Find dy/dx by implicit differentiation 4x^3 + x^2y − xy^3 = 6

The domain of the function [tex]\(f(x, y, z) = 4 - x^2 - y^2 - z^2\)[/tex] is the set of all real numbers for [tex]\(x\)[/tex], [tex]\(y\),[/tex] and [tex]\(z\)[/tex].

To find and sketch the domain of the function [tex]\(f(x, y, z) = 4 - x^2 - y^2 - z^2\)[/tex], we need to determine the set of values for [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex] for which the function is defined, i.e., the values that do not lead to any mathematical inconsistencies.

In this case, the function involves three variables, and it is defined for all real values of [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex]. There are no restrictions on the domain because the square of a real number is always non-negative. Thus, [tex]\(x^2\)[/tex], [tex]\(y^2\)[/tex], and [tex]\(z^2\)[/tex] are non-negative for any real \(x\), \(y\), and \(z\).

In interval notation, we can express this as:

[tex]\[\text{Domain} = (-\infty, \infty) \times (-\infty, \infty) \times (-\infty, \infty)\][/tex]

This domain represents the entire three-dimensional space, and the function is defined for all points within this space. As such, sketching the domain involves visualizing the entire 3D space, which is an unbounded region without any specific shape or boundary.

For more such questions on domain

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The Sinclair family lives 28,512 feet away from Southside Middle School, calculated by multiplying 5.4 miles by the number of feet in one mile, which is 5,280 feet.

The Sinclair family lives 5.4 miles from Southside Middle School. To convert this distance from miles to feet, we use the conversion factor that 1 mile is equal to 5,280 feet. To find the distance in feet, we multiply the number of miles by the number of feet in one mile:

5.4 miles  imes 5,280 feet/mile = 28,512 feet.

Therefore, the Sinclair family lives 28,512 feet away from Southside Middle School.

Answer: answer is (-19/2,-5)

Step-by-step explanation:

The range of normal body temperatures for a camel throughout the day is from 34°C to 40°C, inclusive.

To represent the range of normal body temperatures for a camel throughout the day, we'll use an absolute value inequality. Given that the normal body temperature is 37°C and it varies by up to 3°C, we can express this as:

|T - 37| ≤ 3

Where T represents the temperature of the camel throughout the day. This inequality ensures that the temperature remains within 3 degrees above or below the normal body temperature of 37°C.

To solve this inequality, we'll consider two cases:

1. When T - 37 is positive:

T - 37 ≤ 3

T ≤ 40

2. When T - 37 is negative:

-(T - 37) ≤ 3

-T + 37 ≤ 3

-T ≤ -34

T ≥ 34

Combining the two cases, the range of normal body temperatures for a camel throughout the day is 34°C to 40°C.

Answer:

They are called equivalent expressions since they are two expression that equal the same thing.

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Answer:

△PQR and △RST are not similar.

Step-by-step explanation:

In triangle △PQR, two known interior angles are 34° and 80°. So the measure of third angle is

[tex]180-34-80=66[/tex]

In triangle △RST, two known interior angles are 24° and 90°.

[tex]180-24-90=66[/tex]

Two triangles are similar if their corresponding angles are same and the corresponding sides are proportional.

Since the angles of △PQR and △RST are not same, therefore we can say that the △PQR and △RST are not similar.

The probability that exactly 13 students will take up arts in the coming year is; 76.47%

We are given;

Number of students that study art each year = 17

Now, we want to find the probability that 13 students will take up arts in the following year. This is;

P(13 will take art the next year) = 13/17 * 100%

P(13 will take art the next year) = 76.47%

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That is the correct graph that represents

{3y≥x−9 3x+y>−3

hope i helped =D

we have

[tex]3y\geq x-9[/tex] ----> inequality A

The solution of the inequality A is the shaded area above the solid red line

See the attached figure N [tex]1[/tex]

[tex]3x+y> -3[/tex] ----> inequality B              

The solution of the inequality B is the shaded area above the dotted blue line

See the attached figure N [tex]2[/tex]

The solution of the system of inequalities is the shaded area between the solid red line and the dotted blue line

See the attached figure N [tex]3[/tex]

therefore

the answer in the attached figure

Final answer:

To find the intersection points of the curve r(t) with the paraboloid z = x^2 + y^2, we substituted the parametric forms into the equation and solved for t, yielding the points (0, 0, 0) and (2, 0, 4).

Explanation:

The student is asking about the intersection points of a curve r(t) with a paraboloid defined by z = x2 + y2. To find these points, we must substitute the parametric forms of x, y, and z from the curve into the equation of the paraboloid and solve for t.

Given the curve r(t) = ti + (4t - t2)k, we can identify the components of the curve as x(t) = t and z(t) = 4t - t2. The y-component is missing, which implies that y = 0. Now, substituting x(t) into the paraboloid equation, we get:

z = x2 + y2

4t - t2 = t2 + 02

By solving for t, we can determine the intersection points. Simplifying the equation, we get:

0 = 2t2 - 4t

Which gives us the solutions t = 0 and t = 2. Substituting these back into r(t) gives the intersection points (0, 0, 0) and (2, 0, 4).

The greatest number of identical bracelets that can be made using all the beads is 4. This is found by determining the greatest common divisor (GCD) of 16, 20, and 24, which is 4. Each bracelet will consist of 4 yellow beads, 5 red beads, and 6 orange beads.

The subject of this question is the mathematical concept of the greatest common divisor (GCD). In the given problem, you are tasked with finding the maximum number of identical bracelets you can make with a given number of beads. The concept of GCD is used here.

First, we need to determine the GCD of the quantities of the three different colored beads:

The GCD of 16, 20, and 24 is 4. This means the largest number of identical bracelets you can make, using all of the beads, is 4. Each bracelet will have 4 yellow beads, 5 red beads, and 6 orange beads.

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The rate of change of q with respect to p is the derivative of q with respect to p. However, the function seems to be incorrect as p is expressed as a function of q, not the other way around. The derivative of a typical function q = 20p^2 + 5 would be 40p.

The rate of change of q with respect to p is found by taking the derivative of the given function with respect to p. The function given is p = 20q^2 + 5. Unfortunately, we cannot find the derivative of p with respect to q. Instead, it seems more likely that we need to find the derivative of q with respect to p, which is typically what is intended when asked for the rate of change of one variable with respect to another. If the function was q = 20p^2 + 5, then, the derivative (rate of change) would be dq/dp = 40p. Although in your question, there may be an error as typically we would expect q to be expressed as a function of p.

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7,746.90 times x  = 7,901.84

 divide both sides by x

 x = 7,901.84 / 7,746.90

x = 1.020000258

 round to 1.02