Find the four second partial derivatives and evaluate each at the given point.
f(x,y)=x3+3xy3−4y, Point: (4,3)

Answers

Answer 1

The four second partial derivatives at the given point f(x,y)=x3+3xy3−4y, Point: (4,3) are

f_xx(4, 3) = 24f_xy(4, 3) = 81f_yx(4, 3) = 81f_yy(4, 3) = 216

To find the four second partial derivatives of the given function f(x, y) = x^3 + 3x*y^3 - 4y, we need to find the second order partial derivatives with respect to x and y.

Step 1: Find the first partial derivatives.
f_x(x, y) = ∂f/∂x = 3x^2 + 3y^3
f_y(x, y) = ∂f/∂y = 9x*y^2 - 4

Step 2: Find the second partial derivatives.
f_xx(x, y) = ∂^2f/∂x^2 = 6x
f_xy(x, y) = ∂^2f/∂x∂y = 9y^2
f_yx(x, y) = ∂^2f/∂y∂x = 9y^2
f_yy(x, y) = ∂^2f/∂y^2 = 18x*y

Step 3: Evaluate the second partial derivatives at the given point (4, 3).
f_xx(4, 3) = 6(4) = 24
f_xy(4, 3) = 9(3^2) = 81
f_yx(4, 3) = 9(3^2) = 81
f_yy(4, 3) = 18(4)(3) = 216

So, the four second partial derivatives at the given point (4, 3) are:

f_xx(4, 3) = 24
f_xy(4, 3) = 81
f_yx(4, 3) = 81
f_yy(4, 3) = 216

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Related Questions

Harlan is building a fence. After he sets the corner post, he uses 2 eight-foot posts, 4 braces, and 48 feet of paneling for every 12 feet of fence. Harlan needs to build 60 feet of fence today and he has 208 feet of paneling. How many more feet of paneling does he need?

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32 because Eva told me

Can anyone help me with this pls :)

Can anyone help me with this pls :)

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it should be around -6 and -5 but i’m not very sure

Mr. Siefkes bought 8 grapefruits. Each grapefruit weighed 2.8 ounces. How many pounds did he buy?
(16 ounces = 1 pound)

Answers

Answer:

1.4 pounds

Step-by-step explanation:

Answer:

1.4

Step-by-step explanation:

8x2.8 = 22.4

22.4/16 = 1.4 pound

Find the length of x 10/15=x/20

Answers

I think 40/3 is the answer you’re looking for.

Find the measure of the missing angle.

O 115
0 123
O 58
180

Answers

I think it would help if you included a picture of the question or at least the angles/sides you know so that I can solve it.

please tell the function equation as well too

please tell the function equation as well too

Answers

Answer:

A = Rate of change is y = 4x

This is because it is set up as y/x and for the graph B = y = 3x.

Function A is greater in change than Function B

Because if you substitute x for 1.

A would be 4.

B would be 3.

Sophia's dad paid $43.25 for 12.5 gallons of gas. What is the cost of one gallon of gas

Answers

Answer:

It is $3.46

Step-by-step explanation:

Hope this helped have an amazing day!

A forest covers 54,000 acres. A survey finds that 0.4​% of the forest is​ old-growth trees. How many acres of​ old-growth trees are​ there?

Answers

Answer:

216 acres

Step-by-step explanation:

54,000 x 0.4% = 216

next term in each sequence 2,3,4,0,​

Answers

Answer:

1 is the answers for the question

Step-by-step explanation:

please mark me as brainlest

Answer:

1

Step-by-step explanation:

2,3,4,0,1,2,-2,-1,0...

Feel free to mark this as brainliest! :D

Paul will receive payments of 50 every three months for 10 years. The first payment will be made 3 months from today. The annual effective interest rate is 8%. Calculate the present value of the annuity.
A 1,032.89
B 1,272.23
C 1,367.77
D 1,381.63
E 1,992.06

Answers

The annual effective interest rate is 8%, the present value of the annuity,

is option C: $1,367.77

To calculate the present value of the annuity, we can use the formula for the present value of a series of periodic payments:

\(\[ PV = PMT \times \left(1 - (1 + r)^{-n}\right) / r \]\)

Where:

- PV is the present value of the annuity,

- PMT is the payment amount,

- r is the interest rate per compounding period, and

- n is the total number of compounding periods.

In this case, Paul will receive payments of $50 every three months for 10 years, which is a total of 40 payments (since there are 4 quarters in a year and 10 years equals 40 quarters).

The interest rate is 8% per year, so we need to adjust it for the compounding period. Since the payments are made every three months, the interest rate per quarter is 8% divided by 4, which is 2%.

However, since the first payment will be made 3 months from today, we need to discount the first payment by the interest earned during that period. To do this, we calculate the present value of the first payment using the formula:

\(\[ PV_1 = PMT \times (1 + r)^{-1} \]\)

Substituting the values, we have:

\(\[ PV_1 = 50 \times (1 + 0.02)^{-1} \approx 49.0196 \]\)

Now, we can calculate the present value of the remaining annuity payments using the adjusted interest rate and the total number of periods (39 remaining payments):

\(\[ PV = 50 \times \left(1 - (1 + 0.02)^{-39}\right) / 0.02 \approx 1,367.77 \]\)

Therefore, the correct answer is option C: $1,367.77.

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write the trigonometric expression in terms of sine and cosine

Answers

The trigonometric simplified form of sinθ secθ is tanθ.

To write the trigonometric expression sinθ secθ in terms of sine and cosine, we can use the reciprocal identity for secant:

secθ = 1/cosθ

Substituting this into the expression, we have:

sinθ secθ = sinθ (1/cosθ)

Now, to simplify the expression, we can multiply sinθ by 1/cosθ:

sinθ (1/cosθ) = sinθ/cosθ

Using the quotient identity for tangent, we can rewrite sinθ/cosθ as tanθ:

sinθ/cosθ = tanθ

Therefore, the simplified form of sinθ secθ is tanθ.

The complete question is:

Write the trigonometric expression in terms of sine and cosine, and then simplify.

sinθ secθ

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help meh fvghdbskjwdjcbhfvdcbjskalm

help meh fvghdbskjwdjcbhfvdcbjskalm

Answers

Answer:

D

Step-by-step explanation:

Proportional relationships go through the origin on the graph so we can eliminate A and B. Also the x and y coordinates have the same ratio so the answer is D because 2:3 = 4:6 = 8:12 = 12:18.

the graph of y=3x^4-16x^3+24x^2+48 is concave down for

Answers

The graph of y=3x^4-16x^3+24x^2+48 is concave down for x values greater than or equal to 0.

The graph of y=3x^4-16x^3+24x^2+48 is an example of a polynomial function. To determine the concavity of a polynomial function, we must first identify the intervals where the function is increasing and decreasing. In this case, the function is increasing for all x values greater than or equal to 0.

Next, we must find the second derivative and determine the intervals where the second derivative is negative. If the second derivative is negative, then the graph is concave down. For this polynomial, the second derivative is y'' = -48x + 48, which is negative for all x values greater than or equal to 0. This means that the graph of y=3x^4-16x^3+24x^2+48 is concave down for all x values greater than or equal to 0.

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what is the correlation

what is the correlation

Answers

Answer: moderate, C, B

Step-by-step explanation:

A)  A shows a moderate negative correlation.  It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation.  It is also negative because it has a negative slope

B) C shows the strongest correlation because the points around the line are tight and close.

C)  B should not have been drawn.  The  correlation is very weak.  You do know where the line should be because the points are all over the place.

Picture below has question/answer choices!!

Picture below has question/answer choices!!
Picture below has question/answer choices!!

Answers

The statements that is true about the similarity of the two triangles the option D

D. ΔMNO and ΔJKL are not similar triangles

What are similar triangles?

Similar triangles are triangles which have proportional corresponding sides

The parameters in the question are;

The length of segment MN = 20

Length of segment NO = 12

Length of segment OM = 25

Measure of angle ∠O = 56°

Length of segment LJ =- 15

Length of segment JK = 12

Length of segment KL = 9

Measure of angle ∠L = 56°

Two triangles are similar if the ratio of two sides on one triangle are proportional to two sides of another triangle, and the included  angle between the two sides are congruent

The included angle between sides ON and MO on triangle MNO is congruent to the included angle between segment LK and JL in triangle JKL

However, the ratio of the sides  LK to ON and JL to MO are;

9/12 ≠ 15/25

Therefore, the triangles are not similar

The correct option is option D

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Which is shown below?
12 > 11
A. An operation
B. An inequality
C. An expression
D. An equation
SUBMIT

Answers

Answer:

B Inequality

Step-by-step explanation:

since 12 is greater than 11 they are not equal

> this sign is the greater than sign

Make a table as y=x^2.

Answers

Answer:

-0

Step-by-step explanation:

Factorize: m^4-3m^2 pls help lolz​

Answers

Answer: ^2(^2−3)

Step-by-step explanation:

Answer:

\( {m}^{4} - 3 {m}^{2} \\ {m}^{2} ( {m}^{2} - 3)\)

I hope I helped you^_^

what is the slope of the line thats models this situation ?​

what is the slope of the line thats models this situation ?

Answers

Answer:

-5

Step-by-step explanation:

Answer:

-5 is the answer

Step-by-step explanation:

-5 is the answer

All of the following are equivalent except _____.

-2 4
(-2) 4
(-2)(-2)(-2)(-2)
2 4

Answers

Answer:

\( -2 \: \: 4\)

Step-by-step explanation:

-2 4 is not an equivalent equation

Answer:

c

Step-by-step explanation:

duh

when nesting loops, the inner loop must be completely contained in the outer loop and must use a different control variable. T/F

Answers

True, when nesting loops, the inner loop must be completely contained within the outer loop and must use a different control variable.

When nesting loops, one loop is placed inside another loop. The purpose of nesting loops is to execute a set of instructions repeatedly in a structured manner. In this context, the statement is true: the inner loop must be entirely contained within the outer loop, and a different control variable must be used for each loop.

By containing the inner loop within the outer loop, we ensure that the inner loop executes its iterations every time the outer loop iterates. This nested structure allows for more complex and detailed looping patterns.

Using different control variables for the inner and outer loops is necessary to maintain independent control over their iterations. Each loop should have its own variable to track and control its progress. This distinction is crucial in preventing conflicts and ensuring that the loops function as intended.

Therefore, when nesting loops, it is essential to follow these guidelines: the inner loop must be entirely contained within the outer loop, and a distinct control variable should be used for each loop to ensure proper execution and avoid potential errors.

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A pastry bag filled with frosting has
height 12 inches and radius 4 inches. A cake decorator can
make 15 flowers using one bag of frosting.
a. How much frosting is in the pastry bag?
Round your answer to the nearest
cubic inch.
b. How many cubic inches of frosting are
used to make each flower?

Answers

The answer of this question is b

The histogram below shows the heights, rounded to the nearest inch, of the members of the Oak High School basketball team. A. 1 inch B. 9 inches C. 7 inches D. 5 inches

The histogram below shows the heights, rounded to the nearest inch, of the members of the Oak High School

Answers

Answer:

Range of player's height = 9 inch

Step-by-step explanation:

Given:

Number of players    Height range

4                                     66-67

8                                     68 -69

14                                    70-71

9                                     72-73

1                                      74-75

Find:

Range of player's height

Computation:

Range = Maximum value - Minimum Value

Range of player's height = Maximum height of a player - height of a player

Range of player's height = 75 inch - 66 inch

Range of player's height = 9 inch

Write the equation of the line, in point-slope form. Identify (x1, y1) as the point (-2, -1). Use the box provided to submit all of your calculations and final answers.
--------------
Please explain as thoroughly as you can! I'm reeeeeeeallly bad at math, any help is extremely appreciated! :D

Write the equation of the line, in point-slope form. Identify (x1, y1) as the point (-2, -1). Use the

Answers

Answer:

y + 1 = \(\frac{1}{2}\) (x + 2)

Step-by-step explanation:

The equation of a line in point- slope form is

y - y₁ = m(x - x₁)

where m is the slope and (x₁, y₁ ) a point on the line

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) =(- 2, - 1) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = \(\frac{1+1}{2+2}\) = \(\frac{2}{4}\) = \(\frac{1}{2}\)

with point on line (x₁, y₁ ) = (- 2, - 1 ), then

y - (- 1) = \(\frac{1}{2}\) (x - (- 2) ), that is

y + 1 = \(\frac{1}{2}\)(x + 2) ← equation of line

plz
find the oppisite value of -3

Answers

Answer:

3 ig

Step-by-step explanation:

Hope this helps~! :D

Answer:

3

Step-by-step explanation:

The opposite of negative is a positive so its 3

Maggie has space in her yard for a garden. A scale drawing of the garden is shown below. The scale of the drawing is 1 cm = 2.5 ft.

Answers

Answer:

1 cm = 2.5 ft

or ,1 cm= 0.01

or,0.01= 2.5 ft

2.5/ 0.01= ft

:. ft= 250

Step-by-step explanation:

first we have to know 1cm = 0.01 then after we can divide then solve

What is the value of x?

What is the value of x?

Answers

Answer:

x =127

Step-by-step explanation:

Since this is a 6 sided figure, the sum of the interior angles is 720

128+133+112+x+120+100 = 720

Combine like terms

x+593=720

Subtract 593 from each side

x+593-593 = 720-593

x =127

Hint :

Sum of angles of the 6 sided figure = \( {720}^{o} \)

Answer:

\( {x}^{o} = {127}^{o} \)

Step-by-step explanation:

\( {x}^{o} + {112}^{o} + {133}^{o} + {128}^{o} + {100}^{o} + {120}^{o} = {720}^{o} \\ {x}^{o} + {593}^{o} = {720}^{o} \\ {x}^{o} = {720}^{o} - {593}^{o} \\ {x}^{o} = { 127}^{o} \)

Hope it is helpful....

Easy question! TOTALLY not a lot of points!

Find the scale factor for the figure below.

Easy question! TOTALLY not a lot of points!Find the scale factor for the figure below.

Answers

So the scale factor from small to larger is;
2:6= 1:3 or 1/3
or
Large to small is;
6:2 = 3:1
good luck!

Too easy XD I don’t remember how to do that T-T

the greatest common factor of the binomial 2 x − 4 is 2 . the greatest common factor of the binomial 4 x 8 is 4 . what is the greatest common factor of their product, ( 2 x − 4 ) ( 4 x 8 ) , when it has been multiplied out?

Answers

The greatest common factor of their product is 2

How to determine the greatest common factor of the product

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

GCF of 2x - 4 = 2

GCF of 4 * 8  = 4

Using the above as a guide, we have the following expressions

GCF of 2x - 4 = 2

GCF of 4 * 8  = 2  * 2

Write out the common factors

GCF = 2

This means that the GCF is 2

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11..

Solve the equation using the zero-product property.

-n(5n-4)=0


A. n= -1 or n= 4/5


B. n= 0 or n= -4/5


C. n= -1 or n= -4/5


D. n= 0 or n= 4/5

Answers

Answer:

D. n= 0 or n= 4/5

Step-by-step explanation:

Factor and set each factor equal to zero.

n

=

0

,

4

5

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

n

=

0

,

4

5

Decimal Form:

n

=

0

,

0.8

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