Solve:

4
3
x −4 = 5 + x

Answer:

x=-1.30068.......

Step-by-step explanation:

x( 3x^2 - 2) = -4

Distribute

3x^3 - 2x = -4

Add 4 to each side

3x^3 - 2x +4 = 0

Plot using a graphing calculator

x=-1.30068.......

Answer:

Step-by-step explanation:

(- 3, 3)

The line integral is 2π/3 (in appropriate units).

a) The curve C is formed by the union of C1 and C2, as shown below:

          C2: z >= 0, y = 0, x^2 + z^2 = 1

            ______________

           /              /

          /              /

         /              /

        /______________/

 C1: z = 0, y >= 0, x^2 + y^2 = 1

We choose the orientation of C to be counterclockwise when viewed from the positive z-axis, as indicated by the arrows in the picture.

b) To apply Stokes's theorem, we need to compute the curl of F:

curl F = (∂Q/∂y - ∂P/∂z, ∂R/∂z - ∂Q/∂x, ∂P/∂x - ∂R/∂y)

= (-4x - 6y, -2, 2 - 2y)

Using the orientation of C we chose, the normal vector to C is (0, 0, 1) on C1 and (0, 1, 0) on C2. Therefore, by Stokes's theorem,

∫∫S curl F · dS = ∫C F · dr

where S is the surface bounded by C, which consists of the top half of the unit sphere. We can use spherical coordinates to parametrize S:

x = sin θ cos φ, y = sin θ sin φ, z = cos θ

where 0 ≤ θ ≤ π/2 and 0 ≤ φ ≤ π. We have

∂(x,y,z)/∂(θ,φ) = (cos θ cos φ, cos θ sin φ, -sin θ)

and

curl F · (∂(x,y,z)/∂(θ,φ)) = (-4 sin θ cos φ - 6 sin θ sin φ, -2 cos θ, 2 cos θ - 2 sin θ sin φ)

The surface element is

dS = ||∂(x,y,z)/∂(θ,φ)|| dθ dφ = cos θ dθ dφ

Therefore, the line integral becomes

∫C F · dr = ∫∫S curl F · dS

= ∫0π/2 ∫0π (-4 sin θ cos φ - 6 sin θ sin φ, -2 cos θ, 2 cos θ - 2 sin θ sin φ) · (cos θ, cos θ, -sin θ) dθ dφ

= ∫0π/2 ∫0π (2 cos2 θ - 2 sin2 θ sin φ) dθ dφ

= ∫0π/2 2π (cos2 θ - sin2 θ) dθ

= 2π/3

Therefore, the line integral is 2π/3 (in appropriate units).

Learn more about integral  here:

https://brainly.com/question/18125359

#SPJ11

Answer:

ok

Step-by-step explanation:

Answer: Your asnwer is 2.5 lbs Can i have branliest?

Step-by-step explanation:

Answer:

number of guest tickets, g, is 100 tickets

number of student tickets, s, is 125 tickets

Step-by-step explanation:

Given;

total number of tickets sold, t = 225 tickets

cost of each guest ticket,  = $5.5

cost of each student ticket, = $3.5

total cost of the tickets, Tc = $987.5

number of guest tickets = g

number of student tickets, = s

g(5.5) + s(3.5) = 987.5 ------- (1)

g + s = 225 ----------- (2)

From equation (2); s = 225 - g

Substitute the value of g in equation (1)

5.5g + 3.5(225 - g) = 987.5

5.5g + 787.5 - 3.5g = 987.5

5.5g - 3.5g = 987.5 - 787.5

2g = 200

g = 200 / 2

g = 100 tickets

Then, s = 225 - g

s = 225 - 100

s = 125 tickets

Answer:

1, 2 and 3  (I, II and III)

Step-by-step explanation:

Since the slope is positive (3) in the equation y = 3x + 1, it means that the graph has a positive slope, meaning the line slopes up from left to right.

The y intercept is 1

the x intercept is:  

0 = 3x + 1

x = 1/3

Therefore, the graph of y = 3x + 1 lies in quadrants I, II and III.  Graph the equation to prove this.  

\(\sf( - 4) - ( + 2) \\ = \sf - 4 - 2 \\ \sf \: = - 4 + - 2 \\ = \underline{\bf - 2}\)

\(( - 4) - ( + 2)\)

\( = - 4 - 2\)

\( = - 4 + ( - 2)\)

\( \boxed{ = - 2}\)

Answer:

The answer is y = - 7x + 6

Step-by-step explanation:

A parallel line will have the same slope and since the point that is given is a y intercept, you just plug in -7x + 6 to get your parallel equation

The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

To know more about expression, refer here:

https://brainly.com/question/31800038

#SPJ4

Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

The equation of the parabola with focus (-2, 5) and directrix y = 3 is y = \((1/4)x^2 + x + 5.\)

To write the equation of a parabola with focus (-2, 5) and directrix y = 3, we can use the standard form of the equation of a parabola:

\((x - h)^2 = 4p(y - k)\)

Where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus or directrix.

First, let's determine the vertex of the parabola. The vertex lies halfway between the focus and the directrix, so its y-coordinate is the average of the y-coordinates of the focus and the directrix:

Vertex y-coordinate = (5 + 3) / 2 = 8 / 2 = 4

Since the directrix is a horizontal line, the vertex has the same y-coordinate as the directrix. Therefore, the vertex is (h, k) = (-2, 4).

Next, let's determine the value of p. The distance from the vertex to the focus (or directrix) is p. In this case, the focus is (-2, 5), so the distance from the vertex to the focus is:

p = 5 - 4 = 1

Now we can write the equation of the parabola using the vertex and the value of p:

\((x - (-2))^2 = 4(1)(y - 4)\)

\((x + 2)^2 = 4(y - 4)\)

Expanding the square on the left side:

(x + 2)(x + 2) = 4(y - 4)

(x^2 + 4x + 4) = 4y - 16

Simplifying the equation:

\(x^2 + 4x + 4 = 4y - 16\)

x^2 + 4x + 20 = 4y

Rearranging the terms:

4y = x^2 + 4x + 20

Finally, dividing both sides by 4 to isolate y, we get the equation of the parabola:

\(y = (1/4)x^2 + x + 5\)

So, the equation of the parabola with focus (-2, 5) and directrix y = 3 is y = \((1/4)x^2 + x + 5.\)

To sketch the parabola, plot the focus (-2, 5) and the directrix y = 3 on a graph. The vertex is also located at (-2, 4). The parabola opens upwards because the coefficient of x^2 is positive. Use the equation to plot additional points and sketch the curve symmetrically around the vertex.

For more such questions on parabola visit:

https://brainly.com/question/29635857

#SPJ8

The simplified expression of the expression \((x - y)^p(x^2 + y^2 + q - y)\)while done the simplification through binomial theorm.

\((x - y)^p(x^2 + y^2 + q - y)\)

Expanding the first term using the binomial theorem, we get:

\((x - y)^p = \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^k\)

where [ p choose k ] is the binomial coefficient, given by p! / (k! × (p-k)!).

Substituting this expansion into the original expression, we get:

\(\sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} (x^2 + y^2 + q + y)\)

Expanding the last term, we get:

\(\sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} (x^2 + y^2) + \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} (q+y)\)

The first term can be simplified by distributing the x² and y² terms:

\(\begin{aligned} &\sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} x^{2} + \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} y^{2} \\&= x^{2} \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} + y^{2} \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} \\&= x^{2}(x-y)^{p} + y^{2}(x-y)^{p} \\&= (x^{2}+y^{2})(x-y)^{p}\end{aligned}\)

The second term can be simplified by distributing the x and y terms:

\(\begin{aligned} &\sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} q + \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} y \\&= q \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} - y \sum_{k=0}^{p} {p \choose k} x^{p-k} (-y)^{k} \\&= q (x-y)^{p} - y (x-y)^{p} \\&= (q-y) (x-y)^{p}\end{aligned}\)

Putting these simplified terms together, we get:

\(\begin{aligned}(x-y)^p \cdot (x^2 + y^2 + q - y) &= (x-y)^p \cdot [(x^2 + y^2) + (q - y)] \\&= (x-y)^p \cdot (x^2 + y^2) + (x-y)^p \cdot (q - y) \\&= (x^2 + y^2) \cdot (x-y)^p + (q - y) \cdot (x-y)^p \\&= (x^2 + y^2 + q - y) \cdot (x-y)^p\end{aligned}\)

Therefore, the simplified expression is \((x-y)^p \cdot (x^2 + y^2 + q - y)\)

Learn more about binomial:

https://brainly.com/question/30339327

#SPJ1

Answer:

The surface area is 1,070 ft².

In your test plan, include the number of repetitions you will perform and a method for analyzing the data to account for random errors.

A test plan should account for the presence of systematic and random errors through the following steps:

1. Calibration: Calibration ensures that the instruments used in the experiment are accurate and consistent. By calibrating the equipment, you can minimize the impact of systematic errors on your results. Start your test plan by ensuring all instruments are calibrated and their measurements are reliable.

2. Randomization: Randomization is the process of randomly assigning subjects or samples to different experimental conditions. This helps to eliminate any potential bias or systematic errors caused by the arrangement of the experiment. In your test plan, make sure to include a method for randomizing the experiment to minimize the effect of systematic errors.

3. Repetition: Repeating the experiment multiple times can help reduce the impact of random errors. By performing the experiment multiple times and averaging the results, you can minimize the influence of random errors on your findings.

for such more question on random errors

https://brainly.com/question/10218601

#SPJ11

idea 34 I did 56-22 0.0

Answer:

I think it is -60.71428571 percent.

Answer:

Step-by-step explanation:

The answer is $1,360 (please like)

The annual dividend on 2000 shares at the time would be $3200

Quarterly dividend for 2000 shares :

Annual dividend on 2000 shares :

Therefore, the Annual dividend will be $3200

Learn more : https://brainly.com/question/23105648

Answer:

7

Step-by-step explanation:

Plug it in.....

h(0) = 2.5 * 0 + 7 = 7

Answer:

81 miles

Step-by-step explanation:

378/14=27

The unit rate is 27 miles per hour

27*3 = 81

Answer:

x=−3

Step-by-step explanation:

2(6x+1)−4(x−5)=−2

Step 1: Simplify both sides of the equation.

2(6x+1)−4(x−5)=−2

(2)(6x)+(2)(1)+(−4)(x)+(−4)(−5)=−2(Distribute)

12x+2+−4x+20=−2

(12x+−4x)+(2+20)=−2(Combine Like Terms)

8x+22=−2

8x+22=−2

Step 2: Subtract 22 from both sides.

8x+22−22=−2−22

8x=−24

Step 3: Divide both sides by 8.

8x/8=−24/8

Answer:

\(x=-2-3y\)

Step-by-step explanation:

Subtract  3 y  from both sides of the equation.

Answer:

x=-2-3y

Step-by-step explanation:

She had to pay they have to pay her back $ 132.

Multiply: -

Payback = 360 x 120/100

               = 132

Payback is a financial metric that measures the time it takes to recover the initial investment cost of a project. It is commonly used in investment analysis to evaluate the viability of potential projects by estimating the time it takes for the project to start generating profits.

The payback period is calculated by dividing the initial investment by the expected cash flow of the project on an annual or monthly basis until the investment is fully recovered. The shorter the payback period, the more attractive the project is to investors. Payback is a simple and straightforward metric, but it has some limitations. It does not consider the time value of money or the long-term profitability of the project.

To learn more about Payback visit here:

brainly.com/question/29897703

#SPJ4

Complete Question: -

Paula went to the supermarket and to pay her bill she gave $ 360 if she gave 120% of what she had to pay, how much did they have to pay her back?

Angle relationships are useful when comparing the angles found in parallel lines cut by a transversal because they allow us to determine various angle measures.

For example, the corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles follow specific relationships. These relationships help us identify congruent angles, supplementary angles, or angles that add up to specific values. By applying these angle relationships, we can solve for unknown angle measures and prove geometric properties in parallel line systems. When comparing the angles associated with a triangle, angle relationships are crucial for understanding the triangle's properties and solving geometric problems. The angles in a triangle have specific relationships, such as the sum of interior angles being 180 degrees.

learn more about comparing here:

https://brainly.com/question/29400612

#SPJ11

The given information that X0=1, X1=4, X2=1, X3=3, and X4=3 further restricts the possible values that X5 can take.

The realization of the stochastic process implies that the values of the stochastic process are observed at particular points in time. It is denoted by x(t) and takes the form of a function of time t.

If the process is discrete, then the function is a sequence of values at discrete points in time.

A stochastic process is one that evolves over time and the outcomes are uncertain.

The given expression P(X5=3|X4=3,X3=3,X2=1,X1=4, X0=1) gives the probability of X5 being equal to 3 given that X4 is equal to 3, X3 is equal to 3, X2 is equal to 1, X1 is equal to 4, and X0 is equal to 1.

To understand the above expression, suppose we have a stochastic process with values X0, X1, X2, X3, X4, and X5.

The given expression provides the conditional probability of the value of X5 being equal to 3 given that X0, X1, X2, X3, and X4 take specific values.

The given information that X0=1, X1=4, X2=1, X3=3, and X4=3 further restricts the possible values that X5 can take.

To learn about stochastic process here:

https://brainly.com/question/32574493

#SPJ11

Answer:

\(\sqrt{21}\) does not belong

Step-by-step explanation:

a rational number is defined by any number that ends or repeats.

\(\sqrt{36\\}\) ends because it is just 6

\(\frac{2}{3}\) repeats so it is rational

\(\frac{1}{5}\) ends becuase it is just 0.2

but \(\sqrt{21}\) does not end nor repeat, making it irrational

Answer:

21 is the irrational one

Step-by-step explanation:

you cant multiply to of the same whole numbers by itself and get 21

Answer: 128 cubes

Step-by-step explanation:The dimension of the rectangular prism is not given, assumed not important.

Find the volume of 1 cube:

Volume = 1/4 x 1/4 x 1/4

Volume = 1/64 units³

Find the number of cubes that can go into the prism:

Number of cubes = 2 ÷ 1/64

Number of cubes = 128

Answer:

the value of M(2) would be 43

Step-by-step explanation:

M(2) mean y

y = 9t+25

= y=9(2) + 25

y = 18 + 25

y = 43

Answer:

Step-by-step explanation:

M(2) = 43; If Hazel mows 2 yards, she will earn $43.

Answer: 8.49 inches

Step-by-step explanation:

16.4-7.91=8.49 inches

The JASON group and the NIH Advisory Committee to the Director have issued recommendations that aim to enhance the management of undue foreign influence in research integrity.

The recommendation put forth by both the JASON group and the NIH Advisory Committee to the Director revolves around strengthening measures to address undue foreign influence in research integrity. This includes enhancing the ability of universities and federal agencies to effectively manage and mitigate the risks associated with foreign influence on research activities.

The specific details of the recommendation may vary, but the overarching goal is to establish robust mechanisms for identifying and addressing potential threats to research integrity posed by undue foreign influence. This may involve implementing stricter oversight, transparency, and disclosure requirements, as well as promoting education interest among researchers.

Learn more about interest here:

https://brainly.com/question/30955042

#SPJ11