - 1\)

multiply it by 3

\(3(x - 1)\)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

2x⁴ + x³ - 3x² - 4x + 2

4

Step-by-step explanation:

Given functions:

     f(x) = 2x⁴ - 3x² - 2x + 5

     g(x)  = x³ - 2x - 3

Unknown:

Sum of the polynomials = ?

Order of the sum  = ?

Solution:

The sum of the polynomial is expressed as;

    f(x) + g(x) = 2x⁴ - 3x² - 2x + 5 +  x³ - 2x - 3

                   = 2x⁴ + x³ - 3x² - 2x - 2x + 5 -3

                   = 2x⁴ + x³ - 3x² - 4x + 2

The order of the sum is the highest power which 4.

This polynomial is of the 4th order.

The equation that represents the situation is $160.40 = $100 + $7.55h.

An equation is a statement that consists of numbers or letters and an equal to sign. The amount earned is a function  of the tip, hours worked and the pay per hour.

The form of the equation is:

Total amount earned =tip + (amount earned peer hour)

$160.40 = $100 + ($7.55 x h)

$160.40 = $100 + $7.55h

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Consider the same figure as given above. It is observed that DP/PE = DQ/QF and also in the triangle DEF, the line PQ is parallel to the line EF.

So, ∠P = ∠E and ∠Q = ∠F.

Hence, we can write: DP/DE = DQ/DF= PQ/EF.

The above expression is written as

DP/DE = DQ/DF=BC/EF.

It means that PQ = BC.

Hence, the triangle ABC is congruent to the triangle DPQ.

(i.e) ∆ ABC ≅ ∆ DPQ.

Thus, by using the AAA criterion for similarity of the triangle, we can say that

∠A = ∠D, ∠B = ∠E and ∠C = ∠F.

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The difference between the linear and projectile motion is that "Linear-motion" refers to motion of object in a "straight-line", while "projectile-motion" refers to motion of an object that is thrown into air, in a curved path.

In linear motion, the object moves along a straight line, with its velocity and acceleration aligned in the same direction. The object's speed and direction may change, but its motion remains linear.

In projectile motion, the object moves along a curved path under the influence of gravity. The object is launched into the air with an initial velocity, and then gravity causes it to follow a parabolic path until it lands back on the ground. The motion of the object is influenced by both its initial velocity and the force of gravity.

In both linear and projectile motion, the "horizontal-component" of velocity will usually remain constant because there is no external force acting on the object in horizontal direction, and thus no acceleration.

Therefore, the object will continue to move at a constant velocity in the horizontal direction, as long as there is no external force acting on it.

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Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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Answer:

Step-by-step explanation:

Select

B

C

D

I hope this helps!

Answer:

D is correct

Step-by-step explanation:

because 7×2=14 and 7 times as 2 is 14

please mark me as brainliest answer

The general solution of the heat equation with the given boundary conditions in terms of the Fourier series, u(x,0) = x = ΣA_n sin(nπx/L) ⇒ A_n = 2/L ∫₀^L x sin(nπx/L) dx.

In the problem, we have the Heat equation and boundary conditions as shown below:∂u/∂t = k ∂²u/∂x² ; 0 < x < L ; t > 0u(0,t) = 0 ; u(L,t) = 0u(x,0) = x ; 0 < x < L

We have to solve the above heat equation with the given boundary conditions.

Now, let us use the separation of variables method to obtain a solution of the Heat Equation u(x,t).

We propose a solution u(x,t) in the form of a product of two functions, one of x only and one of t only. u(x,t) = X(x)T(t)

Substituting the above equation in the Heat Equation and rearranging the terms, we get:

X(x)T'(t) = k X''(x)T(t) / X(x)T(t) X(x)T'(t)/T(t)

= k X''(x)/X(x)

= λ (constant)

As both sides of the above equation are functions of different variables, they must be equal to a constant.

Hence, we get two ordinary differential equations:

1. X''(x) - λ X(x) = 0   .......(1)

2. T'(t)/T(t) + λk = 0   .......(2)

Solving ODE (1), we get:

X(x) = A sin(sqrt(λ)x) + B cos(sqrt(λ)x)

As per the boundary conditions given, we have:

u(0,t) = X(0)T(t) = 0

⇒ X(0) = 0...   .......(3)

u(L,t) = X(L)T(t)

= 0

⇒ X(L) = 0...   ...... (4)

From equations (3) and (4), we get: B = 0, and

sin(√(λ)L) = 0

⇒ √(λ)L

= nπ ; λ

= (nπ/L)² ; n = 1,2,3,....

Substituting λ into equation (2), we get:

T(t) = C exp(-λkt) = C exp(-n²π²k/L²)t, where C is a constant of integration.

Substituting λ into the expression for X(x),

we get: \(Xn(x) = A_n sin(nπx/L)\) where \(A_n\) is a constant of integration.

We can write the general solution as: \(u(x,t) = ΣA_n sin(nπx/L) exp(-n²π²k/L²)t.\)

The constants A_n can be obtained by the initial condition given. We have:

u(x,0) = x

= ΣA_n sin(nπx/L)

⇒ \(A_n = 2/L ∫₀^L x sin(nπx/L) dx.\)

Now, we have obtained the general solution of the heat equation with the given boundary conditions in terms of the Fourier series.

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Answer:

That would be a model.

Step-by-step explanation:

Like climate scientists use a model of the Earth's processes to make predictions of climate change.

Answer:

g(3)=11

Step-by-step explanation:

g(3)=3(3)+2

3*3=9

9+2=11

Step-by-step explanation:

To find the angle between a line and the x-axis, we need to calculate the slope of the line first. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Using the points (-2, 2) and (8, 9), we can substitute the values into the formula:

m = (9 - 2) / (8 - (-2))

= 7 / 10

= 0.7

The slope of the line is 0.7. The angle between the line and the x-axis can be found using the inverse tangent (arctan) function. The tangent of an angle is equal to the slope of the line, so we can write:

tan(θ) = 0.7

Taking the inverse tangent of both sides, we find:

θ = arctan(0.7)

Using a calculator, we can evaluate this to be approximately:

θ ≈ 35.87 degrees

Therefore, the angle between the line and the x-axis is approximately 35.87 degrees.

The researcher's approach is known as stratified random sampling, where the population is divided into age groups and a random sample is chosen from each group before combining them into a single sample.

This is known as a stratified random sampling technique. Stratified random sampling involves dividing the population into distinct subgroups or strata based on certain characteristics, such as age groups in this case. The researcher then selects a random sample from each stratum, ensuring representation from each subgroup. Finally, the samples from each stratum are combined to form a single sample that represents the entire population.

The purpose of using stratified random sampling is to ensure that each subgroup is adequately represented in the final sample. By dividing the population into strata and selecting random samples from each, the researcher can obtain a sample that reflects the diversity of the population's characteristics, such as age distribution. This approach helps to minimize sampling bias and improve the accuracy of the sample's representation of the overall population.

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The total value of all the coins in Uncle Ralph's pocket is $3.35, which is represented by the number of each sort of coin.

addressing a problem by a method or action; giving a justification for the remedy. a number of different variable values that all agree with an equation, specifically The solution is any value of a variable in an equation that makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation equal and so fulfills the equality. The act of solving an equation entails locating its solution or solutions. One approach to express a solution's concentration is as a percentage of a solute in the solvent. The mass of the solute to the mass of the solution ratio or the mass of the solute to the mass of the solution ratio are two other ways to calculate the percentage.

given

q represents the number of quarter

17 - q represents the number of dimes

0.25q + 0.10(17 - q) = 3.35

The total value of all the coins in Uncle Ralph's pocket is $3.35, which is represented by the number of each sort of coin.

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"Vary directly" is another way of saying "directly proportional".

In simple English, this just means, as one increases, the other increases too.

a = 6

b = 4

The question says find out what a is when b is 16.

First, lets find how many times larger b has gotten.

16/4 = 4

b had gotten 4 times bigger to go from b=4 to b=16

If a is varying directly, it means that it will also get 4 times bigger.

Therefore, a = 6 x 4 = 24

Answer:

C. -0.7

Explanation:

Given the equation:

First, distribute the bracket on the left-hand side:

The number that makes the given expressions equivalent is -0.7.

The correct choice is C.

The definitions in Column 1 match with the following vocabulary words in Column 2:

A collection of methods for collecting, displaying, analyzing, and drawing conclusions from data: Descriptive statistics

The definitions in Column 1 correspond to specific vocabulary words from Column 2. Each definition describes a statistical concept or method. The corresponding vocabulary words are as follows:

A collection of methods for collecting, displaying, analyzing, and drawing conclusions from data: Descriptive statistics.

The most common result (the most frequent value) of a test, survey, or experiment: Mode.

The score that divides the results in half - the middle value: Median.

The average of a distribution is equal to the summation of x divided by the number of observations: Mean.

The difference between the highest and lowest score in a distribution: Range.

Probability distributions whose graphs can be approximated by bell-shaped curves: Normal distribution.

The average of the squared distances of the data values from the mean: Variance.

The positive square root of the variance: Standard deviation.

The number of standard deviations a point is from the population mean: z-score.

The branch of statistics that involves organizing, displaying, and describing data: Statistics.

These vocabulary words are fundamental in statistical analysis and are used to describe and interpret data in various fields of study

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