The formula for potential energy is p=mgh, where p is potential energy, m is mass , g is gravity and h is height . Which expression can be used to represent g

The rate of change of the side of the square is 1.5 centimeters per second when the area is 3 square centimeters.

Let's denote the side length of the square as s, and the area of the square as A. Then we know that \(A = s^2\). We are given that \(dA/dt = 30 cm^2/s\), which means that the area of the square is increasing at a rate of \(30 cm^2/s\). We want to find ds/dt, the rate of change of the side of the square.

Using the chain rule, we have:

\(dA/dt = d/dt (s^2) = 2s ds/dt\)

Solving for ds/dt, we get:

\(ds/dt = (1/2s) dA/dt\)

When the area is \(3 cm^2\), the side length is \(s = \sqrt{3} cm\). Plugging in dA/dt = 30 cm^2/s and s = sqrt(3) cm, we get:

\(ds/dt = (1/2(\sqrt{3})) (30) = 1.5 cm/s\)

Therefore, the rate of change of the side of the square is 1.5 cm/s when the area is 3 cm^2.

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Answer:

2.12482717E22

Step-by-step explanation:

The number of individuals in the sample is equal to the degrees of freedom (df) plus one. So if the t statistic has df = 30, then the number of individuals in the sample is 30 + 1 = 31. Therefore, there were 31 individuals in the sample.

Here is a step-by-step explanation of how to find the number of individuals in the sample:

1. Identify the degrees of freedom (df) of the t statistic. In this case, df = 30.
2. Add one to the degrees of freedom to find the number of individuals in the sample. In this case, 30 + 1 = 31.
3. The number of individuals in the sample is 31.

So the answer to the question "a researcher conducts a hypothesis test (single sample t) using a sample from an unknown population. if the t statistic has df = 30, how many individuals were in the sample?" is 31.

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Answer:

Step-by-step explanation:

The loop will run an infinite number of times

The gradient field of the function is given by grad f = 6x i + 8y j + k and it passes through the plane z = 1/4, where k = 1.

The given function is f(x, y, z) = 3x² + 4y² + 2z² and it is required to find the gradient field of this function, where the gradient field is Vf = + k. Therefore, the solution is given below.

To determine the gradient of the given function, we must first compute its partial derivatives with respect to x, y, and z.  So, let's calculate the partial derivatives of the given function first:

∂f/∂x = 6x∂f/∂y = 8y∂f/∂z = 4z

The gradient vector field is as follows:

grad f = ∂f/∂x i + ∂f/∂y j + ∂f/∂z k= 6x i + 8y j + 4z k

Now, as given, the gradient field is Vf = + k. Thus, we only have the k-component of the vector field and no i or j-component.

Therefore, comparing the k-component of the gradient vector field with Vf, we get:

4z = 1 (As Vf = k, we only need to compare the k-components.)

Or z = 1/4

Hence, the gradient field of the function is given by grad f = 6x i + 8y j + k and it passes through the plane z = 1/4, where k = 1.

The gradient field indicates that the function is increasing in all directions. In addition, we can see that the z-component of the gradient field is constant.

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Answer:

Degree measure of each angle is 90⁰, 47⁰ and 43⁰

Step-by-step explanation:

since the triangle is right angled, we assume that Q and S are the other angles of this triangle R

Thus using the concept that angles inside a triangle add up to 180⁰ and we already have one angle as 90⁰( since the triangle is right angled). we therefore know that Q + S = 90⁰

5x - 13 + 4x - 5 = 90⁰

9x = 108

x = 12

We now replace x in Q and S to get the angles

Q = 5(12) -13

= 47⁰

S = 4(12) - 5

= 43⁰

As per the question, All four students A, B, C, and D are loss-averse over money and have the same value function as below:v(x dollars)={√x     x ≥ 0   {-2√-x  x < 0They are also loss averse over mugs and have the same value function.

v(y mugs)={3y y ≥ 0
        {4y y < 0
Now, we have to find the values of a, b, c and d as below:
- Student A owns a mug and is willing to sell it for a price of a dollars or more. i.e v(a) = v(0) + v(a-A), where A is the initial endowment of A. According to the given function, v(0) = 0, v(a-A) = 3, and v(A) = 4.
So, a ≥ A+3/2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. i.e v(B-b) = v(B) - v(0), where B is the initial endowment of B. According to the given function, v(0) = 0, v(B-b) = -4, and v(B) = -3.
So, b ≤ B+1/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. i.e v(c) = v(0) + v(c), where C is the initial endowment of C. According to the given function, v(0) = 0, v(c) = 3.
So, c = C/2
- Student D is indifferent between losing a mug and losing d dollars. i.e v(D-d) = v(D) - v(0), where D is the initial endowment of D. According to the given function, v(0) = 0, v(D-d) = -3.
So, d = D/2
2) In this case, value function for money changes to:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
However, the value function for mugs remains the same:v(y mugs)={3y y ≥ 0
         {4y y < 0
Therefore, values for a, b, c, and d will remain the same as calculated in part (1).
3) In this case, students are not loss-averse. Value function for money:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
Value function for mugs:v(y mugs)={3y y ≥ 0
The reference point is the status quo, i.e initial endowment. So,
- Student A owns a mug and is willing to sell it for a price of a dollars or more. The value of mug for A is 3 initially and he would sell it for 3 or more.
So, a ≥ A+3/2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. The value of mug for B is 3 initially and he would buy it for 3 or less.
So, b ≤ B+3/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. The value of the mug for C is 3 initially.
So, c = 3
- Student D is indifferent between losing a mug and losing d dollars. The value of the mug for D is 3 initially.
So, d = 3
4) In this case, value function for money:v(x dollars)={√x     x ≥ 0
            {-√-x   x < 0
Value function for mugs: Mug will have a value of 4 for someone who owns it and 3 for someone who does not own it.
The reference point is the status quo, i.e initial endowment. So,
- Student A owns a mug and is willing to sell it for a price of a dollars or more. The value of mug for A is 4 initially and he would sell it for 4 or more.
So, a ≥ A+2
- Student B does not own a mug and is willing to pay up to b dollars for buying it. The value of mug for B is 3 initially and he would buy it for 3 or less.
So, b ≤ B+3/2
- Student C does not own a mug and is indifferent between getting a mug and getting c dollars. The value of the mug for C is 3 initially and he would like to buy it for 3.
So, c = 3
- Student D is indifferent between losing a mug and losing d dollars. The value of the mug for D is 3 initially.
So, d = 3.

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the ratio 1 is to 2 is equivalent to 3: 6

What is an equivalent ratios?

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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To find the area using the limit of a sum (a Riemann sum) of the region between the graph of y = f(x) and the x-axis from x = a to x = b, the formula is given by: Area = lim n → ∞ ∑ i = 1 n f(x* i )Δx, where f(x* i ) is the height of the ith rectangle and Δx is the width of the ith rectangle.

To find the area between the graph of y = f(x) and the x-axis from x = a to x = b using the limit of a sum, we need to first divide the interval [a, b] into n equal subintervals of length Δx = (b - a)/n. Then, we can choose any point x* i in the ith subinterval [x i-1 , x i ] and use it to determine the height of the ith rectangle f(x* i ).

Finally, we can take the limit as n approaches infinity to obtain the exact area of the region between the graph of y = f(x) and the x-axis from x = a to x = b.

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Answer:

4x^2+3x+4

Step-by-step explanation:

Given (3x^2+2x+3)+(x^2+x+1)

=x^2(3+1)+x(2+1)+(3+1)

=4x^2+3x+4.

Answer:

4x^2 + 3x + 4

Step-by-step explanation:

(3x^2 + 2x + 3) + (x^2 + x + 1)

3x^2 +2x +3 + x^2 + x + 1

4x^2 + 2x + 3 + x + 1

4x^2 + 3x + 3 + 1

4x^2 + 3x + 4

The answer is 4x^2 + 3x + 4.

To write Acos(?0t) + Bsin(?0t) in the form r*sin(?0t - ?), we can use the identities. The relationship among R, r, ? and ? is:
R^2 = r^2 (1 + (A/B)^2), tan? = r/R = B/A

r = sqrt(A^2 + B^2)
tan? = B/A

Therefore, r = sqrt(A^2 + B^2) and tan? = B/A.

To determine the relationship among R, r, ? and ?, we can use the identity:

R^2 = r^2 + (tan?)^2

Therefore, R = sqrt(r^2 + (tan?)^2) and tan? = r/R. Substituting the expression for tan? from earlier, we get:

tan? = B/A = r/R

Solving for R, we get:

R = r/tan? = r/(B/A) = rA/B

And substituting the expression for R in terms of r and tan?, we get:

R = sqrt(r^2 + (r/R)^2) * A/B

Simplifying this expression, we get:

R^2 = r^2 + (A/B)^2 * r^2

R^2 = r^2 (1 + (A/B)^2)

Therefore, the relationship among R, r, ? and ? is:

R^2 = r^2 (1 + (A/B)^2)
tan? = r/R = B/A

To show that Acos(ω₀t) + Bsin(ω₀t) can be written in the form r*sin(ω₀t - θ), we can use trigonometric identities. We know that:

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Comparing this to the given expression, we have:

Acos(ω₀t) + Bsin(ω₀t) = r*sin(ω₀t - θ) = r[sin(ω₀t)cos(θ) - cos(ω₀t)sin(θ)]

Now, let's equate the coefficients of sin(ω₀t) and cos(ω₀t):

A = -r*sin(θ)
B = r*cos(θ)

To find r and θ in terms of A and B, we can use the Pythagorean identity:

A² + B² = (-r*sin(θ))² + (r*cos(θ))² = r²(sin²(θ) + cos²(θ)) = r²

Therefore, r = √(A² + B²).

Now, to find θ, we can use the tangent function:

tan(θ) = -A/B

Now, for the second part, if Rcos(ω₀t - θ) = r*sin(ω₀t - θ), we can use the sine-to-cosine transformation:

Rcos(ω₀t - θ) = Rsin(ω₀t - θ + π/2)

This implies that:

R = r
θ + π/2 = θ'

So, the relationship among R, r, θ, and θ' is:

R = r
θ' = θ + π/2

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Answer:   \(\boldsymbol{-7}m + \boldsymbol{\frac{8}{5}}\)

Work Shown:

\(-\frac{2}{5}(15m-4)-m\\\\-\frac{2}{5}(15m)-\frac{2}{5}(-4)-m\\\\-6m+\frac{8}{5}-m\\\\\boldsymbol{-7}m + \boldsymbol{\frac{8}{5}}\)

Therefore -7 goes in the first box, and \(\boldsymbol{\frac{8}{5}}\) goes in the second box.

Answer:

- 7m + 8/5

Step-by-step explanation:

- 2/5 ( 15m - 4 ) - m

 Multiply - 2/5 with 15m & - 4.

 ( - 2/5 x 15m ) - ( - 2/5 x 4 ) - m

= ( - 2 x 15m )/5 - ( - 2 x 4 )/5 - m

= - 30m/5 - ( - 8 )/5 - m

= - 6m + 8/5 - m

= - 6m - m + 8/5

= - 7m + 8/5

Answer:

x*(3x^2-7x-24)

Step-by-step explanation:

Answer: +6

Explanation: The equation x² - 36 = 0 is called a quadratic equation because he have a squared term as our highest power.

Our first step in this problem is to get the x²

term by itself by adding 36 to both sides.

That gives us x² = 36.

Next we must get the x by itself and in order to do

that we do the opposite of what is happening to x.

Since x is being squared, the opposite

of squaring is square rooting.

So to get x by itself, we square

root both sides of the equation.

On the left the square root of x² is x and on

the right, remember the following rule.

When square rooting both sides of

an equation, always use plus or minus.

So the answer to this problem would be +6.

So our solution to this equation is +6.

Answer:

Ben has 19 marbles

Step-by-step explanation:

First taking that josh and ricks ratio is 1:2, this would set up in an equation as \(2j = r\) and with ben having 15 less than rick, his formula would be \(r = b + 15\) as well as the total of all the boys marbles together being this \(j+r+b=70\)

Now we put all of these equations into a set to answer them.

\(2j = r\\ r = b + 15\\j+r+b=70\)

First we solve for j

\(2j = r\\ j=\frac{1}{2} r\)

Then substitute j

\(j+r+b=70\\ \frac{1}{2}r+r+b=70\\ 2b+3r=140\)

Then simplify and multiply by 2 to even out

\(r = b + 15\\ -b+r=15\\2b+3r=140\)

Now eliminate the b variable and combine equations

\(2b+3r=140\\-2b+2r=30\)

\(5r=170\)

Now divide and solve for r

\(5r=170\\r=34\)

Now we know Rick has 34 marbles of the 70 marbles, so we can substitute his number back into the original equation

\(-b+34=15\\b=19\)

Now we know Ben has 19 marbles of the remaining 36, and can substitute his number as well

\(j=\frac{1}{2}(34)\\j=17\)

And now we know how much everyone has, to check we rewrite all the equations with their respective numbers

\(11+34+19=70\\2(17)=34\\34=19+15\)

\(70=70\\34=34\\34=34\)

Which means the ordered pairing of (b, j, r) is (19, 17, 34)

Answer:

12 is the complete length and 10 is the number of sides

12x10= 120

Answer:

3.     P = 48 units   A = 116 units²

Step-by-step explanation:

A = 12 x 12

= 144

Now we can subtract the missing areas. 4 x 4 = 16 and 6 x 2 = 12.

144 - 16 - 12

= 116 units²

P = 12 + 12 + 12 + 12

= 48 units

Answer:

Step-by-step explanation:

(a) Limitations: Assumes reversible process, constant heat capacity.

(b) Limitations: Assumes constant T and P, and independent DH and DS with temperature.

(c) Limitation: Assumes non-expansion conditions, may not account for volume changes in real scenarios.

a) We have the equation for the height of the ball as y = -114x² + 2x + 3. So when the ball leaves the child's hand, the distance covered is 0, which means that x = 0.

Therefore, y = -114 (0)² + 2(0) + 3

= 3 feet.

So the ball leaves the child's hand at a height of 3 feet.

b) To find the maximum height of the ball, we need to find the vertex of the parabolic equation, which gives us the maximum value of the quadratic function. The vertex of a parabola whose equation is

y = ax² + bx + c is given by (-b/2a, c - b²/4a).

So for the given equation

y = -114x² + 2x + 3, the vertex will be at (-b/2a, c - b²/4a)

= (-2/2(-114), 3 - 2²/4(-114))

= (1/114, 924/19) ≈ (0.0088, 48.63).

Therefore, the maximum height of the ball is about 48.63 feet.

c) To find the distance the ball strikes the ground, we need to find the value of x when y = 0, since the ball strikes the ground when y = 0. Therefore,0 = -114x² + 2x + 3=> 114x² - 2x - 3 = 0 Solving the quadratic equation using the formula,

x = [-(-2) ± √((-2)² - 4(114)(-3))]/[2(114)]

= [2 ± √(4 + 1368)]/228

= [2 ± √1372]/228≈ 0.018 and -0.026So the ball strikes the ground at a distance of about 0.018 or 0.026 feet from the point where it was thrown. Since the distance is very small, we can conclude that the ball lands almost at the same point where it was thrown from.

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The function f(x) = 3x²/3 - 2x has no intercepts, a relative minimum at (1, -1), no points of inflection, and no asymptotes.

Intercepts: To find the x-intercepts, we set f(x) equal to zero and solve for x:

0 = 3x²/3 - 2x

0 = x² - 2x

0 = x(x - 2)

x = 0 or x = 2

Therefore, both x = 0 and x = 2 are not actual x-intercepts, but rather double roots.

Relative Extrema: To find the relative extrema, we take the derivative of f(x) and set it equal to zero,

f'(x) = 2x - 2

0 = 2x - 2

2 = 2x

x = 1

Substituting x = 1 back into the original function, we find f(1) = -1. Therefore, the relative minimum occurs at (1, -1).

f''(x) = 2

Since the second derivative is a constant, it never equals zero. Therefore, there are no points of inflection for this function.

Asymptotes: To determine if there are any asymptotes, we examine the behavior of the function as x approaches positive or negative infinity. Since the highest power of x in the function is 2, the graph does not approach any vertical asymptotes.

For horizontal asymptotes, we look at the limits as x approaches positive or negative infinity:

lim(x→∞) f(x) = lim(x→∞) (3x²/3 - 2x) = ∞

The limits approach positive infinity in both cases, indicating that there are no horizontal asymptotes. Graphically, the function represents a parabola that opens upwards, with a relative minimum at (1, -1).

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Answer:

= 3x -4y

Step-by-step explanation:

Answer:

6 feet by 5 feet by 4 feet

7 feet by 6 feet by 4 feet

Step-by-step explanation:

The surface are of rectangular prism = 140 ft²

Surface area of rectangular prism is given by :

A = 2(lw + lh + wh)

Using trial by error method :

6 feet by 2 feet by 3 feet

A = 2(6*2 + 6*3 + 2*3) = 72ft²

6 feet by 5 feet by 4 feet

A = 2(6*5 + 6*4 + 5*4) = 148 ft²

7 feet by 6 feet by 4 feet

A = 2(7*6 + 7*4 + 6*4) = 188ft²

8 feet by 4 feet by 3 feet

A = 2(8*4 + 8*3 + 4*3) = 136ft²

Answer:

No because there is a initial cost of $200.

Answer:

see below

Step-by-step explanation:

The equation is

y = 200+50x

This is not a proportional relationship because it does not go through the origin

If x=0, y does not equal 0

Answer:

option D is the correct answer of this question .....

Step-by-step explanation:

(c+8 )×(c-5) = c²-5c+8c -40

= c²+3c - 40

plz mark my answer as brainlist plzzzz vote me also

The equation of the line passing through the point (24,-87) with a slope of -4 can be expressed in slope-intercept form as \(y = -2.4x + 0.9\).

The slope-intercept form of a line is \(y = mx + b\), where m is the slope and b is the y-intercept.  The y-intercept is the point at which the line crosses the y-axis.  To find the y-intercept, we substitute the given values for x and y into the equation of the line and solve for b.

We substitute (24, -87) for (x,y) and solve for b:

\(-87 = -2.4(24) + b\\-87 = -57.6 + b\\b = 29.6\)

So the equation of the line passing through (24,-87) with a slope of -2.4 is \(y = -2.4x + 29.6\).

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In the context of property variance, a variance refers to a legal authorization or exception granted to a property owner by the local governing authority. It allows the property owner to deviate from specific zoning regulations or land-use restrictions that would otherwise apply to their property.

The variance process is used when property owners believe that strict adherence to the existing regulations would cause undue hardship or prevent them from fully utilizing their property in a way that is reasonable and consistent with neighboring properties.

The purpose of property variances is to address unique circumstances or hardships that may exist for a particular property. Property variances typically involve submitting an application to the local zoning board or planning department, attending public hearings, and providing evidence or arguments to support the need for the variance.

The governing authority evaluates the application based on factors such as the impact on neighboring properties, public health and safety, and the intent of the zoning regulations. If approved, the property owner is granted permission to proceed with the proposed deviation from the regulations.

Overall, property variances provide flexibility in land-use regulations, allowing property owners to find reasonable solutions that meet their specific needs while still considering the broader community interests and objectives of zoning regulations.

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Answer:

Step-by-step explanation:

a

Answer:

4 1/3, 4.337, 35/8, 4.44

Step-by-step explanation:

4.337, 4 1/3, 35/8, 4.44

4 1/3 = 13/3 = 4.333

35/8 = 4.375

So, the order from least to greatest is: 4 1/3, 4.337, 35/8, 4.44

Answer:

4 1/3, 4.337, 35/8, 4.44

Step-by-step explanation:

"order from least to greatest" means put the smallest first and each next one bigger and the biggest one last.

Change everything to decimals to compare.

A fraction bar is just a division symbol.

1/3 means 1÷3 which is .33333...

4 1/3 = 4.33333...

35/8 means 35÷8

= 4.375

Smallest is 4.333...

So 4 1/3 goes first.

Then 4.337 and next 35/8 (bc 4.375)

Last is biggest 4.44 so it goes last.

In order from least to geatest is:

4 1/3, 4.337, 35/8, 4.44