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Derivative of   [tex]f(x)= (\frac{cosx}{\sqrt{x} })=\frac{-2xsin(x)- cos(x)}{2x\sqrt{x} }[/tex]

How to calculate the derivative?

[tex]f(x) = \frac{cosx}{\sqrt{x} }[/tex]

The derivative is given by,

[tex]= > \frac{d}{dx} (\frac{cosx}{\sqrt{x} })[/tex]

Applying Quotient rule :

[tex](\frac{f}{g} )^{'} = \frac{f^{'}.g - g^{'}.f}{g^{2} } \\[/tex]

[tex]\frac{d}{dx} (\frac{cosx}{\sqrt{x} })=\frac{\frac{d}{dx}(cosx)\sqrt{x} - \frac{d}{dx} \sqrt{x}(cosx)}{(\sqrt{x} )^{2} } \\[/tex]

Considering derivatives in the numerator,

[tex]\frac{d}{dx} (cosx)= - sinx\\\\\frac{d}{dx} (\sqrt{x} )=\frac{1}{2\sqrt{x} }[/tex]

Now,

[tex]\frac{d}{dx} (\frac{cosx}{\sqrt{x} })=\frac{(-sinx)\sqrt{x} - \frac{1}{2\sqrt{x} } (cosx)}{(\sqrt{x} )^{2} } \\\\\text{ Taking LCM }\\\\=\frac{-2xsin(x)- cos(x)}{2x\sqrt{x} }[/tex]

What is a derivative?

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Answer:

[tex]\textsf{C.} \quad r=\dfrac{27-P}{3P}[/tex]

Step-by-step explanation:

Given formula:

[tex]A=P(1+rt)[/tex]

Given values:

Substitute the given values into the given formula and solve for r:

[tex]\begin{aligned}A&=P(1+rt)\\\\\implies 27&=P(1+3r)\\\\\dfrac{27}{P}&=\dfrac{P(1+3r)}{P}\\\\\dfrac{27}{P}&=1+3r\\\\\dfrac{27}{P}-1&=1+3r-1\\\\\dfrac{27}{P}-1&=3r\\\\3r&=\dfrac{27}{P}-\dfrac{P}{P}\\\\3r&=\dfrac{27-P}{P}\\\\\dfrac{3r}{3}&=\dfrac{\dfrac{27-P}{P}}{3}\\\\r&=\dfrac{27-P}{3P}\end{aligned}[/tex]

Solution

[tex]\boxed{r=\dfrac{27-P}{3P}}[/tex]

Carbon sequestering technology has the main purpose of being used To remove carbon from the air and put it into the ground.

Find out more below.

Carbon Sequestering refers to various processes that are used to remove the carbon in the air. This carbon is then stored in various places such as the ground and the oceans.

Carbon Sequestering happens naturally such as the process of photosynthesis. Thanks to Carbon Sequestering technology however, humans are able to use the technology to reduce our carbon footprint on Earth.

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the child would take 11.5 days (working 24 hours per day) to fill the swimming pool

an empty swimming pool is in the shape of a rectangle 10 meters long, 5 meters wide and 2 meters deep.

filling rate =2*10*π*(0.1)^2

or 0.002 π cubic meters per minute

or 0.12 cubic meters per hour

or 2.88 cubic meters per day

volume to fill = 100 cubic meters

how many days to fill ? × days= 2.88π × x=100

this implies x= 100/2.88π

   x= 11.05

the complete question is

an empty swimming pool is in the shape of a rectangle 10 meters long, 5 meters wide and 2 meters deep. a child starts to fill the pool using a saucepan with a circular base having a diameter of 20cm and a depth of 10 cm. the child can fill the saucepan and empty it into the pool twice per minute. how many days would it take the child (working 24 hours per day) to fill the pool? don’t round to the nearest day.

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Step 1: Write out the formula for Probability

Step 2: Writing out the data

The number of times R occur in the word LIBRARY is 2.

The total number of alphabets in the word LIBRARY is 7.

Therefore, number of events= 2

Total number of events= 7

Step-by-step explanation:

If x = 6 and y = 4. Substitute x and y in the expression.

4x+y

4(6)+(4)

24+4

28

2y²

2(6)²

2(36)

72

( x - y )²

(6+4)²

(10)²

100

[tex]\lim_{x \to \\pi } \frac{cosx + sin(2x)+1} {x^2 -\pi^2}[/tex] of the Correct option is (B) i.e.,  1/[tex]\pi[/tex]

Given:

[tex]\lim_{x \to \\pi } \frac{cosx + sin(2x)+1} {x^2 -\pi^2}[/tex]

To solve the above function:

Now, According to the question:

[tex]\lim_{x \to \\pi } \frac{cosx + sin(2x)+1} {x^2 -\pi^2}[/tex]

Differentiate with respect to x above function:

[tex]\lim_{x \to \\pi } \frac{-sinx + 2cosx} {2x}[/tex]

Substitute the value of limit in x tends [tex]\pi[/tex], it means x = [tex]\pi[/tex]

= [tex]\frac{2cos\pi - sin\pi }{2\pi }[/tex]

= 2/ [tex]2\pi[/tex]

= 1/[tex]\pi[/tex]

Hence, The Correct option is (B) i.e.,  1/[tex]\pi[/tex]

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Step 1

Given;

Required; To write the equation in factored form

Step 2

Find the two factors that when added gives you x and when multiplied gives -20x²

Step 3

State the x-intercept

Hence, the x-intercepts are;

x=4

x=-5

Answer:

3/4

-2

Step-by-step explanation:

y = mx + b

Start at the y-intercept. It is (0, -2), so b = -2.

You have

y = mx - 2

Now start at (0, -2). We need to go up and right to the next easy-to-read point on the line. Go up 3 (rise). Go right 4 (run).

slope = rise/run = 3/4 = m.

Now you have

y = 3/4 x - 2

Answer:

See below

Step-by-step explanation:

Use two convenient integer coordinates to calcuate m= slope

I'll use   8,4  and  -4, -5      slope m =   (-5-4)/(-4-8)  = -9/-12 = 3/4

from the graph, the y-axis intercept (b )   is -2

slope - intercept form of a line is given by

y= mx + b

y = 3/4 x -2

Answer:

x = 17

Step-by-step explanation:

Given angles are vertical angles and they have equal measurements.

We can write the following equation to find the value of x based on this information:

8x - 27 = 6x + 7 transfer like terms to the same side of the equation

8x - 6x = 27 + 7 add/subtract

2x = 34 divide both by 2

x = 17

The company’s stock price today would be $33.46.

Dividend per share Year 1 (D1) = $3.30 per share

Dividend per share Year 2 (D2) = $2.52 per share

Stock Price for the Year 2 (P2) = D2(1 + g) / (Ke – g)

= $2.52(1 + 0.042) / (0.1160 – 0.042)

= $2.63 / 0.0740

= $35.48 per share

The company’s stock price is the Present Value of the future dividend payments and the present value the stock price for the year 2

The Stock Price = D1/(1 + r)1 + D2/(1 + r)2 + P2/(1 + r)2

= $3.30/(1 + 0.1160)1 + $2.52/(1 + 0.1160)2 + $35.48/(1 + 0.1160)2

= [$3.30 / 1.1160] + [$2.52 / 1.24546] + [$35.48 / 1.24546]

= $2.95 + $2.02 + $28.49

= $33.46 per share

Hence, the company’s stock price today would be $33.46.

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If the point A(8,4) and B(-7,4) are located one the coordinate plane. Then the graph has been plotted and the distance between the points is 15 units

The first point = A(8,4)

The second point = B(-7,4)

Plot the point on the coordinate plane

The distance between the two points d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Where d is the distance between the two points

[tex](x_1,y_1)[/tex] is the coordinates of the first point

[tex](x_2,y_2)[/tex] is the coordinates of the second point

Substitute the values in the equation

The distance d = [tex]\sqrt{(-7-8)^2+(4-4)^2}[/tex]

= [tex]\sqrt{(-15)^2}[/tex]

= 15 units

Hence, If the point A(8,4) and B(-7,4) are located one the coordinate plane. Then the graph has been plotted and the distance between the points is 15 units

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Answer: The general equation of a parabola with vertex (h,k) is y=a(x−h)2+k y = a ( x - h ) 2 + k . In this case we have (1,3) as the vertex (h,k) and (2,6) is a point (x,y) on the parabola. To find a , substitute the two points in y=a(x−h)2+k y = a ( x - h ) 2 + k .

If 98 out of 350 dog owners bought Pedigree Chum dog food so 28 percentage of the makers that prefer Pedigree Chum.

As per the question statement, In a survey of 350 dog owners and it was found that 98 bought Pedigree Chum dog food. We are supposed to find the percentage of the makers that prefer Pedigree Chum.

Given that, 98 out of 350 dog owners bought Pedigree Chum dog food

So the percentage can be calculated by the formula,

(98/350)*100 = 0.28*100 = 28%

Hence, 28% of the makers that prefer Pedigree Chum.

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The ratio of bream to tench to carp is given by the expression; 12 : 7 : 21

A ratio is a relationship between two or more items, that quantitatively expresses the number of times a unit item can be found within the quantity of each item in the set of items.

The given parameters are;

Number of fish in the pond = 40

The number of fish in the pond that are bream = 12

The number of fish that are tench = 1/4 of the fish that are not bream

The number of the fish that are carp = The rest of the fish that are not bream or carp

Required;

The ratio of bream to tench to carp of the fish in the pond.

Solution;

The number of fish that are either tench or carp = 40 - 12 = 28

The number of the fish that are tench = (1/4) × 28 = 7

Therefore;

The number of fish that are carp = 28 - 7 = 21

Which gives;

Number of bream in the pond = 12

Number of tench in the pond = 7

Number of carp in the pond = 21

The ratio of the number of bream to tench to carp in the pond is given by the expression;

[tex]\displaystyle{ \frac{12}{40}:\frac{7}{40}:\frac{21}{40}}[/tex]

Given that the expression for the ratio cannot be simplified further, we have;

The ratio of bream to tench to pond is 12 : 7 : 21

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The technologies that came in the early 1800s changed transportation and revolutionized D. Communication.

In the early 1800s, technology was making things better in the United States. The use of rail lines changed transportation by making many more areas accessible.

Thanks to this improvement in transportation, communication was also revolutionized. For instance, the rail lines made the Federal Postal Service better able to do its job. The Telegraph was also invented in the early 1800s (1844) and allowed for messages to travel much faster than ever before.

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Answer:

The equation is:

y = -3x + 3

Apply square root to both sides of the equation:

Add 4 to both sides of the question:

The possible measures  for the other two angles will be that the sum of that angle must be 90 degree.

A triangle is considered to be 3-sided polygon in some cases  Each triangle has three sides and three angles, a few of which may be the same. The portion of the plane enclosed by the triangle is said the triangle interior, whereas the leftover portion is the exterior. Since we are  given that  one of the angles of the  given is a right angle, according to one of the rules of the triangle the sum of all the interior angles of a triangle should be 180, for the triangle ABC,

=>A+B+C = 180

=>A+90+C= 180

=>A+C= 180-90

=>A+C=90

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Amanda and Diana given right solution set.

The solution set of given graph of inequality is,

x < 4.

Now, The solution of given created inequality,

Amanda:-  -3x + 5 > -7

       => -3x> -7 -5

       => - 3x > -12

        => 3x < 12

         => x < 4

So, it is correct

Briana:- 1/2 (2x - 4)> 2

       => 2x - 4  > 4

       => 2x > 8

       => x > 4

It is wrong

Courtney:-   -7x+8 > -3x + 24

      =>   -7x + 3x > 24 - 8

      => -4x > 16

      => 4x < -16

     => x < -4

It is wrong

Diana:- 9x -6 < 3x + 18

         => 9x - 3x < 18 + 6

         => 6x < 24

       => x < 4

So, it is right

Hence, Amanda and Diana given right solution set.

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The values needed to complete the relative frequency table in the context of this problem are as follows:

The relative frequency of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

To find the relative frequency for boys, we look at the frequency two-way table, and consider that out of 110 boys, 76 went to 4-year colleges and 34 went to two year colleges, hence the relative frequencies are found as follows:

For girls, we also look at the frequency two-way table, and consider that out of 121 girls, 83 went to 4-year colleges and 38 went to two year colleges, hence the relative frequencies are found as follows:

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Answer: I hope these two answers help please mark me brainlist

Step-by-step explanation:

Simplifying

z = 6(x + -1h)

Reorder the terms:

z = 6(-1h + x)

z = (-1h * 6 + x * 6)

z = (-6h + 6x)

Solving

z = -6h + 6x

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Simplifying

z = -6h + 6x

or another answer

6(x-h)=z

Distribute 6 through the parentheses

6x-6h=z

Swap the sides of the equation

Z= 6x-6h

Profit = Revenue - Cost

Revenue = Q * P

P = 100 - Q/20

C = 0.12Q + 10

Using substitution, we can say that:

Both equations used in the region of profit are linear equations because the exponent or degree used is only 1. Therefore, the region of profit is contained within two linear equations. (Option E)

The two column proof of the right angles to prove that ∠1 ≅ ∠2 is as shown below

From the given image showing two right angles, we can generate the two column proof to be as follows;

Statement 1: m∠1 = 90° and m∠2 = 90°

Reason 1: Given

Statement 2: ∠1 and ∠2 are right angles

Reason 2: Definition of right angles

Statement 3: m∠1 = ∠2

Reason 3: Transitive Property of Congruence

Statement 4: ∠1 ≅ ∠2

Reason 4: Definition of Congruence

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Answer:

y = 1/2x - 1

(fraction form)

or

y = 0.5x - 1

(decimal form)

Step-by-step explanation:

To graph:

Another suggestion, is to use Desmos Graphing Calculator (website) and just plug in the points to see where to graph.

Hope this helps! :)

Answer:

4044

Step-by-step explanation:

2000+2000= 4000

22+22= 44

4000+44= 4044

Given the system of equations :

Add the equations to eliminate x :

divide both sides by 13 to find the value of y :

To find x , substitute with the value of y at the first equation :

So, the solution of the system is :

The solution can be written as the order pair (x,y):