Find (a) the curl and (b) the divergence of the vector field.
F(x,y,z) = xyz i - x^2yk

Complete question :

The latter is leaning against the building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder finally put the ladder in the distance from the bottom of the ladder to the building 15 feet. Find length of the ladder.

Answer:

17

Step-by-step explanation:

From Pythagoras :

Hypotenus = sqrt(opposite² + adjacent²)

From the diagram

l = sqrt((l-9)² + 15²)

l² = (l² - 18x + 81 + 225)

Square both sides

l² = l² - 18x + 306

l² - l² = 306 - 18x

18l = 306

l = 306/18

l = 17

To evaluate dy/dt given the equation y³ = 2x² + 14, along with dx/dt = 3, x = 5, and y = 4, we can use implicit differentiation and substitute the given values.

dy/dt is approximately equal to 0.51 (rounded to two decimal places).

To explain the solution, let's start by differentiating both sides of the equation implicitly with respect to t:

3y²(dy/dt) = 4x(dx/dt)

Now, we substitute the given values x = 5, y = 4, and dx/dt = 3 into the equation:

3(4)²(dy/dt) = 4(5)(3)

Simplifying this expression, we have:

48(dy/dt) = 60

Dividing both sides by 48, we find:

dy/dt = 60/48 = 1.25

Therefore, dy/dt is approximately equal to 1.25. Rounded to two decimal places, the value is 0.51.

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Answer:

4 centimetres per hour.

Step-by-step explanation:

Answer:

this means there is no answer to the problem

Step-by-step explanation:

Answer:

X=25

Step-by-step explanation:

y+2=-7+2=5

[tex]5^{2} =25[/tex]

Complete question

A square pyramid. The square base has side lengths of 6.5 meters and the height of 6 meters.

What is the volume of the pyramid?

Answer:

84.5m³

Step-by-step explanation:

The volume of a square. Pyramid is given as :

V = 1/3 * base * height

Base = l² ; l = side length

Base = 6.5² = 42.25 m²

V = 1/3 * 42.25 * 6

V = 42.25 * 2

V = 84.5

The volume of square pyramid = 84.5m³

Step-by-step explanation:

hey, hope it helps.. :))

Answer:

C

Step-by-step explanation:

It was right on the quiz

Answer:

It’s B

explanation:

The mean absolute deviation of last week's temperatures is 7.2°F.

Given below is the table of last week's and this week's low temperatures:Last week's temperatures: 29°F, 35°F, 42°F, 46°F, 52°FThis week's temperatures: 27°F, 31°F, 35°F, 38°F, 42°F, 46°F, 50°F

The range of this week's temperatures is found by subtracting the smallest value from the largest value. Therefore, the range of this week's temperatures is 50°F - 27°F = 23°F.

Mean absolute deviation is a measure of how much the data deviates from the mean of the data. To find the mean absolute deviation of last week's temperatures, we first need to find the mean of the data set.Using the formula for mean, we have:

Mean = (29 + 35 + 42 + 46 + 52)/5 = 40.8°F

To find the absolute deviations of each temperature from the mean, we need to subtract each temperature from the mean and take the absolute value.Absolute deviations:

|29 - 40.8| = 11.8|35 - 40.8|

= 5.8|42 - 40.8|

= 1.2|46 - 40.8|

= 5.2|52 - 40.8|

= 11.2

Next, we need to find the mean of these absolute deviations. Using the formula for mean again, we have:Mean absolute deviation = (11.8 + 5.8 + 1.2 + 5.2 + 11.2)/5 = 7.2°F

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Answer:

10.10 15.15

Step-by-step explanation:

25.30 15.12 25.13

The proportion of values between 152 and 124 cm is 0.8996 or 89.96%.

Proportion between 152 and 124 cm according to a normal distribution with mu = 138cm and sigma = 7cm is 0.8996.

According to the given question, we know that the mean is μ = 138 cm, standard deviation is σ = 7 cm.

We have to find the proportion that is between 152 and 124 cm.

To solve the problem, first we have to find the z-scores for 152 and 124 cm.

We can calculate the z-scores as follows:Z-score for 152 cm is given by:z152​=(152−138)7=2z_{152}=\frac{(152-138)}{7}=2z152​=(152−138)7=2Z-score for 124 cm is given by:z124​=(124−138)7=−2z_{124}=\frac{(124-138)}{7}=-2z124​=(124−138)7=−2

We can use a z-table or calculator to find the proportion of values between these two z-scores.

The area under the standard normal curve between z = -2 and z = 2 is approximately 0.8996.

Therefore, the proportion of values between 152 and 124 cm is 0.8996 or 89.96%.

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Answer:0.3 m

Step-by-step explanation:

Given

Ken can Jump [tex]1\ \frac{1}{5}\ m[/tex]

Steve can Jump [tex]1.5\ m[/tex]

Converting mixed fraction into a fraction

[tex]\Rightarrow 1\ \dfrac{1}{5}=\dfrac{1\times 5+1}{5}\\\\\Rightarrow \dfrac{6}{5}\ m=1.2\ m[/tex]

The difference between their Jumps is

[tex]\Rightarrow 1.5-1.2=0.3\ m[/tex]

Steve Jumps 0.3 m more than ken

Answer:

{7, 13)

Step-by-step explanation:

IR - 31 = 10

IR = 41

7*13 = 41

(-7)*13 = -41

(-13)*13 = -169

Answer: 40 people like song A whereas 20 people like song B. Thus, it is reasonable to say that more people liked Song A .

Step-by-step explanation:

154 yd ²

the formula is (b • h) / 2 = A

so plug it in (14 • 22) / 2 = 154

Answer:

Hi

Step-by-step explanation:

Answer:

250

Step-by-step explanation:

i did cross multiplication 40/100 = 100/x

100*100 and divide by 40

Answer:

The angles are adjacent because they have a common side and vertex. Basically, they are both right next to each other.

x = 28

Step-by-step explanation:

When (x + 6)° and 56° are added together, they need to equal 90° since they are both parts of a right angle.

(x + 6) + 56 = 90

x + 62 = 90

x = 28

Answer:

12 students.

Step-by-step explanation:

If you had 4 sheets, you would want to start by dividing them all in 3's, since that's easiest. (open the file i just for a better example of how the sheet should look).

Now, let's assume these sheets are regular office sized paper.

Start by handing 1 third out to A student.

Now, since there are 4 sheets, divided in 3 sections, we multiply to see the result of how many sections there are.

4 x 3 = 12.

Therefore, 12 students will receive a third of the tissue paper.

The question is incomplete. Here is the complete question.

Mavis is interested whether military status is related to gender in American Samoa. The data she collected about the population of American Samoa in 2010 is below.

Find the marginal distribution of military status in percentages. Round to the nearest whole percentages.

In Armed Forces:

Military-dependent:

Civilian:

Answer: In Armed Forces: 0%

              Military-dependent: 3%

              Civilian: 97%

Step-by-step explanation: Marginal Distribution is defined as the probability distribution of variables contained in a subset.

For the American Samoa's military status, marginal distribution is

1) In Armed Forces:

[tex]p_{1}=\frac{87}{55,519}*100[/tex]

[tex]p_{1}=0.15[/tex]

2) Military-dependent:

[tex]p_{2}=\frac{1709}{55,519}*100[/tex]

[tex]p_{2}=3.08[/tex]

3) Civilian:

[tex]p_{3}=\frac{53,723}{55,519}*100[/tex]

[tex]p_{3}=96.77[/tex]

Now round each percentage to the nearest whole percentage:

Armed forces: 0%

Military: 3%

Civilian: 97%

The marginal distributions of military status are, in nearest whole percentage:

Armed forces: 0%

Military: 3%

Civilian: 97%

Answer:

The answer is "320".

Step-by-step explanation:

They have to be 1, 3, 5, 7, and 9 as your final digit. Your middle digit may be anything other than the first digit, and only the last digit or 0, is anything.

Now let us take a look at strange digits ending in 1.

This can start from any digit other than 0, so there are 8 options during the first digit.

Its middle digit could only be 1 digit and 1 digit. Even so, it can also be 0, since it has 8 options.

So, [tex]8\times 8 = 64[/tex] strange number ending in 1.

For other strange amounts, the very same logic is working.

And thus there are 64 possible odd numbers for just about any number ending in any of the five odd digits: 1, 3, 5, 7, or 9.

The answer is [tex]5 \times 64 = 320[/tex].

Answer:

21900

Step-by-step explanation:

Find 8% of 7500 (600) and multiply it by 24 (amount of months) then add that to 7500

If the trace of a 2×2 matrix a is tr(a)=12 and the determinant is det(a)=32, the eigenvalues of matrix a are 4 and 8.

To find the eigenvalues of a 2×2 matrix, we can use the following formula:

λ² - tr(a) * λ + det(a) = 0,

where λ represents the eigenvalues, tr(a) is the trace of the matrix, and det(a) is the determinant.

In this case, we are given that tr(a) = 12 and det(a) = 32. Substituting these values into the formula, we have:

λ^2 - 12λ + 32 = 0.

To solve this quadratic equation, we can factorize it or use the quadratic formula. Factoring the equation, we get:

(λ - 4)(λ - 8) = 0.

Setting each factor equal to zero, we find two solutions:

λ - 4 = 0 => λ = 4,

λ - 8 = 0 => λ = 8.

The trace and determinant of a matrix provide valuable information about its eigenvalues. In this case, by substituting the given trace and determinant into the eigenvalue formula, we were able to find the eigenvalues of the 2×2 matrix a.

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The variable "pounds of popcorn" served at a movie theater is a continuous variable that can take any value within a certain range. It is not restricted to specific discrete values or categories.

A continuous variable is one that can take any value within a certain range. In the case of "pounds of popcorn" served at a movie theater, it can have fractional values and can vary continuously from very small amounts to large amounts.

It is not restricted to specific discrete values or categories. In contrast, discrete variables can only take on specific values, while ratio variables have a meaningful zero point and allow for comparisons of ratios. Since the amount of popcorn served can be measured with any level of precision, it falls under the category of a continuous variable.

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Answer:

7.1437 is greater

Step-by-step explanation:

Answer:

7.133 < 7.1437

Step-by-step explanation:

Line up the numbers till you find one that is greater

Answer:

4. 50,000 square miles

5. The office would round to $800,000 instead of $700,000 because they would lose that needed $35,495. If they rounded down, their budget would be cut short, and they won’t have enough money for the office.

6. Five numbers that could also be the population: 577,777; 575,555; 578,999: 578,787; 581,545.

7. 600,000

8.584,000

9. 260,000

Step-by-step explanation:

4. In this question, we’re rounding the number, “54,555” go the nearest ten thousand. When rounding numbers you look at the number next to the digit your rounding. In this case, since the second number is not 5 or higher, we round it to 50,000 as that’s closer than 60,000.

5. Like I stated above: if they round to the lowest amount, they won’t have enough money to but what they need. Therefore, even if according to rounding it needs to be lower, it will not be beneficial to the company.

6. This are all possible numbers cause they can all by round to 580,000 AND 600,000

7. Since the number next to six is not five or higher, we round it to the closest number which is 600,000.

8. Since the number next to 3 is 5, we round it to the higher number. So it’s 584,000

9. Since the number next to the underlined nunber is 6, we round it to the closest number which is 260,000

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Answer:

V = 17,371.8

Step-by-step explanation:

V = π r^2 h

V = π (12)^2 (38.4)

V = 17,371.75073729

V = 17,371.8

You have to calculate the area of the base of the cylinder (the circle) by using the formula π r^2, r = the radius of the circle. You are squaring the r because r^2 = diameter. The formula to get the area of a circle is π r ^2. To get the volume you need to multiply the area of the circle by the height of the cylinder. All together the total formula to get the volume of a cylinder is π r^2 h