DETAILS SCALC9 2.6.001 1. [-/3 Points PRACTICE AN MY NOTES ASK YOUR TEACHER Consider the following 9x2 - (a) Find y' by implicit differentiation y- (b) solve the equation explicitly for y and differentiate to get y' in terms of y- (c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a).

Answer:

204

Step-by-step explanation:

i took the test

Answer:

204

Step-by-step explanation:

I just the quiz

The inequality that represents all the solutions of -2(3x + 6) ≥ 4(x + 7) is x ≤ -4

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

-2(3x + 6) ≥ 4(x + 7)

Divide both sides of the inequality by -2

So, we have the following representation

3x + 6 ≤ -2(x + 7)

Open the brackets

This gives

3x + 6 ≤ -2x - 14

Add 2x to both sides of the inequality

So, we have the following representations

5x + 6 ≤ -14

Subtract 6 from both sides of the inequality

So, we have the following representations

5x ≤ -20

Divide both side of the inequality

x ≤ -4

Hence, the solution is x ≤ -4

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The equivalent expression as per algebra tiles is 3x+3.

One group means (x 1)

or x    1

Three groups mean 3(x 1)

or x   1

   x    1

   x    1

Now, we have to write an equivalent expression.

Algebra tiles are mathematical manipulatives that allow students to better understand ways of algebraic thinking and the concepts of algebra.

For example, one can represent the variable part by any geometric object and add them to represent the addition of variables.

As per algebra tiles

Add integer to integer

So, x + x + x =3x

Add variable to variable

So, 1 + 1 +1 =3

So, 3(x 1) = 3x+3

Therefore, the equivalent expression as per algebra tiles is 3x+3.

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Answer:

your answer issss

Step-by-step explanation:

Model the expression as

✔ 3

groups of x + 1.

There are

✔ 3

x tiles.

There are

✔ 3

+ 1 tiles.

The equivalent expression is

✔ 3x + 3

.

Answer:

they played 20 games together

Step-by-step explanation:

use percentages

Let x be the number of total games.

If 60% is won games then 40% is lost games.

(8/x)*100 = 40

8/x = 4/10

80 = 4x

X = 80/4

Therefore the number of games is 20

Answer:

x = -2 ; y = 1

Step-by-step explanation:

y = -2(x+2) + 1

y = 3x + 7

3x + 7 = -2x - 4 + 1

3x + 2x = -3 - 7

5x = -10

5/5 x = -10/5

x = -2

y = 3 (-2) + 7

y = -6 + 7

y = 1

The process to show the vector field V(x,y,z) as conservative is show  below and the scalar potential f is \(f(x,y,z) =xyz^{2} + e^{\pi }\)   .

A Vector field can be called as conservative if we are able to find the potential function "f" , whose gradient is field .

The Gradient is vector that is made from partial derivatives of potential function .

The Vector function is given as , V(x,y,z) = \((yz^{2} )i + (xz^{2} )j + (2xyz)k\) ,

So , we can write the partial derivatives function of potential function as :

\(\frac{\partial f}{\partial x} = yz^{2}\) ; \(\frac{\partial f}{\partial y} = xz^{2}\) ; \(\frac{\partial f}{\partial z} = 2xyz\),

On Antidifferentiating any of the above three partial derivatives ,

we get ; \(f=xyz^{2} + C\) , here the constant C can take any value ,

so , we take C as \(e^{\pi }\) .

Therefore , the potential Function is \(f(x,y,z) =xyz^{2} + e^{\pi }\) .

The given question is incomplete , the complete question is

Show that the vector field defined by the vector function V(x,y,z) = (yz²)i + (xz²)j + (2xyz)k is conservative by finding a scalar potential f .

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Check the picture below.

\(\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{RP}\\ a=\stackrel{adjacent}{15}\\ b=\stackrel{opposite}{8}\\ \end{cases} \\\\\\ RP=\sqrt{15^2+8^2}\implies RP=\sqrt{225+64}\implies RP=17\)

Answer:

this answer should be -6x - 3

Step-by-step explanation:

The sum of the first 7 terms of the following series is 52

'A geometric sequence is a sequence where every term has a constant ratio to its preceding term. A geometric sequence with the first term a and the common ratio r and has a finite number of terms.'

According to the given problem,

Sequence = 32,40,50

Let the common ratio be r,

Let the first term of the sequence be a,

⇒ a × r = second term

⇒ 32 × r = 40

⇒ r = 40/32

⇒ r = 5/4

We know,

Sum of n number of terms in a geometric sequence can be represented by,

sn=a(1-\(r^{7}\))/1-r

⇒ \(s_{7}\) =32(1 - (5/4)\(^{7}\)/1 - 5/4

⇒ \(s_{7}\) = 32 (1 - (5/4)\(^{7}\)/3/5

⇒ \(s_{7}\) = 5*32(1 - (5/4)\(^{7}\))/3

⇒ \(s_{7}\) = 160(0.972)/3

⇒ \(s_{7}\) = 156/3

=52

Hence, we can conclude, the sum of the first 7 terms of the geometric sequence is 52

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Answer:

d, 1/6

Step-by-step explanation:

so i did a diagram of some sorts to do this and got around six possible outcomes.

h is heads, t is tails.

h-h-h

t-t-t

h-t-h

t-h-t

t-t-h

h-h-t

feel free to correct me if any of this is wrong.

If λ is an eigenvalue of matrix A and x is the corresponding eigenvector, then for any positive integer m, λ^m is an eigenvalue of A^m, and x is the corresponding eigenvector of A^m.

Let λ be an eigenvalue of matrix A with eigenvector x. This means that Ax = λx. Now, consider the matrix A^m, where m is a positive integer. By multiplying both sides of the eigenvector equation by A^(m-1), we have A^(m-1)Ax = A^(m-1)(λx), which simplifies to A^mx = λA^(m-1)x.

Since A^mx = (A^m)x and A^(m-1)x = λ^(m-1)x, we can rewrite the equation as (A^m)x = λ^(m-1)(Ax). Using the initial eigenvector equation Ax = λx, we have (A^m)x = λ^(m-1)(λx), which further simplifies to (A^m)x = λ^m x.

Therefore, we have shown that if λ is an eigenvalue of A with eigenvector x, then for any positive integer m, λ^m is an eigenvalue of A^m with the same eigenvector x. This result demonstrates the relationship between eigenvalues and matrix powers, illustrating that raising the matrix to a power corresponds to raising the eigenvalue to the same power while keeping the eigenvector unchanged.

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The correct option among the options that are given in the question is the third option or option "C". The statement is false. There exists a set that contains fewer vectors than there are entries in the vectors that is linearly dependent. One example is a set consisting of two vectors where one of the vectors is a scalar multiple of the other vector.

Linearly dependent and independent sets of vectors are used in the study of linear algebra and have been discussed in depth to understand the properties of these sets of vectors.

Linearly independent vectors: Vectors that are independent of each other and are not multiples of each other are called linearly independent vectors. No vector in a set can be defined as a linear combination of the others.

Linearly dependent vectors: In contrast, vectors that are not independent and can be described as linear combinations of each other are referred to as linearly dependent vectors.

Therefore, we can conclude that The statement is false. There exists a set that contains fewer vectors than there are entries in the vectors that is linearly dependent. One example is a set consisting of two vectors where one of the vectors is a scalar multiple of the other vector.

So, the correct answer is option C, The statement is false. There exists a set that contains fewer vectors than there are entries in the vectors that is linearly dependent. One example is a set consisting of two vectors where one of the vectors is a scalar multiple of the other vector.

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The magnitude of the x-component of this vector is 9.05m.

The angle of inclination of the vector is calculated as;

θ = 90 ⁰ - 48.4 ⁰

θ = 41.6 ⁰

The magnitude of the x-component of the vector is calculated as;

Vx = 12.1 m x cos ( 41.6 )

Vx = 9.05 m

A vector can be represented by an ordered set of numbers, called components, that indicate the magnitude and direction of the vector in a particular coordinate system. The components of a vector can be added or subtracted using vector addition and subtraction, and multiplied by a scalar (a real number) using scalar multiplication.

Vectors can be visualized as arrows in a two- or three-dimensional space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. Vectors can also be represented as matrices, which can be used to perform various operations on vectors, such as dot product and cross product.

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Complete Question:-

Answer:

Step-by-step explanation:

Use formula:

Find the value:

Answer:

x = 5

2 x 5 = 10

10 - 3 = 7

You could also use a replacement set.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

\(\left[\begin{array}{ccc}5&6&7\\8&9&10\\11&12&13\end{array}\right]\)

And so on.

Please click the thanks button.

Answer:

$73.20

Step-by-step explanation:

original bill: $60

Tip: 22%  $13.20

Total: $73.20

Hope this was helpful! Have a great day!

Answer:

36/7 I believe !!!

Step-by-step explanation:

convert yds to inches

The power of ten is basic concept to solve the largest numbers. The number 1,23456789 x 10⁻⁶is not the same value as 1,23456789000000. So, option(d) is right one.

The powers of 10 refer to the numbers in which the base is 10 and the exponent is an integer. Exponent and power concept is used to simplify the smallest and largest number. For example, 10², 10³ shows different powers of 10. The formula for powers of 10 is 10ˣ , where x is an integer.

We have a number 1,23456789 x 10⁻⁶

As we know, 10⁻ˣ is written as '0 decimal point followed by (x -1) number of zeros followed by 1". We can write the power expansion, 10⁻⁶ = 0.000001. So, the above expression can be represent flin following forms,

Hence, we cannot write it in form of 1,23456789000000.

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Complete question:

1,23456789 x 10^{-6} is not the same value as

a) 1,23456789/1000000

b)1,23.456789

c) 1,23456789/10⁶

d) 1,23456789000000

Answer:

1/6

Step-by-step explanation:

-1/m

-1/-6

1/6

Answer:Descartes’s chief contributions to mathematics were his analytical geometry and his theory of vortices, and it is on his researches in connection with the former of these subjects that his mathematical reputation rests. Who is Rene Descartes is he known for? Descartes has been heralded as the first modern philosopher.

Step-by-step explanation:

To solve a homogeneous differential equation of the form m(x, y)dx + n(x, y)dy = 0, we can use the substitution y = vx.

By following the steps above, you can solve a homogeneous differential equation and obtain the solution in terms of x and y.

1. Compute the derivative of y with respect to x: dy/dx = v + x * dv/dx.
2. Substitute the values of y and dy/dx in the original equation: m(x, vx)dx + n(x, vx)(v + x * dv/dx)dx = 0.

3. Simplify the equation by dividing through by dx: m(x, vx) + n(x, vx)(v + x * dv/dx) = 0.

4. Rearrange the terms to isolate dv/dx: n(x, vx) * dv/dx = -m(x, vx) - n(x, vx) * v.

5. Divide through by n(x, vx): dv/dx = (-m(x, vx) - n(x, vx) * v) / n(x, vx).

6. This is now a separable differential equation. Separate the variables and integrate both sides: ∫(1 / n(x, vx)) dv = -∫[(m(x, vx) + n(x, vx) * v) / n(x, vx)] dx.

7. Integrate both sides with respect to v and x, respectively.

8. Solve for v.

9. Substitute the value of v back into the equation y = vx.

10. This will give you the general solution of the homogeneous differential equation in terms of x and y.

In conclusion, by following the steps above, you can solve a homogeneous differential equation and obtain the solution in terms of x and y.

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Answer:

24 (A)

Step-by-step explanation:

So we know 20%=20/100, reduced to 1/5.

1/5 of 30 is 6, meaning 6 students answered it incorrectly.

Therefore, 24 students answered correctly

Hope this helps :)

Answer:

5

Step-by-step explanation:

The answer is 5

because 3 - 5 = -2

and -2 + 7 = 5

so the answer is 5

Answer: There are no intersections for these two lines, because if you plot them on a graph, they are parallel.

Answer:

3: 55 degrees

4: 128 degrees

Step-by-step explanation:

A straight line is 180 degrees and so you do 180-125 to get 55 degrees

180-58 is 128 degrees

Answer:

Step-by-step explanation:

Interpreting the result, fy(-8, 9) = -243 represents the slope of the function f(x, y) at the point (-8, 9) with respect to the y-direction.

To find the partial derivatives fx(-8, 9) and fy(-8, 9) of the function f(x, y) = \(13 - 9x^4 - y^3,\) we differentiate the function with respect to x and y, respectively, while treating the other variable as a constant.

Taking the derivative of f(x, y) with respect to x, we have:

\(fx(x, y) = -36x^3\)

Evaluating fx at (-8, 9), we substitute x = -8 into the derivative:

\(fx(-8, 9) = -36(-8)^3 = -36 * (-512) = 18,432\)

Interpreting this result, fx(-8, 9) = 18,432 represents the slope of the function f(x, y) at the point (-8, 9) with respect to the x-direction. It indicates the rate at which the function is changing in the x-direction at that point.

Taking the derivative of f(x, y) with respect to y, we have:

fy(x, y) = -\(3y^2\)

Evaluating fy at (-8, 9), we substitute y = 9 into the derivative:

fy(-8, 9) = -\(3(9)^2\) = -3 * 81 = -243

Interpreting this result, fy(-8, 9) = -243 represents the slope of the function f(x, y) at the point (-8, 9) with respect to the y-direction. It indicates the rate at which the function is changing in the y-direction at that point.

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The effort needed to move an object along a curve that is specifically oriented. F(x, y) = (y, x) on the parabola y = 6x² from (0,0) to (2,24) is 48.

A bowl-shaped object is defined as having a curve at the surface created by the intersection of a cone and a plane that is perpendicular to a straight line. Another definition of a curve is one created when a moving point moves such that its distance from a fixed point equals its distance from a fixed line. A quadratic function is known in this form as its standard form. A parabola is a U-shaped curve that represents the quadratic function on a graph.

The given parabola is,

y = 6x²

Here consider x=t

Then,

y=6t²(0≤t≤z)

The work done by F(x, y) would be:

W=\(\int\limits^_c\)F.dr

=\(\int\limits^_c\)(\(y_{i} +x_{j}\))(d\(x_{i}\)+d\(y_{j}\))

=\(\int\limits^_c\)y dx + x dy

=\(\int\limits^2_0\)((6t²)(1)+(t)(12t))dt

=\(\int\limits^2_0\)18t²dt

=48

Therefore, the effort needed to move an object along a curve that is specifically oriented. F(x, y) = (y, x) on the parabola y = 6x² from (0,0) to (2,24) is 48.

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