find the derivative of the function at p0 in the direction of u. g(x,y)=(x-y)/(xy 3)

The learning-curve exponent (b) is approximately 0.291, and the learning-curve rate (R) is approximately 1.047. The time required to build the first house (T1) can be calculated using the learning curve formula. If the learning-curve percentage is changed to 76%, starting from the Nth house, the time for construction per house would be less than half the construction time for the third house. The value of N can be determined by solving the equation.

he learning-curve exponent (b) is approximately 0.291, and the learning-curve rate (R) is approximately 1.047.

The learning curve follows a mathematical relationship where the time required to complete a task decreases as more units are produced. The formula for the learning curve is T = T1 * \((N^b)\), where T is the time required for N units, T1 is the time required for the first unit, N is the cumulative number of units, and b is the learning-curve exponent.

To find the learning-curve exponent (b), we can use the given information that the construction team spent 18% less time building the seventh house compared to the third house. This can be expressed as:

T7 = T3 * \((7^b)\) - 0.18 * T3

Since we know that T7 is 0.82 times T3, we can substitute these values into the equation:

0.82 * T3 = T3 * \((7^b)\) - 0.18 * T3

Simplifying the equation, we get:

0.82 =\(7^b\) - 0.18

Solving for b, we find that b is approximately 0.291.

To calculate the learning-curve rate (R), we can use the formula R = \(2^(^1^-^b^)\). Plugging in the value of b, we get R is approximately 1.047.

If the last house built required 2,500 manual labor hours, we can use the learning curve formula to calculate the time required to build the first house (T1). We know that N = 18 and T = 2,500. Rearranging the formula, we have:

T1 = T / (N^b)

Plugging in the values, we get:

T1 = 2,500 / (18^0.291)

Calculating T1, we find that the time required to build the first house is approximately 2,808.

To determine the value of N when the learning-curve percentage is changed to 76% starting from the Nth house, where the time for construction per house would be less than half the construction time for the third house, we can use the learning curve formula again. In this case, the time required for the Nth house would be 0.5 times the time required for the third house:

T3 * (N^b) * 0.76 = 0.5 * T3

Simplifying the equation, we get:

N^b = 0.5 / 0.76

Taking the logarithm of both sides of the equation, we can solve for N:

b * log(N) = log(0.5 / 0.76)

log(N) = log(0.5 / 0.76) / b

N = 10^(log(0.5 / 0.76) / b)

Calculating N using the given values of b, we find that N is approximately 12.

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To set up the artificial variable LP (Phase I LP) for the given problem, we introduce an artificial variable, LP, to the objective function with a coefficient of 1. The artificial variable is used to identify infeasible solutions.

To set up the artificial variable LP (Phase I LP), we modify the objective function as follows:

Maximize Z = 4x1 + 7x2 + x3 + LP

The artificial variable LP is introduced to the objective function with a coefficient of 1. This allows us to track its value during the iterations.

The initial constraints remain the same:

2x1 + 3x2 + x3 = 20

3x1 + 4x2 + x3 + x4 = 40

8x1 + 5x2 + 2x3 - x5 = 70

The initial basic variables (BV) are the slack variables corresponding to the equality and inequality constraints, namely, x3 and x4. The artificial variable LP is initially a non-basic variable.

The initial artificial variables' basic variable (BVB) values are set to the right-hand side values of the constraints:

x3 = 20

x4 = 40

The initial artificial variable LP's value is set to 0.

Next, the artificial variable LP is selected as the entering variable, as it has a positive coefficient in the objective function. To determine the leaving variable, we perform the ratio test using the ratios of the right-hand side values and the entering column values (coefficients of LP) for the respective constraints.

The leaving variable is determined based on the minimum ratio, ensuring that the corresponding row represents a valid pivot element. If no valid pivot element is found, the problem is infeasible.

This completes the setup of the artificial variable LP (Phase I LP) without performing a complete pivot. Further steps would involve applying the simplex method and iteratively pivoting to find the optimal solution or identify infeasibility.

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Answer:

7x(y^3-11)

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same. The formula for this property can be expressed in real numbers a, b and c. If a × c = b × c.

Property of Equality:

The equivalence property describes the relationship between two equal quantities. If you apply a math operation to one side of the equation, you must also apply it to the other side of the equation to maintain balance.

That is, a property that does not change the truth value of an equation or does not affect the equivalence of two or more quantities is called an equality property. These equality properties help solve various algebraic equations and define equivalence or equilibrium relationships.

Multiplicative Property of Equality:

According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same.

The formula for this property can be expressed as for the real numbers a, b, and c.

If a × b, then, a × c = b × c.

In algebra, the multiplicative property of an equation helps extract unknown terms from an equation. Because multiplication and division are opposites of each other.

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Answer:

Nora spent 102$ yogurt and 3$ of ice cream

Answer:

$99

Step-by-step explanation:

[Ice cream] 17(6) = 102

[Yogurt] 3(1) = 3

[Difference] 102 - 3 = 99

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

the answer might be 'scariest zoo animal'

Step-by-step explanation:

hope this helps

Answer:

i think the answer is "favorite zoo animal"

Step-by-step explanation:

because one thing that can't be an answer is "scariest zoo animal" because otter has the most vote and a lion or bear is scarier than a otter, so it can't be "scariest class pet* cause of the same reason. it can either be *favorite class pet" or "favorite zoo animal". if you see, in that on if we see the chart lion has the second highest votes and lion can't be a class pet, so it is "favorite zoo animal"

Answer:

x = 3

Step-by-step explanation:

x+5=8

x+5-5=8-5

X=3

Answer:

x = 3

Step-by-step explanation:

basically 2 ways

1st: Transposing

1) x + 5 = 8

2) transpose or transfer +5 to the other side

NOTE: transposing numbers and variables switches the signs (positive -> negative and vice versa)

3) x = 8 - 5

x = 3

2nd: Property of Equality (whatever u do one one side, you do the same to the other)

1) x + 5 = 8

2) x + 5 - 5 = 8 - 5

x = 3

the main focus is to isolate x, or to make it be alone in one side of the equation

Answer:

b = -1.4

Step-by-step explanation:

Answer:

\({x}^{2} - 10x + 25\)

Step-by-step explanation:

For this problem, we can break the equation into (x - 5) use FOIL. First, Outer, Inner, Last.

(x - 5) (x - 5)

First, multiply the two Xs together.

X * X =

\( {x}^{2} \)

Now, the outer numbers and values.

X * -5 =

\( - 5x\)

Then, it's the inner numbers and values.

-5 * x =

\( - 5x\)

Finally, multiply the last numbers.

-5 * -5 =

\( 25\)

Now that we have multiplied all of the values, we can put the answers from FOIL together.

\( {x}^{2} - 5x - 5x + 25\)

Now, add any like terms.

\( - 5x - 5x = - 10x\)

The answer is

\( {x}^{2} - 10x + 25\)

Answer:

Im not sure abt the A part. BUT I do know b and c.

Answer: B) 3x^2-13x-30=0

(3x+5) (x-6)=0

3x+5=0          x-6=0

3x=-5               x-6=0

Answers that are the Roots: [ x=-5/3]    and [x=6]

Answer: C) Set factors equal to 0 to find the roots.

Step-by-step explanation:

Don't really need one but hope this helps.

Answer:

5/6 in simpleest form is 5/6

It is already the lowest it can go

Answer:

Step-by-step explanation:

5/ 6  is already in the simplest form. It can be written as 0.833333 in decimal form (rounded to 6 decimal places).

Find the GCD (or HCF) of numerator and denominator

GCD of 5 and 6 is 1

Divide both the numerator and denominator by the GCD

5 ÷ 1

6 ÷ 1

Reduced fraction:  

5/ 6

Therefore, 5/6 simplified to lowest terms is 5/6.

The amount that Sandy has to pay to buy the cell phone is 1.07x dollars.

This is a question of percentages.

Percentage

Percentage means a number or a ratio expressed in terms of fractions of 100. It is denoted using the percentage sign “%”.

It is given in the question that:-

Price of cell phone = x dollars

Additional sales tax = 7 %

We have to find the amount, in dollars, that Sandy had to pay to buy the cell phone.

Total amount Sandy had to pay for the cell phone = x + 7 % of x

x + (7/100)x = x + 0.07x = 1.07x dollars.

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Answer:

14/18

Step-by-step explanation:

Answer:

No

7x7=49 and 8x8=64, 56 does not have an exact square root

Answer:

34/1000

Step-by-step explanation:

34÷1000 equals 0.034

Answer:

Step-by-step explanation:

True.

An enumerator is a special data type in some programming languages that allows us to give names to integer values, making the code more readable and easier to maintain.

However, an enumerator cannot be directly assigned to an int variable because they are not compatible data types. An int variable can only store integer values, while an enumerator is a named constant that represents an integer value.

To assign an enumerator to an int variable, we need to explicitly cast the enumerator to an int using type conversion.

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Answer:

-24

Step-by-step explanation:

The SAS standard for similarity of triangles states that triangles are similar if two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent.

Statement : The statement can be expressed as follows:

If two triangles ABC and DEF are such that

∠A=∠D and AC /DF =AB/DE

then △ABC∼△DEF

Proof :

Given: △ABC and △DEF are such that

AC /DF =AB/DE and ∠A=∠D

To Prove : △ABC∼△DEF

Construction : Draw a line PQ such that DP= AB , DQ= AC

In △ABC and △DPQ

AB = DP ( by construction)

DQ= AC ( by construction)

∠A=∠D (given)

=> △ABC ≅△DPQ (by SSA congruence property)

AB/DE = AC/DF (given )

=> DP/DE = DQ/DF ( using AB = DP ; DQ= AC)

=> PQ||EF (by converse of B.P.T)

Now , ∠P =∠E and ∠Q =∠F ( by corresponding angles)

△DEF ≅ △DPQ (Using AAS congruence )

=> △ABC ∼△DEF ( because two congrunt triangles are always similar )

Hence proved .

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6 weeks from now, you will have $215 in your bank account

The given parameters are:

b = 60 + (20+6)w

When the account balance is $215, we have

60 + (20+6)w = 215

Subtract 60 from both sides

(20+6)w = 155

This gives

26w = 155

Divide both sides by 26

w = 5.96

Approximate

w = 6

Hence, 6 weeks from now, you will have $215 in your bank account

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The simplified expression is -48r² + 40r. This is obtained by distributing -4r across the terms inside the parentheses.

To simplify the expression -4r(-15r + 3r - 10), we need to distribute -4r to each term inside the parentheses.
-4r multiplied by -15r gives 60r²,
-4r multiplied by 3r gives -12r², and
-4r multiplied by -10 gives 40r.

Combining these terms, we have 60r² - 12r² + 40r. Simplifying further, we get -48r² + 40r.

Thus, the simplified expression is -48r² + 40r. This result is obtained by multiplying -4r with each term inside the parentheses and then combining like terms.

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The power \( m \) in the Paris' crack propagation rate equation for the 7075-T6 alloy is 3.63, and the pre-exponential constant \( A \) is 0.29 x 10^(-9) MPa.m^(0.5). By analyzing this data, the values of \( m \) and \( A \) can be obtained.

Paris' crack propagation rate equation relates the crack growth rate da/dN to the stress intensity factor range \(\Delta K\) during fatigue loading. It can be expressed as da/dN = A(\Delta K)^m, where \( A \) is the pre-exponential constant and \( m \) is the power. To determine \( m \) and \( A \), the equation requires experimental data. Figure 3 likely represents the experimental data for crack growth rate versus stress intensity factor range.

For the 7075-T6 alloy, the power \( m \) in Paris' equation is 3.63, and the pre-exponential constant \( A \) is 0.29 x 10^(-9) MPa.m^(0.5). These values describe the relationship between crack growth rate and stress intensity factor range. By analyzing this data, the values of \( m \) and \( A \) can be obtained.

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Answer:

See Explanation

Step-by-step explanation:

Given [Missing Information]

\(Red = 12\)

\(Blue = 10\)

\(Green = 15\)

\(Yellow = 13\)

Way 1:

Add up the total marbles that are not red.

\(Not\ Red = Blue + Green + Yellow\)

\(Not\ Red = 10 + 15 + 13\)

\(Not\ Red = 38\)

Divide by total marbles to get the probability;

\(Probability = \frac{Npt\ Red}{Total}\)

\(Probability = \frac{38}{38 + 12}\)

\(Probability = \frac{38}{50}\)

\(Probability = 0.76\)

Way 2:

Calculate the probability of choosing red

\(P(Red) = \frac{Red}{Total}\)

\(P(Red) = \frac{12}{50}\)

\(P(Red) = 0.24\)

Apply complement rule (i.e. subtract it from 1)

\(P(Not\ Red) = 1 - P(Red)\)

\(P(Not\ Red) = 1 - 0.24\)

\(P(Not\ Red) = 0.76\)

Answer:

27

Step-by-step explanation:

You can easily find it by counting how much line are between point and and point B

there are 27 lines (including the line on point B)

The total possible combination of ordered pairs from the element of the given set is 9

To find the ordered pairs of the equation, we simply have to find the total possible combinations from the element of the set.

The element of set given is x ∈ {-1, 0, 1}

The possible combinations of x ∈ {-1, 0, 1} are;

(-1, -1)

(-1, 0)

(0, -1)

(1, 1)

(-1, 1)

(1, -1)

(0, 1)

(1, 0)

(0, 0)

We have 9 possible ordered pairs

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Step-by-step explanation:

Tanø=opp/adj

Tan30=x/7. (× b.s 7)

x=7Tan30

x= 4.04

Answer:

2x+1

Step-by-step explanation:

\((9x-3)-(7x-4)\)

\(9x-3-7x+4\)

\(2x+1\)