an adult dolphin weighs about 1800 n. with what speed i must he be moving as he leaves the water in order to jump to a height of 2.10 m. ignore any effects due to air resistance.

a. The estimated value of ∬R​f(x,y)dA is 105

b. The estimated average value of the function f(x, y) is 7.

a. The rectangle R=[−3,6]×[−1,4] is divided into m = 2 subintervals along the x-axis and n = 3 subintervals along the y-axis. Therefore, each subinterval has a width of Δx = (6 - (-3))/2 = 9/2 and a height of Δy = (4 - (-1))/3 = 5/3.

We can calculate the midpoint of each subrectangle using the formula:

\(x_i = x_min + (i - 0.5) * \Delta x\\y_j = y_min + (j - 0.5) * \Delta y\)

where i = 1, 2, ..., m and j = 1, 2, ..., n.

Using the midpoint rule, the estimate of the double integral is given by:

∬R​f(x,y)dA ≈ Δx * Δy * ∑∑\(f(x_i, y_j)\)

where the double summation is taken over all the midpoints (x_i, y_j) of the subrectangles.

Calculate the midpoints of the subrectangles.

\(x_1 = -3 + (1 - 0.5) * (9/2) = -3 + 4.5 = 1.5\\x_2 = -3 + (2 - 0.5) * (9/2) = -3 + 9 = 6\\y_1 = -1 + (1 - 0.5) * (5/3) = -1 + (1/2) * (5/3) = -1 + 5/6 = -1/6\\y_2 = -1 + (2 - 0.5) * (5/3) = -1 + (3/2) * (5/3) = -1 + 5/2 = 9/2\\y_3 = -1 + (3 - 0.5) * (5/3) = -1 + (5/2) * (5/3) = -1 + 25/6 = 19/6\)

Evaluate the function at each midpoint.

\(f(x_1, y_1) = 2\\f(x_1, y_2) = -1\\f(x_1, y_3) = 0\\f(x_2, y_1) = 1\\f(x_2, y_2) = 3\\f(x_2, y_3) = 2\)

∬R​f(x,y)dA ≈ Δx * Δy * ∑∑\(f(x_i, y_j)\)

           = (9/2) * (5/3) * (2 + (-1) + 0 + 1 + 3 + 2)

           = (9/2) * (5/3) * 7

           = 15 * 7

           =  105

b. To estimate the average value of the function f(x, y), we can divide the double integral by the area of the rectangle R, which is A = Δx * Δy * m * n.

The average value is then given by:

f_ave ≈ (∬R​f(x,y)dA) / A

Now let's perform the calculations:

Step 1: Calculate the area of the rectangle.

A = Δx * Δy * m * n

 = (9/2) * (5/3) * 2 * 3

 = 15

Step 2: Calculate the average value.

f_ave ≈ (∬R​f(x,y)dA) / A

     = 105 / 15

     = 7

Therefore, the estimated value of ∬R​f(x,y)dA is 105 and the estimated average value of the function f(x, y) is 7.

To know more about estimated value, refer here:

https://brainly.com/question/32263011

#SPJ4

Answer:

sin θ = 22.62°

cos θ = 22.62°

tan θ = 22.62°

Step-by-step explanation:

From the diagram above

Opposite = 5

Adjacent = 12

Hypotenuse = 13

a) sin θ = Opp/Hypotenuse

sin θ = 5/13

sin θ = 0.3846153846

arc sin 0.3846153846

= 22.619864948°

Approximately = 22.62°

b) cos θ = Adjacent/ Hypotenuse

θ = 12/13

= arccos(0.9230769230769231)

22.619864948°

Approximately = 22.62°

c) tan θ = Opposite/Adjacent

θ = 5/12

= arctan(0.4166666666666667)

= 22.619864948°

= 22.62°

Greetings from Brasil....

Every rational number is written as:

A/B   where A ∈ ℤ and B ∈ ℤ* (B ≠ 0)

So in our case, 2/9 is a rational number, because we have the division of 2 by 9 and 2 ∈ ℤ and 9 ∈ ℤ*

Answer:

y = x² - w / 2z (D)

Step-by-step explanation:

w = x² - 2yz

w - x² = - 2yz

multiply both sides by -1

-1(w - x²) = -1 (-2yz)

-w + x² = 2yz

x² - w = 2yz

2yz = x² - w

divide both sides by 2z

y = x² - w / 2z

The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.

1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.

These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.

To learn more about partial derivative, click here: brainly.com/question/2293382

#SPJ11

Answer: Red line

Step-by-step explanation:

2y+x=0

2y=-x

y=-x/2

So we need a line with a slope of -1/2 that passes through the origin, which is the red line.

Answer:

-5/2

Step-by-step explanation:

slope = (difference in y)/(difference in x)

slope = (1 - 6)/[-3 - (-5)]

slope = -5/2

Answer:

-5 / 2

Step-by-step explanation:

y2 - y1 / x2 - x1

1 - 6 / -3 - (-5)

-5 / 2

Answer:

Step-by-step explanation:

4x - 3y = 8

5x - 2y = -11

8x - 6y = 16

-15x + 6y = 33

-7x = 49

x = -7

4(-7) - 3y = 8

-28 - 3y = 8

-3y = 36

y = -12

Answer:

40,000 baldosas

Step-by-step explanation:

Lo primero que debemos hacer aquí es calcular el área del patio rectangular.

El mejor enfoque para esto es convertir primero sus medidas a centímetros

Matemáticamente, 100 cm = 1 m, entonces 10 m se convierten en 1000 cm y 12 m se convierten en 1200 m.

El área de un rectángulo es L * B y, por lo tanto, tenemos 1200 * 1000 = 1,200,000 cm ^ 2

Ahora, para saber la cantidad de azulejos que tendrá el patio, necesitaremos dividir el área del patio por el área de los azulejos

Matemáticamente, eso sería 1,200,000 / 30 = 40,000 fichas

As per results are shown in the relative frequency table government should target age group 18-21.

"A relative frequency is defined as the number of times a particular event occur in the given data set."

According to the question,

Relative frequency of the voter survey for against Undecided,

Ages: 18-21         0.26             0.2                  0.53             0.5

Ages: 22-32       0.15               0.11                  0.11               0.04

Ages: 33-43       0.23              0.05               0.05              0.12

Ages: 44-54       0.18               0.48                0.18             0.14

Ages: Over 55   0.18                0.16                 0.13              0.2

Total of undecided voters as per given relative frequency we get,

Ages: 18-21     = 1.49

Ages: 22-32    = 0.41

Ages: 33-43     = 0.45

Ages: 44-54     = 0.98

Ages: Over 55  = 0.67

As per given condition,

Government wants to concentrate on the largest number of undecided voters to assure that the proposed legislation passes the public vote

Therefore,

Age group of largest number of undecided voters = 18 - 21

Hence, as per results are shown in the relative frequency table government should target age group 18-21.

Learn more about relative frequency here

https://brainly.com/question/16832475

#SPJ2

The SAS Similarity Theorem states that if two triangles are similar, then the ratio of their sides is equal to the ratio of their corresponding angle measures.

What is the SAS Similarity Theorem?

SAS Similarity Theorem states that if two triangles have two pairs of sides that are proportional and have a pair of included congruent angles, both triangles are said to be similar to each other.

If the two sides of a triangle are in the same proportion as the two sides of another triangle, and the angle inscribed by the two sides in both triangles are equal, then two triangles are said to be similar.

Thus, if ∠A = ∠X and AB/XY = AC/XZ then ΔABC ~ΔXYZ.

This is how we can solve similarities in SAS.

Hence, we have explained the way of solving the similarities in SAS.

To learn about the SAS similarity theorem, visit:

brainly.com/question/21308208

#SPJ4

Answer:

6x - 7 = 2x + 13

6x - 2x = 13 + 7

4x = 20

x = 20/4

x = 5

Hope it helps!

The value of x , y and z in the parallel line is 50 degrees.

When parallel lines are crossed by a transversal line, angle relationships are formed such as vertically opposite angles, alternate interior angles, alternate exterior angles, adjacent angles, corresponding angles etc.

Therefore, let's use the angle relationships to find the angle, x, y and z as follows:

Therefore,

x = 360 - 310(sum of angles in a point)

x = 50 degrees

Therefore,

x = y(alternate interior angles)

Alternate interior angles are congruent.

Hence,

y = 50 degrees

Therefore,

x = z(alternate interior angles)

z = 50 degrees.

learn more on angles here: https://brainly.com/question/17043791

#SPJ1

The Existence and Uniqueness Theorem states that if a system of linear equations has a unique solution, then the solution can be found by solving the associated augmented matrix.

To determine whether a system of linear equations has a unique solution, the number of equations must equal the number of unknowns. Additionally, the equations must not be linearly dependent. If these criteria are met, then the Existence and Uniqueness Theorem guarantees that there is exactly one unique solution.

To illustrate, consider the system of equations:

x1 + x2 - x3 = 2  

2x1 - x2 + 2x3 = 8

3x1 + 2x2 - 4x3 = 0

= 4. Therefore, the Existence and Uniqueness Theorem guarantees that there is exactly one unique solution for this system.

See more about  existence and uniqueness at: https://brainly.com/question/30153142

#SPJ11

Answer:

$12.43

Step-by-step explanation:

multiply 0.54 by 12 to get 6.48

add 6.48 and 5.95

= 12.43

Therefore, the height of the tree is approximately 3.67 meters making triangle.

Let h be the height of the tree. Then, using the properties of similar triangles, we can set up the following proportion:

h / 1.25 = (h + x) / 15.45

where x is the length of Gabriella's shadow. To find x, we can use a similar proportion:

h / 10.2 = 1.25 / x

Solving the second proportion for x, we get:

x = 10.2 * 1.25 / h

Substituting this expression for x into the first proportion, we get:

h / 1.25 = (h + 10.2 * 1.25 / h) / 15.45

Multiplying both sides by 15.45 * h * 1.25, we get:

15.45 * h - 15.45 * 1.25 = h * 10.2

Expanding and rearranging, we get a quadratic equation in h:

15.45h - 19.3125 = 10.2h

5.25h = 19.3125

h = 3.67 meters (rounded to two decimal places)

To know more about triangle,

https://brainly.com/question/28600396

#SPJ11

Answer:15

Step-by-step explanation: So we have this triangle but it's not a right triangle right so we can't just Pythagorean theorem our way out. So we have to treat the sizes as ratios.  2:12 is the ratio of the smaller triangle. 12 increases to 78 which means side 2 has to increase as well by the same ratio so 78/12 = 6.5 and 6.5*2=13 so PQ is 13 and to find NQ just add NP and PQ or 2+13 = 15

Hope it helps :)

Answer:

1 week

Step-by-step explanation:

After 1 week

Saving account: $25 + $5 = $30

Checking amount: $50 + $10 = $60

30 x 2 = 60

So it's 1 week

Step-by-step explanation:

The equation system serves as the foundation for this query. As a result, the number of sliders and onion rings in the combination meal could both be calculated using the system of equations 2s = r and r(70) + s(200) = 1020.

Given:

Each onion ring at one eatery contains 70 calories, while each slider has 200 calories. An onion ring and slider combo meal has 1020 calories overall and twice as many sliders as onion rings, according to research.

According to the question:

Let r be the number of onion rings and s be the number of sliders.

Now, it is stated that there are twice as many sliders as onion rings. mathematical form, it is expressed as,

The first system of equations is 2s = r.

Additionally, each onion ring contains 70 calories, and each slider contains 200 calories. A combined lunch of sliders and onion rings has 1020 calories overall. This indicating as

The second set of equations reads as follows: r(70) + s(200) = 1020.

As a result, the number of sliders and onion rings in the combination meal could both be calculated using the system of equations 2s = r and r(70) + s(200) = 1020.

Simplified Version:

r = onion rings amount

s = sliders amount

system of equations

2s = r

r(70) + s(200) = 1020

Answer:

D, 1.20

Step-by-step explanation:

7.20 divided by 6 = 1.2 and 1.2 is the same as 1.20

The applicant who should be offered the job based on the aptitude test scores is Reyna. Reyna scored 87 on her version of the test, which has a mean of 73 and a standard deviation of 10.

Demetria scored 301.8 on her version of the test, which has a mean of 288 and a standard deviation of 23. Pierce scored 8.56 on his version of the test, which has a mean of 7.3 and a standard deviation of 0.6. The scores of Reyna, Demetria, and Pierce can be compared by standardizing them and calculating the z-scores. Standardizing involves subtracting the mean from the score and dividing by the standard deviation, resulting in z-scores. This can be used to compare the performance of each applicant relative to their own version of the test. Reyna's z-score is 1.37, Demetria's z-score is 0.86, and Pierce's z-score is 14.27. This shows that Reyna performed better than Demetria, and significantly better than Pierce. Reyna should therefore be offered the job based on her performance on the aptitude test.

for more suc question on deviation

https://brainly.com/question/475676

#SPJ11

By using the concept of Permutation and Combination, Counting Principle  Phyllis can make 168 ways to select students.

Permutation and Combination are about making arrangements and making selections on the basis of certain formulas

The re-arranging of any given sorted/ordered set is called a permutation. The “permutation” word actually tells us that change the linear order of the ordered set.

Selecting items from a large collection without taking any care about their order is called combinations.

We need to select one freshman out of 12 freshmen. So selecting r things from n things we can do selection in nr ways, so we can do a selection of freshmen in 12c1 ways

Similarly, we need to select one sophomore out of 14 sophomores, so we can do a selection of sophomores in 14c1 ways

We know that ncr is equivalent to \(\frac{n!}{r!(n-r)!}\)

So, using this concept total number of ways to select a student

= ((12c1)×(14c1))

=12×14

=168 ways

Hence Phyllis can select students in 168 ways

To know more about Counting Principle, Permutations and Combinations visit here:

https://brainly.com/question/28720645

#SPJ4

Answer:

Yes

Step-by-step explanation:

I think the test

The domain of f + g is (-∞, ∞).

The domain of ff is (-∞, ∞).

The domain of f/g is (-∞, 1) ∪ (1, ∞).

To find the domain of the given functions, we need to consider any restrictions that may occur. In this case, we have the functions f(x) = x + 2 and g(x) = x - 1. Let's determine the domains of the following composite functions:

f + g:

The function (f + g)(x) represents the sum of f(x) and g(x), which is (x + 2) + (x - 1). Since addition is defined for all real numbers, there are no restrictions on the domain. Therefore, the domain of f + g is (-∞, ∞), which includes all real numbers.

ff:

The function ff(x) represents the composition of f(x) with itself, which is f(f(x)). Substituting f(x) = x + 2 into f(f(x)), we get f(f(x)) = f(x + 2) = (x + 2) + 2 = x + 4. As there are no restrictions on addition and subtraction, the domain of ff is also (-∞, ∞), encompassing all real numbers.

f/g:

The function f/g(x) represents the division of f(x) by g(x), which is (x + 2)/(x - 1). However, we need to be cautious about any potential division by zero. If the denominator (x - 1) equals zero, the division is undefined. Solving x - 1 = 0, we find x = 1. Thus, x = 1 is the only value that causes a division by zero.

Therefore, the domain of f/g is all real numbers except x = 1. In interval notation, the domain can be expressed as (-∞, 1) ∪ (1, ∞).

for such more question on domain

https://brainly.com/question/16444481

#SPJ8

Answer:

5 days

Step-by-step explanation:

20 + 8(5) = 60

50 + 2(5) = 60

The sampling technique used for this situation is given by:

c) Cluster.

Samples may be classified as:

In this problem, the population is divided into groups, and each element of the groups are survived, hence cluster sampling was used.

More can be learned about sampling techniques at https://brainly.com/question/16587013

#SPJ1

Answer:

add all........

Step-by-step explanation:

-3+(-4)+(-3)

-3-4-3

-10

D. 62% of women in the sample are the primary investor in their household.Inference: Women in the United States are likely to be the primary investors in their households.

The answer to this question is D. 62% of women in the sample are the primary investor in their household. This is an example of the descriptive branch of statistics because it summarizes the data collected in the survey. The inference based on the results of the survey is that women in the United States are likely to be the primary investors in their households.

62% of women in the sample are the primary investor in their household.

Inference: Women in the United States are likely to be the primary investors in their households.

Learn more about sample here

https://brainly.com/question/25894237

#SPJ4

By incorporating this information into the similarity measure, we can produce more accurate and informative results in clustering and classification tasks.

To modify the definition of clustering similarity to take into account the position of shared neighbors in the two nearest neighbor lists, we can introduce a weighting factor that considers the rank of the shared neighbor in each list. This can be achieved by multiplying the regular SNN similarity value by a weight factor that is calculated as the reciprocal of the sum of the ranks of the shared neighbors in the two lists. For example, if two points have a shared neighbor that is ranked 2nd in one list and 3rd in the other list, the weight factor would be 1/(2+3) = 0.2. This weight factor would then be multiplied by the regular SNN similarity value to produce a modified SNN similarity score that gives higher similarity to points that share the same nearest neighbors ranked higher in the nearest neighbor lists. This modification is justified because it takes into account the fact that having shared neighbors that are ranked higher in the nearest neighbor lists is a stronger indicator of similarity than having shared neighbors that are ranked lower.

Learn more about clustering here

https://brainly.com/question/29888905

#SPJ11