Work out the unknown angle

The point(s) on the ellipsoid x2 + 4y2 + z2 = 9 at which the tangent plane is parallel to the plane z = 0 are (0, ±3/2, 0).

To find the point(s) on the ellipsoid where the tangent plane is parallel to the plane z=0, we first take the partial derivative of the given equation with respect to z. This gives us 2z = 0, or z=0. Substituting this value of z in the original equation of the ellipsoid, we get the equation x2 + 4y2 = 9, which represents an ellipse in the xy-plane. Now, we find the gradient of this equation, which is <2x, 8y, 0>. Setting this equal to the normal vector of the plane z = 0, which is <0, 0, 1>, we get the system of equations 2x = 0 and 8y = 0. Solving for x and y, we get x = 0 and y = ±3/2. Thus, the points on the ellipsoid where the tangent plane is parallel to the plane z = 0 are (0, ±3/2, 0).

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Answer:

The answer is

9xy2-6x2y+5x3

The additive inverse of a polynomial is the same polynomial with the signs of the terms changed.

The additive inverse of the given polynomial is (9xy² - 6x²y + 5x³).

The additive inverse of a polynomial can be obtained by multiplying the  polynomial with (- 1).

The given polynomial is (- 9xy² + 6x²y - 5x³)

Therefore, the additive inverse of the given polynomial is

= - (- 9xy² + 6x²y - 5x³)

= (9xy² - 6x²y + 5x³)

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Answer: 3500

Step-by-step explanation:

7 x 10 to the 5th power = 700000

2 x 10 squared = 200

700000/200 = 3500

Answer:

4201750

Step-by-step explanation:

7*10^5/2*10^2

7*10=70

2*10=20

70^5/20^2

70^5 =1680700000

20^2=400

1680700000/400=4201750

Answer:

Step-by-step explanation:

358 in

A=2(wl+hl+hw)=2·(6·15.5+4·15.5+4·6)=358

The surface area of the rectangular prism is 358 square inches.

Given dimensions of the prism are:

The formula to find the surface area of a rectangular prism is:

Surface Area = 2*(length * width + length * height + width * height)

Plugging in the values we have:

Surface Area = 2*(15.5 * 6 + 15.5 * 4 + 6 * 4) = 2*(93 + 62 + 24) = 2*(179) = 358 square inches

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Step-by-step explanation:

Yes division and multiplication can means same as for example

17÷88 means same as 17 × 1/88

The value of (f∘g)(2) is -53.

The correct Option is a) -53.

Given:

f(x) = -7x + 3

g(x) = x² + 4

First,

let's find g(2):

g(2) = (2)² + 4

    = 4 + 4

    = 8

Now, substitute g(2) into f(x):

(f∘g)(2) = f(g(2))

        = f(8)

        = -7(8) + 3

        = -56 + 3

        = -53

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The linear approximation of the function at the indicated point is as follows: F(x,y) = x -5y - 1

The linear approximation of a function is nothing more than estimating the value of the function at a location using a line. When we see a curve (of a function) with a point on it, we recall the idea of the tangent line. If we determine the equation of the tangent line at the given position, the value of the function at any location extremely near to the given point can be estimated using the equation of the tangent line. Since the tangent line is used in this process, the idea is also referred to as the "tangent line approximation" or "linear approximation."

How to solve?

In this case, our goal is to locate the linear approximation of the provided function at the stated location.

We start by replacing the values, then determine the partial derivative with regard to x and finally y.

We now sum these values, having first substituted the x and y values into the differentiated partial equation. The findings are then added up.

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The given system of equations is \(8x + 5y = 29\), and \(2x -3y = 5\). The solution of the given system of equations is \((x, y) = (2, 3)\).

We have given the system of equations as follows:\(8x + 5y = 292x - 3y = 5\).

The first step is to eliminate the fractions and decimals. We can multiply the second equation by 5 to eliminate the decimals as shown below.

\(10x - 15y = 25\).

Multiplying equation 1 by 3, and equation 2 by 8 we get:

\(24x + 15y = 8716x - 24y = 40\).

Adding these equations:

\(40x = 127x = 12.7\).

Substitute this value of x in any of the given equations.

Let’s substitute in the first equation:

\(8(12.7) + 5y = 295y = 29 - 101y = 4.8\).

Therefore, the solution of the system of equations is \((x, y) = (12.7, 4.8)\). However, the solution \((12.7, 4.8)\) does not satisfy the second equation. So, the given system of equations does not have any solution. Therefore, the answer is NO SOLUTION.

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The probability that a randomly selected month's number of order is more than 150 is 0.13%

Given, shawn finds that the monthly number of take-out orders at a restaurant is normally distributed with mean 132 and standard deviation 6.

⇒ mean = 132

⇒ standard deviation = 6

Analysis:

Set the monthly number of take out order as x.

From the question, we know:

P(x > 150) = P(x-132/ > 150-132/6)

= P(x=132/6 > 3)

= 1 - P(x-132/6 ≤ 3)

≈ 1 - 0.9987 {standard normal distribution table}

≈ 0.0013

= 0.13%

Hence we get the probability as 0.13%.

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Answer:

0.833

Step-by-step explanation:

Because 1 and 2/3=1.666

0.833 x 2=1.666 so that's how it's your answer

Have a great day :}

Answer:

1st option

Step-by-step explanation:

3z and 2z are adjacent angles on a straight line and sum to 180° , that is

3z + 2z = 180

5z = 180 ( divide both sides by 5 )

z = 36

Then

3z = 3 × 36 = 108°

2z = 2 × 36 = 72°

Step-by-step explanation:

3x - 5 = 2x - 25

3x - 2x = -25 + 5

x = -20

The value of x from the given figure is 42°.

The given angles are (3x-5)° and (2x-25)°.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

from the given figure,

y+(2x-25)°=180° (Adjacent angles adds up to 180°)

⇒ y=180°-2x+25°

⇒ y=205°-2x

Here, (3x-5)°=y (Corresponding angles are congruent)

⇒ (3x-5)°=205°-2x

⇒ 3x+2x=205+5

⇒ 5x=210

⇒ x=42°

Hence, the value of x from the given figure is 42°.

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The range of the data set is 16 inches.

The range of a data set represents the difference between the highest and lowest values in the set. In this case, the data set consists of the following heights (in inches):

59, 62, 62, 62, 64, 66, 67, 67, 67, 71, 72, 75

To find the range, we need to determine the minimum and maximum values in the set. By sorting the data set in ascending order, we can identify the minimum and maximum values more easily:

59, 62, 62, 62, 64, 66, 67, 67, 67, 71, 72, 75

The smallest value in the set is 59, which is the minimum value, and the largest value is 75, which is the maximum value.

To calculate the range, we subtract the minimum value from the maximum value:

Range = Maximum value - Minimum value

Range = 75 - 59

Range = 16 inches

Therefore, the range of the given data set is 16 inches. This means that the difference between the tallest and shortest student in the class is 16 inches.

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Answer:

Linear

Step-by-step explanation:

If you plotted points like 1,2 (1 for every day and the 2 for each gallon) then 2,4 then 3,6 it would go up in a straight line.

4x - 5y = -9

-4x + y = -7

Step 1

Eliminate variable x

Different sign eliminate x and add.

-5y + y = -9 + (-7)

- 4y = -9 - 7

- 4y = -16

y = -16/-4

y = 4

Step 2

Substitute y in any equation and find x.

-4x + y = -7

-4x + 4 = -7

-4x = -7 - 4

-4x = -11

x = -11/-4

x = 11/4

X = 11/4 Y = 4

Answer:

The answer is "The first choice"

Step-by-step explanation:

In the given question the first choice is correct because When the zero assumption was valid, it would have been at least as bad to also be 2% to demonstrate a discrepancy as observed difference.

The amount each paid was (1.3h + 2.6)

Here, we want to get the amount paid by the two given the tip percentage

From the question, Harriet's cost was h

She paid or added a 30% tip

Mathematically, that would be;

Lucy had a dinner that cost an extra 4

The amount she would be paying is $(h+4)

We proceed to find the 30% tip and add

That would be;

The total cost of the bill is thus;

To find the individual amount paid, we divide this value by 2, which is;

Answer:

in total 21 miles

Step-by-step explanation:

Adding 16 to the given equation we get:

Simplifying the above result we get:

Dividing the above equation by 7 we get:

Simplifying the above result we get:

Answer:

Answer:

Step-by-step explanation:

7x-16=-2how do i find the solution of x

7x - 16 = -2

7x = - 2 + 16

7x = 14

x = 14 : 7

x = 2

-------------------------------

check

7 × 2 - 16 = -2               (remember PEMDAS)

14 - 16 = -2

-2 = -2

the answer is good

Answer:

2.5 centimeters

Step-by-step explanation:

The radius is half the diameter of a circle.

The diameter of the burger is 5 cm.

5/2 = 2.5

The radius of the burger should be 2.5 centimeters.

Hope this helps!

Answer:

The marginal utility per dollar spent for the second burger is 4 utils and the utility per dollar spent for the second burger is 4.5 utils.

Step-by-step explanation:

To prove that A* search always finds the optimal goal, we need to show that it satisfies two properties 1. Completeness: A* search is guaranteed to find a solution if one exists. 2. Optimality: If a solution is found by A* search, it is guaranteed to be the optimal solution.

1. Completeness:

  To prove completeness, we need to show that A* search is guaranteed to find a solution if one exists.

  A* search explores the search space by expanding nodes based on the estimated cost of reaching the goal, which is determined by the heuristic function. The heuristic function used in A* search is admissible, meaning it never overestimates the actual cost to reach the goal.

  A* search maintains a priority queue of nodes to be expanded, and it always selects the node with the lowest estimated cost (f-value) to expand next. Since the heuristic is admissible, the f-value of the goal node will never decrease as we explore the search space.

  If a solution exists, A* search will eventually reach the goal node because it explores nodes in order of increasing estimated cost. Once the goal node is reached, A* search will terminate and return the solution. Therefore, A* search is complete.

2. Optimality:

  To prove optimality, we need to show that if a solution is found by A* search, it is guaranteed to be the optimal solution.

  Suppose there exists an optimal solution that is different from the one found by A* search. Let's assume this alternative solution has a lower cost than the one found by A* search.

  Since the heuristic function used in A* search is admissible, it never overestimates the actual cost to reach the goal. This implies that the estimated cost (h-value) of any node in the search space is less than or equal to the actual cost (g-value) of reaching the goal from that node.

  Now, consider the node in the alternative solution where it deviates from the path found by A* search. This node must have a lower estimated cost (h-value) than the corresponding node in the A* search path because the alternative solution has a lower overall cost.

  However, since A* search always selects the node with the lowest estimated cost (f-value) to expand next, it would have chosen the node in the alternative solution before the corresponding node in the A* search path. This contradicts our assumption that the alternative solution has a lower cost.

  Therefore, we can conclude that if a solution is found by A* search, it is guaranteed to be the optimal solution.

By establishing both the completeness and optimality properties of A* search, we have shown that A* search always finds the optimal goal.

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Answer:

C

X=6

Step-by-step explanation:

7+5x-15=22

5x-8=22

5x=22+8

5x=30

X=30/5

X=6

The numerical length of the line segment FG is 10 units.

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Point G is on FH, hence:

FH = FG + GH

Given that GH = 8, FH = 3x + 3, FG = 2x, hence:

3x + 3 = (2x) + 8

x = 5

FG = 2x = 2(5) = 10

The numerical length of the line segment FG is 10 units.

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a, c, c, b, d hope this helps

Answer:

  B. increase his income by $28.00

Step-by-step explanation:

You want to know what Will can do to balance his budget when he has expenses of $70, 56, 14, and 35, and income of $147.

Will's total expenses for the week are ...

  $70 +56 +14 +35 = $175

When he subtracts these from his income for the week, he finds the difference to be ...

  $147 -175 = $(-28)

The negative sign means expenses exceed income. In order for the difference to be zero (balanced budget), Will must increase income or decrease expenses, or both. Among the offered choices, the one that makes the appropriate adjustment is ...

  B. increase his income by $28.00

The equilibrium wage rate as a function of labor demand N is w = z, and the firm's profit π = 0.

a. To find the equilibrium wage as a function of labor demand N, we need to maximize the profit of the firm while taking into account the utility function of the consumer.

The firm's profit function is given by π = zN - wN, where w represents the wage rate.

To maximize the firm's profit, we take the derivative of the profit function with respect to N and set it equal to zero:

dπ/dN = z - w = 0

This implies that the equilibrium wage rate w is equal to z.

Therefore, the equilibrium wage as a function of labor demand N is simply w = z.

b. The firm's profit π is given by π = zN - wN, where w represents the wage rate. In this case, we have already established that the equilibrium wage rate is w = z.

Substituting w = z into the profit function, we have:

π = zN - zN = 0

Therefore, the firm's profit π is zero.

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