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By applying implicit differentiation to the equation \(x^2\) + x + y = \(y^2\) + 9, we found that dy/dx is equal to (2x + 1) / (2y).

The implicit differentiation process allows us to find the derivative of a function that is not explicitly defined in terms of x.

For the given equation, \(x^2\) + x + y = \(y^2\) + 9, we can find dy/dx using implicit differentiation.

To begin, we differentiate both sides of the equation with respect to x.

For the left side, we apply the power rule to \(x^2\) and x, giving us 2x + 1.

For the right side, we differentiate \(y^2\) using the chain rule, which yields 2y(dy/dx).

Since y is a function of x, we multiply by dy/dx.

Now we have 2x + 1 = 2y(dy/dx).

To find dy/dx, we isolate the term by dividing both sides of the equation by 2y, resulting in:

dy/dx = (2x + 1) / (2y).

This is the derivative of y with respect to x, obtained by implicit differentiation of the given equation.

In summary, by applying implicit differentiation to the equation \(x^2\) + x + y = \(y^2\) + 9, we found that dy/dx is equal to (2x + 1) / (2y).

This derivative represents the rate of change of y with respect to x for any point satisfying the given equation.

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Answer: Positive correlation

Step-by-step explanation:

As you go up and along the graph the values go up.

Both have to be increasing basically.

The x axis of the equation is x2 = (2k / (2π)2)y2, which can be calculated by multiplying both sides of the equation by (2π)2 and then dividing both sides by 2k.

The x axis of the equation is determined by isolating the x variable in the equation. We can do this by first multiplying both sides of the equation by (2/π):

(2/π) * y = 2k * (2/π) * (2xy)

Then we can divide both sides of the equation by 2k to isolate the x variable:

(2/π) * y / 2k = (2/π) * (2xy)

Finally, we can divide both sides of the equation by 2 to get the x axis of the equation:

x = y / 2k

Therefore, the x axis of the equation is y / 2k.

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Answer:

5b - 0.9b, distributive property

Step-by-step explanation:

The expression that is used to find the price of 5 loaves of bread is given by :

5(b-0.18b)

We need to rewrite the above expression.

Distributive property : a(b+c) = ab + ac

Here, a = 5, b = b and c = -0.18b

5(b-0.18b) = 5(b) + 5(-0.18b)

= 5b - 0.9b

So, the equivalent expression is 5b - 0.9b. The distributive property was used to rewrite the expression.

Answer: For the linear relationship in A, the y-intercept is the point where the line crosses the y-axis. This point represents the starting balance on Ailee's gift card before she makes any purchases.

The y-intercept of this linear relationship is the point (0, 20), which represents the fact that Ailee's gift card has a starting balance of $20 before she makes any purchases.

For the linear relationship in B, the y-intercept is the point where the line crosses the y-axis. This point represents Duncan's starting elevation before he begins to hike.

The y-intercept of this linear relationship is the point (0, 1000), which represents the fact that Duncan starts his hike at an elevation of 1000 feet.

Step-by-step explanation:

Answer:

64.8 ounces

Step-by-step explanation:

48 nails times 1.35 ounces gives you 64.8 ounces.  

The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.

The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.

Given the production function q = 1000KL, we can differentiate it with respect to L:

d(q)/d(L) = 1000K

Therefore, the RTS of the isoquant for production level q is 1000K.

The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.

Labor cost = $20/hour

Capital cost = $40/machine/hour

Ratio of labor to capital cost = Labor cost / Capital cost

                              = $20/hour / $40/machine/hour

                              = 0.5

The ratio of labor to capital cost is 0.5.

To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.

Let C(K, L) be the total cost function.

The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:

C(K, L) = 40K + 20L

To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.

The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.

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Answer:y is 60 slope is -10

Step-by-step explanation:

No. of teeth on the pinion(TP)=17.

Diametral pitch(pd)=8 teeth/in.

Rotational speed of the pinion(NP)=1120 rev/min or 1120 rpm.

Rotational speed of the gear(NG)=544 rev/min or 544 rpm.

To calculate:

No. of teeth on gear(TG) & theoretical centre to centre distance(C).

Solution:

We know that;

Diametral pitch(pd)=No. of teeth in the gear/Diameter of the gear

For pinion,

pd=TP/DP  

Pittiong the values in above eq.

8 teeth/in =17/DP    =>DP=17/8 in.

or DP=2.125 in.

Gear ratio(G)=(NP/NG)=(TG/TP)=(DG/DP)

=>(NP/NG)=(TG/TP)

=>1120/544 =TG/17 =>TG=35

No. of teeth the gear(TG)=35 {Ans}

Also from gear ratio formula,

(NP/NG)=(DG/DP)

=>1120/544=DG/2.125

=>DG=4.375 in.

In the next fig. I have drawn a rough diagram of the pinion and gear arrangement which will help you to understand how to calculate the centre to centre distance(C)

centre to centre distance,C=rP+rG {Where rP and rG are the radii of pinion and gear respectively}

=>C=(DP+DG)/2

Diameter =2*radius}

=>C=(2.125+4.375)/2 in. =3.25 in.

Theoretical centre to centre distance (C)=3.25 in.

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To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

The domain of the function f(x) = ln(x-3) is x > 3, since the natural logarithm is undefined for non-positive values. The x-intercept occurs when f(x) = 0, so ln(x-3) = 0, which implies x - 3 = 1. Solving for x gives x = 4 as the x-intercept.

There are no vertical asymptotes for the function f(x) = ln(x-3) since the natural logarithm is defined for all positive values. However, the graph approaches negative infinity as x approaches 3 from the right, indicating a vertical asymptote at x = 3.

To sketch the graph of f(x) = ln(x-3), we start with the x-intercept at (4, 0). We can plot a few more points by choosing values of x greater than 4 and evaluating f(x) using a calculator.

As x approaches 3 from the right, the graph approaches the vertical asymptote at x = 3. The graph will have a horizontal shape, increasing slowly as x increases. Remember to label the axes and indicate the asymptote on the graph.

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Answer:

154 m^2

Step-by-step explanation:

Area of a circle:  A = (pi)(radius)^2

Here, r = 7 m, so A = (3.14)(7 m)^2 = 154 m^2

Answer:

D

Step-by-step explanation:

D includes all possible outcomes.

Answer:

D

Step-by-step explanation:

D show all the possible answers so D.

Answer:

A and e

Step-by-step explanation:

The value of the average of all three numbers is,

⇒ 7

We have to given that,

The average of two numbers is 6.

And, A third number of 9 is now included.

Let us assume that,

Tow numbers are x and y.

Hence, We get;

(x + y) / 2 = 6

x + y = 12

Now, A third number of 9 is now included.

Then, the average of all three numbers are,

= (x + y + 9) / 3

= (12 + 9)/ 3

= 21 / 3

= 7

Thus, The value of the average of all three numbers is,

⇒ 7

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Answer:

Step-by-step explanation:

PART A. Graph the linear equation

- Look at the Graph below as an attachment

PART B. Interpret the slope and the y-intercept

- The slope-intercept form in the linear equation is: y=mx+b

Solve

y=mx+b

y=-15x+375

slope=-15

y-intercept=375

Hope this helps!! :)

Please let me know if you have any questions

2

1

3

5/8 = 0.625

1/3 = 0.3333...

17/24 = 0.70833333

Answer:

\( \frac{4}{(g + 4) ^{2} }\)

Step-by-step explanation:

\( \frac{g}{g(g + 4)} - \frac{g}{(g + 4) ^{2} } \)

\( \frac{1}{g + 4} - \frac{g}{(g + 4) ^{2} } \)

\( \frac{g + 4}{(g + 4) ^{2} } - \frac{g}{(g + 4) ^{2} } \)

\( \frac{g + 4 - g}{(g + 4) ^{2} } \)

\( \frac{4}{(g + 4) ^{2} } \)

\( \frac{4}{g^{2} + 8g + 16 } \)

Hope It's Help

Answer:

I will help

Step-by-step explanation:

Answer:

1920

Step-by-step explanation:

What we can do is split this into two sections: the volume of the rectangle and the volume of the square.

Rectangle: We can follow the equation V = lbh, so we have 14x8x10, giving us 1120.

Square: We can use the same equation, V = lbh, giving us 10x10x8 which is 800.

Final Answer: To get the full volume, we have to add these together, so, 1120 + 800 = 1920.

A system of linear inequalities represented by the graph include the following:

Inequality 1: y ≥ -3x + 2

Inequality 2: y ≥ 2x/3 - 2

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

0 2 1 -1

First, we would determine the slope of line 1;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-1 - 2)/(1 - 0)

Slope (m) = -3/1

Slope (m) = -3.

At data point (0, 2) and a slope of -3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = -3(x - 0)

y = -3x + 2

y ≥ -3x + 2 (since the solid line is shaded above)

For line 2, we have:

Slope (m) = (0 + 2)/(3 - 0)

Slope (m) = 2/3

y - 0 = 2/3(x - 3)

y = 2x/3 - 2

y ≥ 2x/3 - 2 (since the solid line is shaded above)

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use sin

sin(50) = x/6

sin(50) x 6 = x

x = ~4.5963

Answer:

120

Step-by-step explanation:

The current through the inductor to reach one-half of its maximum value after closing the switch is approximately 12.5 microseconds.

To determine the time it takes for the current through the inductor to reach one-half of its maximum value, we can use the time constant formula for an RL circuit:

t = (1/2)(L/R)

Given:

Plugging in the values, we have:

t = (1/2)(0.00125 H) / (50.0 Ω)

Simplifying the equation, we find:

t = 0.0000125 s or 12.5 μs

Therefore, the current through the inductor will reach one-half of its maximum value approximately 12.5 microseconds after closing the switch.

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Answer:

I'm almost positive it's H, but not completely positive....It starts 12n, because n=nuggets, than you add the amount of calories of the large order of fries which is 193.5 calories.....

Step-by-step explanation:

Really sorry if I am wrong. I tortured my brain WITH THIS!!!!!!!

Eric's who worked as an electrical engineer, pension payout will be $99,264 per year.

Average, also known as mean, is a measure of central tendency that is calculated by adding together a set of values and dividing the total by the number of values. It is commonly used in statistics and mathematics to describe a typical value in a set of data.

To calculate Eric's pension payout, we need to first calculate the average of his last 5 years of employment.

The average of his last five years of employment is:

($120,000 + $122,500 + $124,000 + $127,900 + $130,000) / 5 = $124,080

Next, we need to calculate Eric's pension payout using the formula provided by his pension plan:

Pension payout = 2% x Average salary x Years of employment

Eric worked as an Electrical Engineer for 40 years, so his pension payout is:

Pension payout = 2% x $124,080 x 40 = $99,264

Therefore, Eric's pension payout will be $99,264 per year.

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Roadway density is the amount of vehicles occupying a specific length of roadway, normally a mile or a kilometer, at a given point in time. It is often used to determine traffic flow and congestion. The space mean speed of traffic on a roadway segment is 50 miles per hour and 150 vehicles per hour are traveling on the segment.

To determine the roadway density, we use the formula: Roadway density = number of vehicles / length of roadway segment Roadway density is expressed in terms of vehicles per mile. Therefore, using the formula above: Roadway density = 150 / (50/1) = 150 / 50 = 3 vehicles/mile. Therefore, the roadway density is 3 vehicles per mile.

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Answer:  21

Step-by-step explanation:

k(x) =x^3-2x

k(3) =3^3-2*(3)

k(3) =27-6

k(3) = 21

one possible set of coordinates for points P and R are (6, 0) and (0, 7), respectively.

We can use the Pythagorean theorem to find the length of the hypotenuse PR:

PR² = PQ² + QR²

PR² = 6² + 7²

PR² = 36 + 49

PR² = 85

PR = sqrt(85)

Therefore, the length of the hypotenuse PR is approximately 9.22 units (rounded to two decimal places).

Since we know that point Q is the right angle, we can place it at the origin (0, 0). We can also assume that point P is on the x-axis, and point R is on the y-axis.

One possible set of coordinates for point P is (6, 0), since it lies 6 units to the right of Q along the x-axis.

One possible set of coordinates for point R is (0, 7), since it lies 7 units above Q along the y-axis.

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