b) Find second order direct and cross partial derivatives of: G=-7lx;+85x+x2 + 12x; x3 – 17x," +19xź + 7x3x3 – 4xz + 120

Answers

Answer 1

The second-order cross partial derivatives ∂²G/∂x∂z = -4 and ∂²G/∂z∂x = 0.

To find the second-order partial derivatives of the given function G, we need to differentiate it twice with respect to each variable separately. Let's go step by step:

First, let's find the second-order partial derivatives with respect to x:

1. Partial derivative with respect to x:

∂G/∂x = -7 + 85 + 2x + 12x^2 - 17x^2 + 19x^2 + 7(3x^2) - 4z + 120

Simplifying this expression, we get:

∂G/∂x = 63 + 7x^2 - 4z + 120

2. Second-order partial derivative with respect to x:

∂²G/∂x² = d(∂G/∂x)/dx

Taking the derivative of the expression ∂G/∂x with respect to x, we get:

∂²G/∂x² = d(63 + 7x^2 - 4z + 120)/dx

∂²G/∂x² = 14x

So, the second-order partial derivative with respect to x is ∂²G/∂x² = 14x.

Next, let's find the second-order cross partial derivatives:

1. Partial derivative with respect to x and z:

∂²G/∂x∂z = d(∂G/∂x)/dz

Taking the derivative of the expression ∂G/∂x with respect to z, we get:

∂²G/∂x∂z = d(63 + 7x^2 - 4z + 120)/dz

∂²G/∂x∂z = -4

2. Partial derivative with respect to z and x:

∂²G/∂z∂x = d(∂G/∂z)/dx

Taking the derivative of the expression ∂G/∂z with respect to x, we get:

∂²G/∂z∂x = d(-4)/dx

∂²G/∂z∂x = 0

In summary, the second-order direct partial derivative is ∂²G/∂x² = 14x, and the second-order cross partial derivatives are ∂²G/∂x∂z = -4 and ∂²G/∂z∂x = 0.

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Related Questions

A basketball coach had her team practice free throws. The team attempted 308 free throws altogether. They made 6 times as many free throws as they missed. How many free throws did the team miss?

Answers

Let the number missed = x

They made 6 times that amount which would be 6x

The total of missed and made is 308:

X + 6x = 308

Combine like terms

7x = 308

Divide both sides by 7

X = 44

They missed 44

Help please it will mean a lot to me

Help please it will mean a lot to me

Answers

Answer: Whole= Part x %/100

Step-by-step explanation:

All of the other equations are algabraecally correct when solving for either part whole or percent but Whole \(\neq\) Part x %/100

In ΔDEF, the measure of ∠F=90°, the measure of ∠D=70°, and EF = 4.4 feet. Find the length of FD to the nearest tenth of a foot.

In DEF, the measure of F=90, the measure of D=70, and EF = 4.4 feet. Find the length of FD to the nearest

Answers

Answer:

1.6

Step-by-step explanation:

Answer:

1.6 degrees

Step-by-step explanation:

find series solution for the following differential equation. your written work should be complete (do not skip steps).y'' 2xy' 2y=0

Answers

To find the series solution for the differential equation y'' + 2xy' + 2y = 0, we can assume a power series solution of the form:

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

∑(n=0 to ∞) aₙn(n-1) xⁿ⁻² + 2x ∑(n=0 to ∞) aₙn xⁿ⁻¹ + 2 ∑(n=0 to ∞) aₙxⁿ = 0

We can simplify this equation by combining the terms with the same powers of x. Let's manipulate the equation step by step:

We can combine the three summations into a single summation:

∑(n=0 to ∞) (aₙ₊₂(n+1)n + 2aₙ₊₁ + 2aₙ) xⁿ = 0

Since this equation holds for all values of x, the coefficients of the terms must be zero. Therefore, we have:

This is the recurrence relation that determines the coefficients of the power series solution To find the series solution, we can start with initial conditions. Let's assume that y(0) = y₀ and y'(0) = y'₀. This gives us the following initial terms:

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Evaluate the following by writing it as a difference of two squares first:
103^2 − 97^2

Answers

Answer:

1200

Step-by-step explanation:

A difference of 2 squares factors in general as

a² - b² = (a - b)(a + b) , then

103² - 97²

= (103 - 97)(103 + 97)

= 6 × 200

= 1200

The correct answer is 1200.

What is the difference between two squares called?

Where one perfect square is subtracted from another, is called a difference of two squares. It arises when (a − b) and (a + b) are multiplied together. This is one example of what is called a special product.

A difference of 2 squares factors in general is written as

a² - b² = (a - b)(a + b) , then

103² - 97²

= (103 - 97)(103 + 97)

= 6 × 200

= 1200

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Find the sum of the geometric sequence -3,15,-75,375,... when there are 9 terms

Answers

Answer:

-976,563.

Step-by-step explanation:

The common ratio is 15/-3 = -75/15 = 375/-75 = -5.

Sum of n terms = a1. (r^n - 1) / (r - 1)

so S9 = -3 * ((-5)^9 - 1)) /  (-5 - 1)

= -976,563.

the teacher workroom has a small room used for the meetings that it shaped like a square . if one wall measures 8 feet what is the area of the floor of that meeting room

Answers

The area of the floor of the meeting room is 64 square feet.

The area of the teacher workroom is 64 feet squared

Question 8(Multiple Choice Worth 5 points)
(Experimental Probability MC)

Thirty students were surveyed about the number of siblings they have. Their results were recorded and placed on a card face down.


Outcome Frequency
1 6
2 12
3 9
4 or more 3


Determine P(2) when picking a random card.
40%
60%
70%
90%

Answers

The correct answer is a 40%

a city has 12575 residents a number president grown by 1.6% every year to the nearest whole resident what will the city population be in 2 years​

Answers

Answer:

12977.4 or just 12977

Step-by-step explanation:

someone give me the answer pls

someone give me the answer pls

Answers

The measure of the triangle for the value of x is x = 11.

What is defined as the triangle?

A triangle is a 2-dimensional closed shape with three sides, three angles, and three vertices. A triangle is a type of polygon.

The sum of a triangle's three interior angles is always 180°.The sum of any two triangle sides is always larger than the length of a third side.A triangle's area is equal to half the product of the its base and height.

For the given value of triangle;

The three angles are given as;

3x + 84x + 1184

By the sum of all angles of triangle property.

The sum of all three angles of the triangle is 180°

Thus,

3x + 8 + 4x + 11 + 84 = 180

Simplifying;

7x = 180 - 103

7x = 77

x = 11

Thus, the solution of x of the given triangle is found as x = 11.

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The equation k = 1.6d gives an approximate relationship between d miles and k kilometers. The distance between Boise, Idaho, and Reno, Nevada, is 430 miles. Express the distance in kilometers.


A.
431.6 km


B.
268.8 km


C.
688 km

Answers

Answer:  C) 688 km

=================================================

Work Shown:

k = 1.6d

k = 1.6*430

k = 688

430 miles is roughly equivalent to 688 km.

More accurately, 430 miles = 692.01792 km, so this approximation isn't too far off.

Answer: the answer is C. 688 km

RESULT

The distance between Boise, Idaho and Reno, Nevada is 688 kilometers.

Step-by-step explanation:

The equation k = 1.6d gives an approximate relationship between d miles and k kilometers. Express each distance in kilometers. the 430 miles between Boise, Idaho, and Reno, Nevada

k = 1.6 d

Where k is in kilometers n d in miles

The distance between Boise, Idaho and Reno, Nevada is 430

Substituting d= 430 we get,

k = 1.6(430)

k = 688

RESULT

The distance between Boise, Idaho and Reno, Nevada is 688 kilometers.

25.63 as expanded notation using decimals

Answers

Answer:

25.63 as an expanded notation =

2 × 10 + 5 × 1 + 6 × 0.1 + 3 × 0.01

= 20 + 5 + 0.6 + 0.03

Step-by-step explanation:

25.63 as expanded notation using decimals

This is written as:

25.63= 2 × 10 + 5 × 1 + 6 × 0.1 + 3 × 0.01

25.63 = 20 + 5 + 0.6 + 0.03

help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer: 9.7 seconds

Step-by-step explanation:

\(16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7\)

f(x)=|x-7|-|x+8|, -f(a)= ___

Answers

The value of -f(a) in the absolute value problem is; -f(a) = 15

How to Solve Absolute Value Problems?

We are given the absolute value problem;

f(x) = |x - 7| - |x + 8|

When we say absolute value, it means that it must not be negative but the positive absolute value. Thus;

f(a) = |a - 7| - |a + 8|

Since the value inside the absolute value bracket must be positive, then it means that;

f(a) = (a - 7) - (a + 8)

Provided a is not less than 7.

Thus;

-f(a) = -(a - 7 - a - 8)

= -(-15) = 15

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Write an equation for a parabola with x-intercept (-3,0) and (2,0) which pae through the point (1,-20)

Answers

An equation for a parabola with x-intercept (-3,0) and (2,0) which pass through the point (1,-20) is  "\(5x^2+5x-30\)".

parabola is a major conic section that has wide applications in science and technology. know according to the condition by following intercepts we begin with an equation

                            \(y=a(x+3)(x-2)\)

where a is any number that restricts the parabola to pass through (1,-20)

know we have to choose a for what the above equation got its require achievements. substitute (1,-20) in   \(y=a(x+3)(x-2)\) we get

                           \(-20=a(1+3)(1-2)\\\\-20=a(4)(-1)\\\\a=5\)

substituting a back in the first equation we get the equation of the parabola. so, the parabola has an equation  y= f(x)=\(5x^2+5x-30\).

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Please, I’ll give brainiest answer if you give the right one. I need his one in like 10 minutes please help.

Please, Ill give brainiest answer if you give the right one. I need his one in like 10 minutes please

Answers

Answer:

3rd one and 4 th

Step-by-step explanation: just look at them its clearly easy

There are 24 girls and 14 boys on a school bus. Three students are randomly selected and replaced. When finding the probability of selecting 2 girls and 1 boy, identify the compound events.

Answers

The probability of these three events occurring together is 14.7%.

The compound events involved in selecting 2 girls and 1 boy are:

Choosing a girl on the first draw, with a chance of 24/38 (due to the fact that, after one student has been chosen and replaced, there are 24 girls and 38 total passengers on the bus).

The likelihood of choosing a different girl on the second draw is 24/38 (because there are still 24 girls and 38 overall students on the bus after two pupils have been chosen and replaced).

Choosing a boy on the third draw, with a chance of 14/38 (due to the fact that there are now 14 boys and 38 total students on the bus after three kids were chosen and replaced).

To find the probability of these three events occurring together (i.e., selecting 2 girls and 1 boy), we multiply their probabilities:

P(2 girls and 1 boy) = (24/38) * (24/38) * (14/38)

= 0.14696019828, or approximately 14.7%.

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Please help me and example pleaseee!!!! due TODAY!

Please help me and example pleaseee!!!! due TODAY!

Answers

Answer:

i think x=4

Step-by-step explanation:

I'm too late aren't I... :c

substituting x= -3 in x2 + 5x +4 gives?​

Answers

Answer:

-2

Step-by-step explanation:

If we replace all the spots where x is with -3, we get this: (-3)^2 + 5(-3) + 4. Then we get... 9 + -15 + 4 which equals -2

An equivalent form for a conditional statement is obtained by reversing and negating the antecedent and consequent. true or false

Answers

False. The statement you described is not an equivalent form for a conditional statement. The process you mentioned, which is reversing and negating the antecedent and consequent, is known as forming the contrapositive of the statement.



A conditional statement has the form "If P, then Q," where P is the antecedent and Q is the consequent. The contrapositive is formed by negating both the antecedent and consequent, and reversing their order: "If not Q, then not P." The contrapositive is equivalent to the original conditional statement.

However, simply reversing the antecedent and consequent without negating them gives you the converse, which is "If Q, then P." The converse is not equivalent to the original conditional statement.

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Integrate by hand the following functions: adr b) (42³-2r+7) dz Upload Choose a File

Answers

The integral of (42³ - 2r + 7) dz is equal to (42³ - 2r + 7)z + C.

To integrate the function (42³ - 2r + 7) dz, we treat r as a constant and integrate with respect to z. The integral of a constant with respect to z is simply the constant multiplied by z:

∫ (42³ - 2r + 7) dz = (42³ - 2r + 7)z + C

where C is the constant of integration.

Note: The integral of a constant term (such as 7) with respect to any variable is simply the constant multiplied by the variable. In this case, the variable is z.

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did we prove the conclusion true for every isosceles triangle or only for this specific isosceles triangle?

Answers

∠A = ∠C for every isosceles triangle and not only for this specific isosceles triangle.

We are given that:

AB = BC

Now, draw a angle bisector from point B to the line AC in a way that it intersects AC at D.

Now, we get that:

∠ABD = ∠CBD ( BD is the angle bisector)

BD = BD ( common line)

So, ΔABD ≅ Δ CBD ( SAS property)

So,

∠A = ∠ C ( CPCT rule)

Also, it will be true for every isosceles triangle.

Therefore, we get that, ∠A = ∠C for every isosceles triangle and not only for this specific isosceles triangle.

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Your question was incomplete. Please refer the content below:

There is an isosceles triangle with AB = BC. Prove that ∠A = ∠C.

Did we prove the conclusion true for every isosceles triangle or only for this specific isosceles triangle.

did we prove the conclusion true for every isosceles triangle or only for this specific isosceles triangle?

The table to the right lists probabilities for the corresponding numbers of girls in three births. What is the random variable, what are its possible values, and are its values numerical?

Answers

The true statement is (b) the random variable is x, the possible values are 0 to 3 and the values are numerical

How to determine the true statement?

The table is added as an attachment

From the attached image, we have:

Number of girls (x)          P(x)

0                                         0.125

1                                         0.375

2                                         0.375

3                                         0.125

In the above, the random variable is x, while P(x) represents its probabilities.

Also, the possible values are 0 to 3 as shown in the table.

0 to 3 are numerical digits, and the values are numerical

Hence, the true statement is (b)

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The table to the right lists probabilities for the corresponding numbers of girls in three births. What

Graph of triangle ABC in quadrant 3 with point A at negative 8 comma negative 4. A second polygon A prime B prime C prime in quadrant 4 with point A prime at 4 comma negative 8. 90° clockwise rotation 180° clockwise rotation 180° counterclockwise rotation

Answers

The rotation rule used in this problem is given as follows:

90º counterclockwise rotation.

What are the rotation rules?

The five more known rotation rules are given as follows:

90° clockwise rotation: (x,y) -> (y,-x)90° counterclockwise rotation: (x,y) -> (-y,x)180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y)270° clockwise rotation: (x,y) -> (-y,x)270° counterclockwise rotation: (x,y) -> (y,-x).

The equivalent vertices for this problem are given as follows:

A(-8,-4).A'(4, -8).

Hence the rule is given as follows:

(x,y) -> (-y,x).

Which is a 90º counterclockwise rotation.

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Evaluate 4-0.25g+0.5h4−0.25g+0.5h4, minus, 0, point, 25, g, plus, 0, point, 5, h when g=10g=10g, equals, 10 and h=5h=5h, equals, 5.

Answers

The equation, 4 - 0.25g + 0.5h, will be evaluated as equal to: 4.

How to Evaluate an Equation?

To evaluate an equation, plug in the values of the variables in the equation and solve to get the simplified value.

Given the equation, 4 - 0.25g + 0.5h, where:

g = 10

h = 5

Substitute g = 10 and h = 5 into the equation 4 - 0.25g + 0.5h, then evaluate:

4 - 0.25(10) + 0.5(5)

Simplify

= 4 - 2.5 + 2.5

= 4 + 0

= 4

Therefore, if g = 10 and h = 5, the equation 4 - 0.25g + 0.5h, is evaluated as: 4.

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The Question:

Evaluate 4 - 0.25g + 0.5h when g = 10 h = 5.

Given the size of pizzas in a pizza restaurant is normally distributed. The average size is 9 inches, and standard deviation is 0.8 inches. What is the probability that 4 randomly selected pizza is smaller than 9.5 inches

Answers

The probability that 4 randomly selected pizzas are all smaller than 9.5 inches is approximately 0.284, or 28.4%.

To solve this problem, we first need to standardize the variable using the formula:
z = (x - μ) / σ
where:
x = 9.5 inches (the cutoff for being considered "smaller")
μ = 9 inches (the mean)
σ = 0.8 inches (the standard deviation)
z = (9.5 - 9) / 0.8 = 0.625
Next, we need to find the probability that a randomly selected pizza is smaller than 9.5 inches using a standard normal distribution table or calculator.

This probability can be denoted as P(Z < 0.625), where Z is a standard normal random variable.
The probability that all 4 randomly selected pizzas are smaller than 9.5 inches, we will raise the probability to the power of 4:

Probability = 0.734 ≈ 0.291 So, the probability that 4 randomly selected pizzas are smaller than 9.5 inches is approximately 0.291 or 29.1%.
Using a standard normal distribution table or calculator, we can find that P(Z < 0.625) is approximately 0.734.

This means that the probability of a randomly selected pizza being smaller than 9.5 inches is 0.734.
To find the probability that 4 randomly selected pizzas are all smaller than 9.5 inches, we need to multiply this probability by itself four times, since the selection of each pizza is independent of the others.

This gives:
P(4 pizzas smaller than 9.5 inches) = 0.734 = 0.284
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The probability that 4 randomly selected pizzas are all smaller than 9.5 inches is approximately 0.284, or 28.4%.

To solve this problem, we first need to standardize the variable using the formula:

z = (x - μ) / σ

where:

x = 9.5 inches (the cutoff for being considered "smaller")

μ = 9 inches (the mean)

σ = 0.8 inches (the standard deviation)

z = (9.5 - 9) / 0.8 = 0.625

Next, we need to find the probability that a randomly selected pizza is smaller than 9.5 inches using a standard normal distribution table or calculator.

This probability can be denoted as P(Z < 0.625), where Z is a standard normal random variable.

The probability that all 4 randomly selected pizzas are smaller than 9.5 inches, we will raise the probability to the power of 4:

Probability = 0.734 ≈ 0.291

So, the probability that 4 randomly selected pizzas are smaller than 9.5 inches is approximately 0.291 or 29.1%.

Using a standard normal distribution table or calculator, we can find that P(Z < 0.625) is approximately 0.734.

This means that the probability of a randomly selected pizza being smaller than 9.5 inches is 0.734.

To find the probability that 4 randomly selected pizzas are all smaller than 9.5 inches, we need to multiply this probability by itself four times, since the selection of each pizza is independent of the others.

This gives:

P(4 pizzas smaller than 9.5 inches) = 0.734 = 0.284

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bicycle rental company charges a $5 flat fee plus $1.20 per hour. Select the expression that represents renting a bicycle for h hours. A. 5h + 120h B. (5 + 1.20)h C. 5 + 1.20h D. 5h + 1.20

Answers

Answer:

a

Step-by-step explanation:

I need help with this question please

I need help with this question please

Answers

Answer:

Make the variables different then just try random numbers

Step-by-step explanation:

May someone please answer this question. I am a nice handsome growing boy who needs help. Find the area of the polygon please show work. This is due in 20 minutes

May someone please answer this question. I am a nice handsome growing boy who needs help. Find the area

Answers

Answer:

hey, can you drop the worksheets name? or you can just type the worksheets name in searchbar and you'll get all the answers :-)

Step-by-step explanation:

also im pretty sure you just multiple them

Asking again cause last time i got spam answers

Asking again cause last time i got spam answers

Answers

Answer:

A, D, and F, it has the MOST potential at A.

Step-by-step explanation:

Higher objects (with further to fall) have greater potential energy.

I'm assuming A, D, and F. Or just A.

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