What is product of (3x + 4)(x2 + 3x - 2)

1) It is a conservative force, yes.

2) At (5m, 5m), the potential energy is 20 J.

1) If the work that a force performs when moving an item depends only on the object's initial and final positions and not on the path travelled, the force is said to be conservative.

Let's verify if this condition is met for the force in this problem:

- For moving from (0 m, 0 m) to (5 m, 5 m), the work done is 20 J (A)

Then we can go from (0 m, 0 m) to (5 m, 5 m) through a different path:

- from (0 m, 0 m) to (5 m, 0 m) (work done: 25 J)

- from (5 m, 0 m) to (5 m, 5 m) (work done: -5 J)

Total work done in the second path: 25 J + (-5 J) = 20 J --> same as (A)

We can also go from (0 m, 0 m) to (5 m, 5 m) through a different path:

- from (0 m, 0 m) to (0 m, 5 m) (work done: 35 J)

- from (0 m, 5 m) to (5 m, 5 m) (work done: -15 J)

Total work done in the third path: 35 J + (-15 J) = 20 J --> same as (A)

So, the force is conservative, since the work done does not depend on the path taken.

2) For a conservative force, the change in potential energy of the object moved by the force is equal to the work done by the force in moving the object from A to B.

Here have:

Point A: (0m, 0m)

Point B: (5m, 5m)

In this problem, the potential energy at the origin (point A) is zero, so,

\(W = U_{b} - U_{a}\)

Also we know that the work done is W = 20 J

So, we find

\(U_{b} = W + U_{a}\\=20 + 0\\= 20J\)

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Correct Question:

A force does work on a 50 g particle as the particle moves along the following straight paths in the xy-plane: 25 J from (0 m, 0 m) to (5 m, 0 m); 35 J from (0 m, 0 m) to (0 m, 5 m); -5 J from (5 m, 0 m) to (5 m, 5 m); -15 J from (0 m, 5 m) to (5 m, 5 m); and 20 J from (0 m, 0 m) to (5 m, 5 m).

Is this a conservative force?

If the zero of potential energy is at the origin, what is the potential energy at (5m, 5m)?

Answer:

Remaining zeros x= 4+i

Step-by-step explanation:

since complex roots always occur in conjugate pairs.

so if one root is 4-i the other one will be 4+i

Answer:

Below,...

Step-by-step explanation:

Your equation:

\(\frac{63}{7-(2*3)} =\frac{63}{7-6} =\frac{63}{1}=63\)

Hope it helps,... Chow,...!

It will take the golf ball 12 seconds to hit the ground using the kinematic equation for vertical motion.

To determine the time it takes for the golf ball to hit the ground, we can use the kinematic equation for vertical motion:

\(h = ut + (1/2)gt^2\)

Where:

h is the height (0 feet, as the ball is on the ground)

u is the initial velocity (192 feet per second)

g is the acceleration due to gravity (-32 feet per second squared, considering downward direction)

t is the time we want to find

Plugging in the given values, we get:

\(0 = (192)t + (1/2)(-32)t^2\)

Simplifying the equation, we have:

\(-16t^2 + 192t = 0\)

Factoring out t, we get:

t(-16t + 192) = 0

Setting each factor equal to zero, we have:

t = 0 (not applicable in this case)

-16t + 192 = 0

Solving for t, we get:

-16t = -192

t = 12

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The time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

The time it takes for the golf ball to hit the ground can be determined using the equation of motion. We can use the formula:

h0 = 0

v0 = 192

g = 32.2

a = 16.1

b = 192

t1 = 0

t2 = -b / a

t(-16t + 192) = 0

Setting each factor equal to zero, we have:

t = 0 (not applicable in this case)

-16t + 192 = 0

Solving for t, we get:

-16t = -192

t = 12

t2 >= 0:

   time_to_hit_ground = t2

   time_to_hit_ground = t1

The time it takes for the golf ball to hit the ground is approximately", round(time_to_hit_ground, 2 seconds.

The time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

Since time cannot be negative in this context, we discard the negative solution. Therefore, the time it takes for the golf ball to hit the ground is approximately 11.92 seconds.

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The point e. x = 5, y = 0 satisfies the two linear constraints simultaneously. We have two linear constraints which are given as;

2x + 5y ≤ 10 (Equation 1)

10x + 6y ≤ 42 (Equation 2)

We need to find the point which satisfies both equations. Let us plug in the values one by one to check which one satisfies the two equations simultaneously.

a. x= 6, y = 2

In Equation 1:2x + 5y = 2(6) + 5(2) = 17

In Equation 2:10x + 6y = 10(6) + 6(2) = 66

Thus, this point does not satisfy equations 1 and 2 simultaneously.

b. x=6, y=4

In Equation 1:2x + 5y = 2(6) + 5(4) = 28

In Equation 2:10x + 6y = 10(6) + 6(4) = 72

Thus, this point does not satisfy equations 1 and 2 simultaneously.

c. x=2, y = 1

In Equation 1:2x + 5y = 2(2) + 5(1) = 9

In Equation 2:10x + 6y = 10(2) + 6(1) = 26

Thus, this point does not satisfy equations 1 and 2 simultaneously.

d. x=2, y = 6

In Equation 1:2x + 5y = 2(2) + 5(6) = 32

In Equation 2:10x + 6y = 10(2) + 6(6) = 52

Thus, this point does not satisfy equations 1 and 2 simultaneously.

e. x = 5, y = 0

In Equation 1:2x + 5y = 2(5) + 5(0) = 10

In Equation 2:10x + 6y = 10(5) + 6(0) = 50

Thus, this point satisfies both equations simultaneously.

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The dimensions of the field should be 125m by 100m to enclose the maximum area.

To solve this problem, we can use the fact that the area of a rectangle is given by A = lw, where l and w are the length and width of the rectangle, respectively. Since the field is to be subdivided into four congruent plots, we can express the width in terms of the length as w = (1/4)(l).

We can then use the fact that the total length of fencing available is 6000m to set up an equation for the perimeter of the rectangle, which is given by P = 2l + 5w. Substituting w with (1/4)(l), we get P = 2l + 5((1/4)(l)) = (9/2)l.

Solving for l in terms of P, we get l = (2/9)P. Substituting this expression for l into the equation for the area, we get A = (1/4)(l)(w) = (1/4)(l)((1/4)(l)) = (1/16)l^2.

We can now express the area in terms of P as A = (1/16)((2/9)P)^2 = (4/81)(P^2). To find the maximum area, we can take the derivative of A with respect to P and set it equal to zero, which gives dA/dP = (8/81)P = 0. This implies that P = 0 or P = 81/8. Since P cannot be zero, we have P = 81/8.

Substituting this value of P back into the equation for l, we get l = (2/9)(81/8) = 18.75. Finally, substituting l and w = (1/4)(l) into the equation for A, we get A = (1/16)(18.75)(4.6875) = 117.1875. Therefore, the dimensions of the field should be 125m by 100m to enclose the maximum area.

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Answer:

The equation of the line that passes through the point (3,-3) and has a slope of 0 will be:

\(0=y+3\)

Step-by-step explanation:

The point-slope form of the equation of a line is:

\(\:y\:-\:y_1\:=\:m\left(x-x_1\right)\)

where

As the slope is \(m=0\), and the point is \((3,-3)\)

so

Equation of the line will be:

\(\:y\:-\:y_1\:=\:m\left(x-x_1\right)\)

\(y\:-\:\left(-3\right)\:=\:0\left(x-3\right)\)

Further simplifying

\(0=y-\left(-3\right)\)

\(0=y+3\)

Therefore, the equation of the line that passes through the point (3,-3) and has a slope of 0 will be:

\(0=y+3\)

We are supposed to prove that the first player has a winning strategy for the game of Chomp if the initial board is two squares wide.

Let us assume that the board is of 2 x m size.

Then by using c we will prove that the first player has a winning strategy.

Base Case: If the board is 2 x 1, then the only square left is the bottom left square, so the second player will take it and win the game.

Inductive Hypothesis: Assume that for some positive integer k, whenever we have a board with 2 x m squares, where 1 ≤ m ≤ k, the first player has a winning strategy.

Inductive Step: Now we must prove that the first player has a winning strategy for a board of size 2 x k + 1.

The first move of the first player is to chomp the cookie in the bottom row at the far right. This leaves a board of size 2 x k.

By the inductive hypothesis, the first player has a winning strategy for this board. Therefore, the second player has to make the second move.

He can either chomp a cookie in the bottom row to the left of the chomped cookie or a cookie in the top row. If he chomps a cookie in the bottom row, the first player uses the same strategy as for a board of size 2 x k. If he chomps a cookie in the top row, the first player chomps the corresponding cookie in the bottom row, leaving a board of size 2 x k. By the inductive hypothesis, the first player has a winning strategy for this board.

Therefore, the first player has a winning strategy for a board of size 2 x k + 1 whenever he starts by chomping the cookie in the bottom row at the far right.

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The probability that the first failed inspection occurs on Fatima's 5th inspection i.e P(c = 5) is 0.05..

In probability and statistics,the geometric distribution defines the probability of the first success occurring after k trials. The probability of success is p

P r ( X = k ) = ( 1 − p )⁽ᵏ⁻¹⁾ p.

We have given that,

An emissions inspections on cars is conducted by Fatima.

Probability that car fail the inspection, p = 6% = 0.06

let c denoted the number of cars that are inspected until one car fail to inspection.

The random variable c here. Here c follow geometric probability distribution with probability of success (0.06).

Plugging all known values in above formula we get, p(c= 5) = (1-0.06)⁴ × 0.06

= (0.94)⁴ (0.06)

=0.0468449376~ 0.05

so, the answer is 0.05

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Complete question:

Fatima conducts emissions inspections on cars. She finds that 6%, percent of the cars fail the inspection. Let C be the number of cars Fatima inspects until a car fails an inspection. Assume that the results of each inspection are independent.

Required:

Find the probability that the first failed inspection occurs on Fatima's 5th inspection

Answer:

20% decrease

Step-by-step explanation:

Below are the steps that we will follow:

Now, lets apply it to the problem:

Starting Value: 465 students

Final value: 372 students

Let's do step #1:

465-372 = 93

Now, let's do step #2:

93/465 = 0.2

Now, we can do step #3:

0.2x100 = 20

Step #4 does not apply to us, so we can ignore that.

20% decrease is the answer.

Hope this helps and happy learning! :)

Answer:

0.7 is a rational number

Step-by-step explanation:

Rational numbers are defined as numbers that result when two integers are divided.

Answer:

your answer is B.

Step-by-step explanation:

mode is 76, mean is 79, the median is 76.

The compensation point of fern plants that grow on the forest floor occurs at 10.00 am. In my opinion, the Ficus plant, which grows higher in the same forest, will achieve its compensation point at midday or early afternoon.

Compensation point is the point where the rate of photosynthesis is equal to the rate of respiration. It is the point where the carbon dioxide taken up by the plants in photosynthesis is equal to the carbon dioxide released in respiration. At this point, there is no net uptake or release of carbon dioxide. In other words, the rate of carbon dioxide production and consumption is balanced. When the light intensity is low, photosynthesis cannot meet the plant's energy needs, and respiration occurs at a higher rate, resulting in a net release of CO2. When the light intensity is high, photosynthesis happens at a faster rate than respiration, resulting in a net uptake of CO2.

In conclusion, the Ficus plant that grows higher in the same forest would achieve its compensation point at midday or early afternoon.

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Answer:

y=-3.5

Step-by-step explanation

Answer:

y = -3.5

Step-by-step explanation:

This is a horizontal line ( the y value does not change)

Horizontal lines are of the form

y=   constant

y = -3.5

Emily new boots cost a total of $71.4 with the tax included as 5% and the original cost of the boots being $68.

The sales tax rate in Emily's city = 5% and the cost of Emily's new boots is $68

we need to find the amount of sales tax Emily will pay for her boots,

The formula we will use =

Sale tax = Percent sales tax x Cost of the product

when we put the values in the formula, we get:

Sales tax = 5% x $68

= $3.4

now we need to also calculate the total cost for Emily's boots,

Therefore, the total cost = Cost of boots + Sales Tax

when we put the values in the formula, we get:

Total cost = $68 + $3.4

= $71.4

Therefore, the total cost Emily will pay for her boots is $71.4

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Answer:

Step-by-step explanation:

Dont do it. Just take the detention

Answer:Divide 50 by 20, that is unless you don't like to divide. If you would rather multiply, you can always multiply 50 by . 

Answer:

50 pounds?

Step-by-step explanation:

The expression that will help to calculate the area of the figure is A = (n-6)² and the area will be 25 units² when n = 11.

A term may be a number, a variable, the product of two or more variables, a number and a variable, or any combination of these.

A single term or a collection of phrases can be used to create an algebraic expression.

For instance, 4x and y are the two terms in the formula 4x + y.

So, we have a square as a figure.

The side of the figure is (n - 6).

Now, the expression to find the area of the square will be:

A = (n-6)²

Now, evaluate when n = 11 as follows:

A = (n-6)²

A = (11-6)²

A = (5)²

A = 25 units²

Therefore, the expression that will help to calculate the area of the figure is A = (n-6)² and the area will be 25 units² when n = 11.

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The correct statement about their work is: Both Adler and Erika solved for k correctly because either the addition property of equality or the subtraction property of equality can be used to solve for k.

Adler started with the equation (13/8) = k(1/2) and subtracted 1/2 from both sides to get (13/8) - (1/2) = k(1/2) - (1/2). Then simplifying, Adler obtained (9/8) = k.

Erika started with the equation (13/8) = k(1/2) and multiplied both sides by -1/2 to get (13/8)(-1/2) = k(1/2)(-1/2). Simplifying, Erika obtained (9/8) = k.

Both Adler and Erika arrived at the correct value of k = 9/8, despite using slightly different approaches. The inverse of addition (subtracting 1/2) and the opposite of one-half (multiplying by -1/2) were correctly applied in their respective calculations.

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Answer:

I believe not

-2 divided by 10

-2/10

10 divided by -2

10/-2

1 divided by 5

1/5

5 divided by 1

5/1

Answer:

Step-by-step explanation:

SAS Congruence Postulate

the volume of a region bounded by the curve and the -axis between is 19.47787445 cubic units.

What is volume of cone?

The area or volume that a cone takes up is referred to as its volume. Cones are measured by their volume in cubic units such as cm3, m3, in3, etc. By rotating a triangle at any of its vertices, a cone can be created. A cone is a robust, spherical, three-dimensional geometric figure.. Its surface area is curved. The perpendicular height is measured from base to vertex. Right circular cones and oblique cones are two different types of cones. While the vertex of an oblique cone is not vertically above the center of the base, it is in the right circular cone where it is vertically above the base.

So the

V = (1/3)πr²h.

V = π ∫ (x^2)^2 dx - π ∫ 0 dx = π ∫ (x^4) dx - 0 = π (x^5 / 5)

Evaluating from 2 to 1 yield the following:

π (2^5 / 5 - 1^5 / 5) = π (32/5 - 1/5) = 31π/5 cubic units, approximately equal to 19.47787445 cubic units

Hence, the volume of a region bounded by the curve and the -axis between is 19.47787445 cubic units

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synonym: a word of opposite meaning

contrast:  to show noticeable differences

Answer:

1/6 and 1/6^1 so the second and 4th one.

Step-by-step explanation:

Look it up bud

Answer: (c)

Step-by-step explanation:

Given

The inequality is \(7y+1<8y-9\\\)

Solving the above inequality

\(\Rightarrow 7y+1<8y-9\\\\\Rightarrow 1+9<8y-7y\\\\\Rightarrow 10<y\ \text{or}\\\\\Rightarrow y>10\)

Thus, option (c) is correct.

Since the function we want to integrate is a polynomial, we use the following general rule:

Then, in this case we have:

Now we must evaluate F(b)-F(a). We have that a=-1 and b=4, then:

Therefore, the integral of 4x^2-3x+7 evaluated from -1 to 4 is 595/6

The greatest common factor of 12 and 78 is 6, and the GCF of 18 and 176 is 2, determined using Euclid's algorithm.

a. To find the greatest common factor (GCF) of 12 and 78 using Euclid's algorithm, we start by dividing the larger number, 78, by the smaller number, 12:

78 ÷ 12 = 6 remainder 6

We then divide the divisor of the previous step, which is 12, by the remainder of the previous step, which is 6:

12 ÷ 6 = 2 remainder 0

Since the remainder is 0, we have found that the GCF of 12 and 78 is the divisor of the last non-zero remainder, which is 6.

Therefore, GCF (12, 78) = 6.

b. To find the GCF of 18 and 176 using Euclid's algorithm, we start by dividing the larger number, 176, by the smaller number, 18:

176 ÷ 18 = 9 remainder 14

We then divide the divisor of the previous step, which is 18, by the remainder of the previous step, which is 14:

18 ÷ 14 = 1 remainder 4

We continue this process by dividing the divisor of the previous step, which is 14, by the remainder of the previous step, which is 4:

14 ÷ 4 = 3 remainder 2

Finally, we divide the divisor of the previous step, which is 4, by the remainder of the previous step, which is 2:

4 ÷ 2 = 2 remainder 0

Since the remainder is 0, we have found that the GCF of 18 and 176 is the divisor of the last non-zero remainder, which is 2.

Therefore, GCF (18, 176) = 2.

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The complete question is:

Find the largest common factor between the following pairs of numbers using Euclid's algorithm:

a. GCF (12, 78)

b. GCF (18, 176)