Josh made $242 for 11 hours of work.
At the same rate, how much would he make for 7 hours of work?

The answer is three

None, one or infinitely many solutions

A chart that compares three sets of values in a three-dimension chart is called surface.

A two-dimensional collection of points (flat surface), a three-dimensional collection of points with a curved cross section (curved surface), or the perimeter of any three-dimensional solid are all examples of surfaces in geometry.

A surface is typically a continuous boundary that separates two areas of a three-dimensional space. For instance, a sphere's surface divides its interior from its exterior, and a horizontal plane divides the half-planes above and below it. Despite the fact that regions they contain are three-dimensional and have a volume, surfaces are basically two-dimensional and have an area. Despite this, surfaces are frequently referred to by the names of the regions they surround. Differential geometry studies the characteristics of surfaces, particularly the concept of curvature.

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Angle 2 is the angle of elevation from point Q to point R.

What is angle of elevation ?

The angle of elevation is the angle formed between a horizontal line and the line of sight from the observer's eye to an object located above the observer's level. In other words, it is the angle between the horizontal and an imaginary line drawn upwards from the observer to the object being viewed. It is typically measured in degrees or radians.

Given,

Point Q is at the far left side of the top line, point R is at the far right of the second line, and point S is at the far left side of the bottom line.

Lines are drawn from point Q to point R and from point R to point S.

angle of depression from point R to point S.

The angle of depression from point S to point R is angle 3.

Therefore, Angle 2 is the angle of elevation from point Q to point R.

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Answer:

the angle of depression from point R to point S is angle 3

the angle of elevation from point S to point R is angle 4

angle 2 is the angle of elevation from point R to point Q

angle 1 is the angle of depression from point Q to point R

Step-by-step explanation:

Answer: - 13/7

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Answer:

Step B is incorrect because the factors of \(x^2 + 4x + 3\) should be:

\((x + 3)(x + 1)\)

Answer:

23

Step-by-step explanation:

one angle  = 134

Other two angles are the base angles which are  same.

x + x + 134 = 180   {Angle sum property}

2x + 134 = 180

2x = 180 - 134

2x = 46

x = 46/2

x = 23

Other two angles are 23 , 23

The minimum amount of green paint he has to throw away so he can use  rest to add blue or yellow paint in order to get exactly 5 liters of correct shade of green is 5/3 liter.

We know that "original-shade" of green color requires "2-liters" of blue paint and "3-liters" of yellow paint.

So, the original-ratio of "yellow-paint" to "total-paint" is = 3 : 5,

He mixes 3-litres of "blue" and 2-litres of "yellow" for 5 liters of paint,

So, he has more blue-paint in mixture than it is required to make green color,

He needs to throw some of green-paint and add yellow-paint to get required shade-of-green.

Let the painter throw away "x-liters" of paint from his mixture and adds "x-liters" of yellow-paint into mixture.

So, New mixture will have same ratio as 3:5,

So, the equation in x is,

⇒ (2/5)×(5 - x) + x = (3/5)×5,

⇒ 2 - (2/5)x + x = 3,

⇒ (3/5)x = 1,

⇒ x = 5/3.

Therefore, the painter needs to throw away 5/3 liters of paint.

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The optimal feasible solution is x1 = 1, x2 = 0.4, and the problem is a regular linear programming problem.

To solve the given linear programming problem, let's define the decision variables and formulate the objective function and constraints:

Decision Variables:

x1, x2

Objective Function:

Maximize: 2x1 + 6x2

Constraints:

2x1 + 5x2 ≤ 4

4x1 + x2 ≤ 6

x1, x2 > 0

To find the optimal feasible solution, we can use a linear programming solver. Here is the optimal solution for the given problem:

Optimal Solution:

x1 = 1

x2 = 0.4

The maximum value of the objective function is obtained when x1 = 1 and x2 = 0.4. The maximum value is 2(1) + 6(0.4) = 4.8.

Now let's analyze if the solution is a special case of linear programming.

This problem falls under the category of Linear Programming (LP) problems. However, it does not represent any specific special case of LP such as degeneracy, unboundedness, or infeasibility. The given problem has a feasible solution, and the objective function is maximized within the given constraints. Hence, it is a regular LP problem without any special case conditions.

Note: Since the solution is text-based, there is no need to scan or provide a separate file.

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Answer:

A= 2,2

B= 0,0

C= -2,2

here is your answer

Answer:

I think it's. y=-2/1x+2

Answer:

1) 25 miles

2) 20 m

Step-by-step explanation:

Number 1 is going to be

\(a^{2} + b^{2} = c^{2}\) because it's a right triangle

So

\(24^{2}\) + \(7^{2}\) = \(c^{2}\)

625 = \(c^{2}\)

c = 25 mile

Number 2 uses the same process, but changing to using C instead of A

a^2 = c^2 - b^2

a^2 = 625 - 225

a = \sqrt(400)

a = 20m

(a) There are 21 different ways to choose two different restaurants.

(b)There are 42 different ways to choose two different restaurants.

(c) There are 49 different ways to choose two different restaurants.

In the given question,  suppose Ches Tahoe restaurant is one of the 7 largest restaurants in x city.

a. We would like to choose two different restaurants from them. So we have to find how many different ways are there.

There are total 7 largest restaurants in x city.

We have to choose two different restaurants.

So different ways:

n = \(^{7}C_{2}\)

Using, \(^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

n = \(\frac{7!}{2!(7-2)!}\)

After solving

n = 21

There are 21 different ways to choose two different restaurants.

b. We would like to choose two different restaurants. one is for our lunch and the other one is for our dinner. We have to find how many different ways are there.

There are total 7 largest restaurants in x city.

We have to choose two different restaurants one for our lunch and the other one for our dinner.

So different ways:

n = \(^{7}P_{2}\)

Using, \(^{n}P_{r} = \frac{n!}{(n-r)!}\)

n = \(\frac{7!}{(7-2)!}\)

After solving

n = 42

There are 42 different ways to choose two different restaurants.

c. We would like to choose two restaurants. one is for your lunch and the other one is for your dinner. We are OK for going to the same restaurants. We have to find how many different ways are there.

There are total 7 largest restaurants in x city.

We have to choose two different restaurants one is for your lunch and the other one is for your dinner OK to the same

So different ways:

n = (7)^2

n = 49

There are 49 different ways to choose two different restaurants.

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Step-by-step explanation:

5k-12k-1+k

= 5k-12k+k-1

= -6k-1

The time it will a take them for both ricardo and his father to finish the painting if they work together is;

t = 2.4 hours

Time for ricardo to paint the set of kitchen cabinets = 6 hours

Time for Ricardo's father to finish painting = 4 hours

This means that ricardo in 1 hour paints 1/6 of the cabinets

His father in 1 hour paints 1/4 of the cabinets

If they work together, in one hour, they would have painted;

1/6 + 1/4 = 5/12 of the cabinet

then 12/12 will be done in; ((12/12) × 1)/(5/12)

⇒ 1 × 12/5

⇒ 2.4 hours

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The correct answer is:  " 2 hours and 24 minutes ";

or; write as:  " 2.4 hours " .

____

Step-by-step explanation:

\(\frac{x}{4} + \frac{x}{6} = 1\)  ;  → { " 1 (one) whole job." }.

       We want to solve for "x" ; the total time, in "hours", that will take them if they work together.
        What is the LCD (least common denominator of "4" and "6" ?
→  Note that "4 * 6 = 24" ;  so, "24" would work, but let's see if we can find the LCD —a number less then "24" ;

4:  2, 4,  12, 16, 20, 24,

6: 1, 2, 3, 6, 12

⇒  We see that "12" is the LCD.
_____
So, " \(\frac{x}{4} = \frac{?}{12}\) " ;  to solve for "?" ;

 →  4 * (what value?) = 12 ?
   →   12 ÷ 4 = (that value) ; ⇒   =  " 3 " .
 _____
So:  \(\frac{x}{4} = \frac{(x*3)}{(4*3)} = \frac{3x}{12}\) ;
_____
 Now:  " \(\frac{x}{6} = \frac{?}{12}\) " ; to solve for "?" ;

→  6 * (what value?) = 12 ?
   →   12 ÷ 6 = (that value) ;  ⇒   =  " 2 " .

 _____

So:  " \(\frac{x}{6} = \frac{(x*2)}{(6*2)} = \frac{2x}{12}\) ;

Now:  →  \(\frac{x}{4} + \frac{x}{6} = 1\) ;

Substitute our converted values:
         →   \(\frac{3x}{12} + \frac{2x}{12}=1\) ;

Then simplify the "left-hand side" of the equation:
_____
        →   \(\frac{3x}{12} + \frac{2x}{12} = \frac{(3x+2x)}{12}\)  = \(\frac{5x}{12}\)  ;

Now, rewrite the simplified equation; and bring down the "1" :
_____

        →   \(\frac{5x}{12} = 1\)   ;

Now, solve for "x" ; as follows:
_____
 ⇒   5x  =  ( 1 * 12 )  ;

  →   5x  =  12  ;

Now, divide Each Side of the equation by "5" ;

to isolate "x" on one side of the equation; & to solve for "x" (in hours):
 _____
  →   5x / 5  =  12 / 5  ;

_____
to get:   x =  (12/5) hours.
_____
Now:  We have (12/5) of 1 hour ;     24/10

Note the exact conversion:  " 60 min. = 1 hr." :

So, 12/5 of 60 minutes;

=  " \(\frac{12}{5}\) * \(}\frac{60}{1}\) "  (minutes) ;
____
The "5" cancels to a "1" ;  and the "60" cancels to a "12" :

  {since:  "60 ÷ 5 = 12" ;  & since:  "5 ÷ 5 = 1 " .}.

→ And we can rewrite as:
    " \(\frac{12}{1} * \frac{12}{1}\) "  (minutes) =  "12 * 12" minutes =  144 minutes.
⇒  " 144 minutes" equals:  How many hours?  " 144 ÷ 60  =  2.4  hours " ;

or; more specifically:

⇒ We have "2 hours and _(some) minutes".

→ that is;  " 2 hours plus 0.4 hour(s) " .

⇒  \(\frac{(0.4) hr}{1}*\frac{(60)min}{1 hr} = [(0.4)*(60)] minutes\) ;

                              =  24 minutes.

____

Alternate method:
____
(12/5 hours) = (12 ÷ 5) hours =   " 2.4 hours " ;  (and continue if desired).
____

So:  The correct answer is:  " 2 hours and 24 minutes ";

                                       or; write as:  " 2.4 hours " .

____
Hope this is helpful to you!  Best of luck!

____

Answer:

2383.14286

Step-by-step explanation:

The volume of a prism is length times width times height. Since we already know the height and length of the prism, we can divide the volume of the prism by the height and length. This becomes: 50046/3 = 16682. Next we divide by 7: 16682/7 = 2383.14286. Hope this helps!

Answer:

The answer is 2

Step-by-step explanation:

2x3=6 +1 =7

Answer:

answer is : 2

Step-by-step explanation:

2x3=6+1=7

The correct answer is A. The selling price of a bond is affected by the coupon rate and the market interest rate.

If the coupon rate is less than the market interest rate, investors will not be interested in buying the bond because they can get a higher return elsewhere. This results in the selling price of the bond being less than its face value of $10,000.
The selling price of a $10,000 5-year bond will be less than $10,000 if the:
A. Coupon rate is less than the market interest rate

This is because when the coupon rate (the interest paid by the bond) is lower than the market interest rate, investors would prefer to invest in other options that offer a higher return. Therefore, to attract buyers, the bond's selling price would be discounted to compensate for the lower coupon rate.

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The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

We are 95% certain that the average hourly earnings for waitresses in Iowa City

Based on the given data, the sample mean hourly earnings of waiters in Weston, West Virginia is x = 17.1 dollars. The standard deviation of the hourly earnings is given as $4.50. We can use this information to estimate the mean hourly earnings for all waitresses in Iowa City with 95% confidence.

To do this, we use the formula for the confidence interval:

CI = x ± t*(s/√n)

where CI is the confidence interval, x is the sample mean, t is the t-value from the t-distribution with (n-1) degrees of freedom and a confidence level of 95%, s is the sample standard deviation, and n is the sample size.

Using the given data, we have:

x = 17.1
s = $4.50
n = 10

To find the t-value, we look up the value in a t-table with (10-1) = 9 degrees of freedom and a confidence level of 95%. The t-value is 2.262.

Plugging in the values, we get:

CI = 17.1 ± 2.262*($4.50/√10)
CI = 17.1 ± $3.76
CI = ($13.34, $20.86)

Interpretation:

We can interpret this confidence interval as follows: if we were to take many random samples of 10 waiters in Weston, West Virginia, and calculate a confidence interval for each sample, we would expect that 95% of these intervals would contain the true mean hourly earnings for all waitresses in Iowa City. Based on this particular sample of 10 waiters, we are 95% confident that the true mean hourly earnings for all waitresses in Iowa City lies between $13.34 and $20.86.
To estimate the mean hourly earnings with 95% confidence for all waitresses in Iowa City, we will use the sample data from Weston, West Virginia, and assume that the standard deviation is the same in both locations.

Given the mean (x) of the sample is 17.1, and the sample size (n) is 10, with a standard deviation (σ) of $4.50, we can calculate the margin of error for the 95% confidence interval using the formula:

Margin of Error = (Z * σ) / square root n

For a 95% confidence interval, the Z-score is 1.96.

Margin of Error = (1.96 * 4.50) / square root 10 = 2.775

Now, we can calculate the confidence interval:

Lower Bound = x - Margin of Error = 17.1 - 2.775 = 14.325
Upper Bound = x + Margin of Error = 17.1 + 2.775 = 19.875

We can conclude with 95% confidence that the mean hourly earnings for all waitresses in Iowa City fall within the range of $14.325 to $19.875. This means that we are 95% certain that the average hourly earnings for waitresses in Iowa City, including tips, is between these values.

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Part A: The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: The point (8, 2) is not included in the solution area.

Part C: The point (3, 1) represents one feasible solution that meets the constraints of the problem.

Part A: The graph of the system of inequalities consists of two lines and a shaded region. The line x + 3y = 8 is a solid line because it includes the equality symbol, indicating that points on the line are included in the solution set. The line x + y = 2 is also a solid line. The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: To determine if the point (8, 2) is included in the solution area, we substitute the x and y values into the inequalities:

8 + 3(2) ≤ 8

8 + 6 ≤ 8

14 ≤ 8 (False)

Since the inequality is not satisfied, the point (8, 2) is not included in the solution area.

Part C: Let's choose a point in the solution set, such as (3, 1). This point satisfies both inequalities: x + 3y ≤ 8 and x + y ≥ 2. In the context of the real-world scenario, this means that Michelle can buy 3 servings of dry food (x = 3) and 1 serving of wet food (y = 1) with her $8 budget. This combination of dog food allows her to feed at least two dogs at the animal shelter while staying within her budget. The point (3, 1) represents one feasible solution that meets the constraints of the problem.

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Answer:

7.8

0.2

Step-by-step explanation:

2 is in the ones place, to get to six you need the value of 2 in the tenths place (0.2)

2+5.8 is 7.8 (add the ones places together to get 7)

0.2+5.8=6 (add in the tenths place)

SOLUTION

From the question

And a poster is in a shape of a rectangle. The area of a rectangle is measured as

So, the expression for the area of the poster becomes

Hence the answer is

Answer: 2.7 kg

1 kilogram (kg) = 2.204623 pounds (lb)

\(\frac{6 lb}{1}\) × \(\frac{1 kg }{2.204623 lb}\) = 2.721553753 kg

You place 1 kg over 2.204623 lb since they are equal. In the above equation, the pounds (lb) cancel out since one is in the numerator (the number on top of the fraction) and one is in the denominator (the number on the bottom of the fraction). You multiply 6 by the 1 in the numerator and multiply the 1 in the denominator by 2.204623. This turns the equation into:

\(\frac{6 kg}{2.204623}\) =2.721553753 kg

You divide 6 by 2.204623 to get 2.721553753

To round to the tenths place, you include only the first number to the right of the decimal, which is 7. Since the number to the right of the 7 is less than five, it stays 7. If it were five or bigger, 7 would turn into 8.

The answer: 2.7 kg

Answer:

2 hours

Step-by-step explanation:

Answer:

About 2.5 hours

Step-by-step explanation:

divide 130 by 52 = 2.5

The integral can be solved using integration by parts. Integration by parts states that for two functions u and v,

int uv' dx=u\int v' dx-\int u'v dx Suppose u= z and v' = e^(-2r)dr, then:

v = (-1/2) e^(-2r). Putting these values into the equation above gives:int z e^{-2r}dr = ze^{-2r}/(-2) - int (-1/2)e^{-2r} dz= (-1/2)ze^{-2r}+C Where C is the constant of integration. This can be solved using partial fractions. We need to factor the denominator to get a(x-b)(x-c). Let's factorise:  3x^2 - x - 6 as (3x+6)(x-1). Therefore we can write:  3x^2 - x - 6 = A(x-1) + B(3x+6). To solve for A and B, let x = 1 then we get -4A = -6 and so A = 3/2.Let x = -2 then we get -12B = -6 and so B = 1/2.Substituting back into the equation, we get:

int frac{3}{2(x-1)}+\frac{1}{2(3x+6)} dx= frac{3}{2}\ln\mid x-1 \mid + \frac{1}{2}\ln\mid 3x+6 \mid + C

Where C is the constant of integration.

To determine the integrals of a function z e^(-2r) and 3x^2 - x - 6, integration by parts and partial fractions, respectively, can be used. Using these methods, we have found that: int z e^{-2r}dr = (-1/2)ze^{-2r}+C int \frac{3}{2(x-1)}+\frac{1}{2(3x+6)} dx = \frac{3}{2}\ln\mid x-1 \mid + \frac{1}{2}\ln\mid 3x+6 \mid + C

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The fully factorized form of expression 5r² - 27r - 18 is (r - 6)(5r + 3)

To factorize the quadratic expression 5r² - 27r - 18, we can use a factoring method such as grouping or quadratic factoring.

One possible approach is to use quadratic factoring.

We look for two binomials that, when multiplied together, give us the quadratic expression.

The quadratic expression 5r² - 27r - 18 can be factored as follows:

5r² - 27r - 18

5r² - 30r+3r - 18

5r(r-6)+3(r-6)

= (r - 6)(5r + 3)

So, the fully factorized form of 5r² - 27r - 18 is (r - 6)(5r + 3)

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Answer:

0.0768 or 7.68%

Step-by-step explanation:

(5 choose 4)*0.4^4*0.6=0.0768

This problem involves the concept of parametric differentiation. We are given parametric equations:

1. \(\(x(t) = e^{-3t}\)\)

2. \(\(y(t) = e^{3t}\)\)

We are asked to find \(\(\frac{d^2 y}{d x^2}\), the second derivative of \(y\) with respect to \(x\). Here are the steps to solve this problem:

Step 1: Calculate \(\(\frac{dy}{dt}\) and \(\frac{dx}{dt}\)\)

\(\(\frac{dy}{dt} = \frac{d}{dt} e^{3t} = 3e^{3t}\)\)

\(\(\frac{dx}{dt} = \frac{d}{dt} e^{-3t} = -3e^{-3t}\)\)

Step 2: Calculate \(\(\frac{dy}{dx}\)\)

By the chain rule, we can express \(\frac{dy}{dx}\)\) as \(\frac{dy}{dt} / \frac{dx}{dt}\)\).

Hence,

\(\(\frac{dy}{dx} = \frac{3e^{3t}}{-3e^{-3t}} = -e^{6t}\)\)

Step 3: Calculate  \(\(\frac{d^2 y}{dx^2}\)\)

Now, we find the second derivative. Here we have to apply the chain rule again, but now it's a bit trickier because \(\(\frac{dy}{dx}\)\) itself is a function of t, not x So we need to take \(\(\frac{d}{dt}\)\) of \(\(\frac{dy}{dx}\)\) and then divide by \(\(\frac{dx}{dt}\)\)

\(\(\frac{d^2 y}{dx^2} = \frac{d}{dt} (\frac{dy}{dx}) / \frac{dx}{dt}\)\)

Taking the derivative of \(\(\frac{dy}{dx} = -e^{6t}\)\) with respect to t, we get:

\(\(\frac{d}{dt} (\frac{dy}{dx}) = -6e^{6t}\)\)

So,

\(\(\frac{d^2 y}{dx^2} = \frac{-6e^{6t}}{-3e^{-3t}} = 2e^{9t}\)\)

So, the answer is (D)  \(2e^{9t}\)\)

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The second derivative d²y/dx² in terms of t is \(2e^{(9t)\).

Calculus's essential idea of derivatives is how quickly a function changes in relation to its independent variable. They offer details about how a function is altering for a certain input or point.

We must use the chain rule to determine the second derivative of y with respect to x (d²y/dx²) in terms of t.

According to the chain rule, the derivative of y with respect to x is given by dy/dx = (dy/dt) / (dx/dt) if we have a parametric curve defined by x = f(t) and y = g(t).

In this case, we have \(x(t) = e^{(-3t)\) and \(y(t) = e^{(3t)\).

First, we'll find the first derivatives dx/dt and dy/dt:

dx/dt = d/dt \((e^{(-3t)}) = -3e^{(-3t)\)

dy/dt = d/dt \((e^{(3t)}) = 3e^{(3t)\)

Next, we can find dy/dx:

dy/dx = (dy/dt) / (dx/dt)

\(= (3e^{(3t)}) / (-3e^{(-3t)})\\= -e^{(6t)\)

Finally, we differentiate dy/dx with respect to x to find d²y/dx²:

d²y/dx² = \(d/dx (-e^{(6t)})\)

\(= d/dt (-e^{(6t))} \times (dt/dx)\\= -6e^{(6t)} \times (1 / (-3e^{(-3t)}))\\= 2e^{(9t)\)

Therefore, the second derivative d²y/dx² in terms of t is \(2e^{(9t)\).

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By using first principle, the value of Dy/Dx is,

⇒ Dy/Dx = - 7 / x²

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ y = 7 / x

Now, Differentiate the function with respect to x, we get;

⇒ y = 7 / x

⇒ Dy/ Dx = D / Dx (7 / x)

                = 7 D/Dx (1/x)

                = 7 (- 1 × x⁻¹⁻¹ )

                = 7 (- x⁻²)

                = - 7 / x²

⇒ Dy/Dx = - 7 / x²

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