Flooring costs £10 per m². How much will it cost to buy enough flooring for this room?​

Using the area of rectangle, the dimensions of the rectangle with maximum area are 5√2 and 5/√2.

In the given question we have to find the dimensions of the rectangle with maximum area.

Given Semicircle Radius is 5.

As we know that standard equation of circle is [tex]x^2+y^2=a^2[/tex]

a=5, so the equation is [tex]x^2+y^2=(5)^2[/tex]

[tex]x^2+y^2=25[/tex]

Therefore, Half circle y=[tex]\sqrt{25-x^2}[/tex]

Area of Rectangle(A) =xy

Because Half of the rectangle is lies in first quadrant and half lies in second quadrant

Therefore,

Area of Rectangle(A) = 2xy

Now putting the value of y

Area(A) = 2x[tex]\sqrt{25-x^2}[/tex]

Here we need to maximize the area of Rectangle, so find derivative and set equal to zero.

A'= [tex]\frac{d}{dx}(2x\sqrt{25-x^2})[/tex]

A'= 2[tex][x\frac{d}{dx}\sqrt{25-x^2}+\sqrt{25-x^2}\frac{d}{dx}x][/tex]

A'= 2[tex][x\cdot\frac{-x}{\sqrt{25-x^2}}+\sqrt{25-x^2}\cdot1][/tex]

A'= 2[tex][\frac{-x^2}{\sqrt{25-x^2}}+\sqrt{25-x^2}][/tex]

A'= 2[tex](\frac{-x^2+25-x^2}{\sqrt{25-x^2}})[/tex]

A'= 2[tex](\frac{25-2x^2}{\sqrt{25-x^2}})[/tex]

For critical Number A' = 0

2[tex](\frac{25-2x^2}{\sqrt{25-x^2}})[/tex] = 0

25-2x^2 = 0

2x^2=25

x^2=25/2

x=±√25/2

x=±5/√2

Therefore,

Base of the Rectangle = 2x

Base of the Rectangle = 2×5/√2

Base of the Rectangle = 5√2

and

height of rectangle = [tex]\sqrt{25-x^2}[/tex]

height of rectangle = [tex]\sqrt{25-(5/\sqrt{2})^2}[/tex]

height of rectangle = [tex]\sqrt{25-(25/2)}[/tex]

height of rectangle = √(50-25)/2

height of rectangle = √25/2

height of rectangle = 5/√2

Hence, the dimensions of the rectangle with maximum area are 5√2 and 5/√2.

To learn more about area of rectangle link is here

brainly.com/question/20693059

#SPJ4

According to the given voltage function, the value of the voltage for the power of 576 watts is 48 watts.

Function:

The relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Given,

The voltage V of an audio speaker can be represented by V=2√P, where P is the power of the speaker. An engineer wants to design a speaker with 576 watts of power.

Here we need to find the voltage of the given power.

In the given question we have the voltage function

v = 2√P

Where P refer the power of the speaker.

Here we have to find the voltage if engineer wants to design a speaker with 576 watts of power.

Which means the value of P is 576.

Then the value of V is calculated as,

v = 2 √576

We know that the value of √576 = 24,

So,

v = 2 x 24

v = 48.

Therefore, the voltage is 48 watts.

To know more about Function here.

https://brainly.com/question/28303908

#SPJ1

The length and the width vary inversely.

A variation is a relation between a set of values of one variable and a set of values of other variables.

In the equation y = mx + b, if m is a nonzero constant and b = 0, then you have the function y = mx (often written y = kx), which is called a direct variation.

If first rectangle length = 72cm and width = 56cm

Then, area = length x width = 72 x 56 = 4032[tex]cm^{2}[/tex]

If length of second rectangle = x

and width = 21

Area of second rectangle = 21x

so both areas are equal, which means

21x = 4032

x = 4032/21

x = 192cm

Since the first rectangle had a width of 56cm and length, 72 and second rectangle has a reduced width 21 cm and an increased length 192cm. it means that the length and the width vary inversely since the reduction in width led to an increase in length.

In conclusion, the two quantities length and width vary inversely.

Learn more about variation: https://brainly.com/question/6499629

#SPJ1

The sample size must be 543 so the sample proportion is will not differ by 5%

We are given the following in the question:

Margin of error = 5%

Confidence interval:

p ±z√(p'(1 - p')/n)

Margin of error =

p = ±z√(p'(1 - p')/n)

Since no particular proportion is given, we take

p' = 0.5

Z critical at α 0.02 is ± 2.33

Putting values, we get,

p = ±z√(p'(1 - p')/n)

2.33 x √(0.5(1 - 0.5)/n)

√n = 2.33x 0.5/0.05

n = 542.89 = 543

Thus, the sample size must be 543 so the sample proportion is will not differ by 5%

To learn more about confidence interval refer here

https://brainly.com/question/15712887

#SPJ4

Using the concepts of area of rectangle, we got that  72 feet  is the the least amount of fencing he can use to create the area for his sheep.

Lets, suppose that the length of rectangle as x feet,

and width of rectangle as y feet.

So perimeter of rectangle as 2×( length + breadth)

We are given perimeter of rectangle as 72 feet

So, length of two sides of rectangle + width of rectangle=72feet.

=>2x+y=72 feet----------(eq1)

Now, we know that area of rectangle is given by =(length × breadth),or

=>(x × y)=20000

Putting values of y from eq1,we get

=>x × (72-2x)=20000

=>72x-2x²=20000

We need to find the least amount of fencing, so we find the local minima by using the differentiation

=>d(72x)/dx-d(2x²)/dx=d(20000)/dx

=>72-4x=0

=>x=18feet

Therefore, y=72-2×18=72-36=36feet

Hence, length of rectangle is 18 feet, and width is 36 feet

Therefore, length of fencing is =2x+y=2×18+36=72 feet.

Hence, if a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. he wants the area to be 20,000 square feet, then the least amount of fencing he can use to create the area for his sheep is 72 feet.

To know more about area of rectangle, visit here:

https://brainly.com/question/20693059

#SPJ4

(Complete question) is:

a farmer is enclosing a rectangular area for his sheep to graze, where one side will be a wall that already exists. Perimeter of rectangle is given as 72 feet. He wants the area to be 20,000 square feet. what is the least amount of fencing he can use to create the area for his sheep?

Answer:

I would say answer D is correct since it is closest to 1,760 yards.

Step-by-step explanation:

;)

Answer:

w = 6 units

Step-by-step explanation:

The perimeter is found by adding all the sides of a rectangle. The perimeter can be found using this equation:

[tex]P=2w+2l[/tex]

Where w represents width and l represents length.

To find the width, rearrange the equation so it is in terms of w:

[tex]P=2w+2l\\2w=P-2l\\w=\frac{P-2l}{2}[/tex]

Now, plug in the known values!

[tex]w=\frac{20-2(4)}{2}[/tex]

Simplify!

[tex]w=\frac{12}{2} \\w=6[/tex]

Answer:

b

Step-by-step explanation:

it is the answer

The point we get after 180 degree clockwise rotation is E' (-3,-1)

When rotating 180° clockwise about the origin the coordinates of the image will be the same x and y numbers but the opposite sign of the pre-image.

Using the above as an example, pre-image E is located at (3,1) so the rotated image would be E' (-3,-1).

Pre-image D is located at (-1,3) so the rotated image would be D' (1,-3).

Pre-image F is located at (2,-2) so the rotated image would be F' (-2,2).

Hence we get the required point.

Learn more about Rotation here:

brainly.com/question/26249005

#SPJ1

first off let's convert the mixed fractions to improper fractions and then divide.

[tex]\stackrel{mixed}{2\frac{4}{3}}\implies \cfrac{2\cdot 3+4}{3}\implies \stackrel{improper}{\cfrac{10}{3}} ~\hfill \stackrel{mixed}{1\frac{8}{7}}\implies \cfrac{1\cdot 7+8}{7}\implies \stackrel{improper}{\cfrac{15}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{10}{3}\div \cfrac{15}{7}\implies \cfrac{10}{3}\cdot \cfrac{7}{15}\implies \cfrac{10}{15}\cdot \cfrac{7}{3}\implies \cfrac{2}{3}\cdot \cfrac{7}{3}\implies \cfrac{14}{9}\implies 1\frac{5}{9}[/tex]

Answer:

1. 0

2. 7

3. -2

4. 10

5. -7

6. -8

7. -2

8. -6

9. -4

10. -5

11. 2

12. -9

13. -9

14. -9

Step-by-step explanation:

Phil invests £800 for 3 years at the rate of 2% then the total amount after 3 years is £848.

The simple interest method, which adds interest to the starting principal amount at the same rate every day, is a quick and easy technique to calculate the interest on that money.

Simple interest is a way to calculate the amount of interest that will be charged on a certain amount of money at a certain rate and for a certain period of time.

As per the given information in the question,

Principal amount, P =  £800

Time, T = 3 years.

Rate, R = 2%

[tex]SI=(Principle*Rate*Time)/100[/tex]

SI = (800 × 2 × 3)/100

SI = 4800/100

SI = £48

Then, the total amount at the end of 3 years,

= £48 + £800

Total amount = £848

To know more about Simple Interest:

https://brainly.com/question/25845758

#SPJ1

The two additional roots are:-0.17-7i and -2i

Given,

A polynomial function P(x) with rational coefficients has the given roots.

P(x) = 0.17+7i and 2i

we are asked to determine the two additional roots of the given P(x).

we know that a+bi is a root of P(x)=0, then a-bi is also a root of P(x)=0

we have:

0.17+7i and 2i are two roots pf P(x)

so, -0.17-7i and -2i are two additional roots of P(x).

Hence we get the required roots.

Learn more about Roots here:

brainly.com/question/25841119

#SPJ1

Answer:

There are roughly 2,488,600 more people living in Chicago.

The algebraic expression is 2n - 3 if Julie runs three miles less than twice the number n that Hannah runs. So option (a) is correct

An algebraic expression is a mathematical expression made up of variables, constants, and algebraic operations.

It is assumed:

"Julie runs three miles less than twice as far as Hannah runs," the expression goes.

It states three miles less than a number, so you get a -3 and twice the number n, which is the same as 2n, and then you rearrange it to get 2n-3

The expression is 2n - 3

Thus, the algebraic expression is 2n - 3, if Julie runs three miles less than twice the number n that Hannah runs.

To learn more about algebraic expression visit

https://brainly.com/question/23903377

#SPJ1

Answer:

The is no number that I can substitue in for x to make the statement true.

Step-by-step explanation:

s + 3 = x -6  Subtract x from both sides

3 = -6  We get a false statement.

Answer:

75%

Step-by-step explanation:

To solve this equation, we need to turn the fraction 72/96 into a percentage.

72 ÷ 96 = 0.75

0.75 as a percentage is 75%

Therefore, 75% of the coffees were regular.

Absolute value of Complex Number -2 + 3i is [tex]\sqrt{13}[/tex]

Absolute value of complex number:

                                                          z = x + iy is the general form of the complex number where x is real part and y is the imaginary part.

                 If we talk about absolute value of complex number z = x + iy then it is represented by |z| = |x + iy|.It is also rad as modulus of z.Absolute value is always going to be a positive value.

              and,

                       |z| = |x + iy|

                            = [tex]\sqrt{x^{2} + y^{2} }[/tex]

Now,

      We have to find the absolute value of complex number, 3i - 2

             z = 3i - 2

                = -2 + 3i

  Absolute value of z is,

                                     |z| = | -2 + 3i |

                                          = [tex]\sqrt{(-2)^{2} + 3^{2} }[/tex]

                                          = [tex]\sqrt{4 + 9}[/tex]

                                          = [tex]\sqrt{13}[/tex]

Thus,

       Absolute value of  Complex number  -2 + 3i is [tex]\sqrt{13}[/tex]

To learn more about Absolute value of complex number visit :

https://brainly.com/question/12541796

#SPJ1

Answer: y = 1/2x + 5

Step-by-step explanation:

3x-6y= -30

Step 1: Subtract 3x to cancel it out and put it on the other side.

3x-6y= -30 -3x

- 3x

After doing that, the equation should look like this: -6y = -3x - 30

Step 2: Divide by -6 to get y alone

-6y/-6= (-3x - 30)/-6

Step 3: Solve

After dividing everything by -6, we get our answer!!

y = 1/2x + 5

*Slope-Intercept form will always end up being in the same format as y=mx+b

I hope this helps :))

If the 5-day simple moving average was $54.27, then the stock's closing price on Thursday was $56.24.

The table shows the closing stock prices of a new energy company for the past 5 days. One of the closing prices is missing from the table. The 5-day simple moving average is $54.27. The closing price of the stock on Monday, Tuesday, Wednesday, and Friday was $52.45, $53.18, $52.37, and $57.11. We need to find the closing price on Thursday. Let the missing value of the stock price be denoted by the variable "x". The average is the sum of all the values divided by the total number of values. We can solve the given equation.

A = (52.45 + 53.18 + 52.37 + x + 57.11)/5

54.27 = (52.45 + 53.18 + 52.37 + x + 57.11)/5

54.27*5 = (52.45 + 53.18 + 52.37 + x + 57.11)

271.35 = 215.11 + x

x = 271.35 - 215.11

x = 56.24

Hence, the closing price of the stock on Thursday is $56.24.

To learn more about average, visit :

https://brainly.com/question/16956746

#SPJ1

If O is the midpoint of LM and N is the midpoint of KM  then the measure of NO is 10.

Linear equations are a combination of constants and variables where the value of the variable is calculated using mathematical operations.

We have given that Triangle KLM, N is the midpoint of KM and O is the midpoint of LM if NO equals 3+ 7X and KL equals 4X +16, we are supposed to find the measure of NO.

Using the Midpoint theorem, we can say that in Triangle KLM;

NO = KL / 2

Substituting values,

3+ 7X =  4X +16/ 2

3+ 7X =  2X + 8

7x - 2x = 8 - 3

5x = 5

x = 1

NO = 3+ 7X

NO = 3+ 7(1) = 10

NO equals 10

Hence the measure of NO is 10.

To learn more about linear equations, click the link below:

brainly.com/question/13738061

#SPJ1

The next two tems of the Fabonacci sequence are (a) 14, 23 (b) 23, 37 (c) 26, 42.

What is Fabonacci type sequence ?

The first two terms are already defined in the this sequence. The nth term of a Fabonacci type sequence is given by the following expression:

[tex]F_n=F_{n-1}+F_{n-2}[/tex]

(a)

In this case 5 terms are given hence, calculate the 6th term.

[tex]F_6=F_5+F_4\\F_6=9+5\\F_6=14[/tex]

Now, calculate the 7th term.

[tex]F_7=F_6+F_5\\F_7=14+9\\F_7=23[/tex]

(b)

Calculate the 4th term.

[tex]F_4=F_3+F_2\\F_4=14+9\\F_4=23\\[/tex]

Calculate the 5th term.

[tex]F_5=F_4+F_3\\F_5=23+14\\F_5=37[/tex]

(c)

The series is 4, 6, 10, 16, ...

[tex]F_5=F_4+F_3\\F_5=16+10\\F_5=26[/tex]

[tex]F_6=F_5+F_4\\F_6=26+16\\F_6=42[/tex]

Hence, the next two tems of the Fabonacci sequence are (a) 14, 23 (b) 23, 37 (c) 26, 42.

Learn more about Fabonacci sequence from the following link:

https://brainly.com/question/11149413

#SPJ1

Answer:

4/20=1/5 or 20% or 0.2

Step-by-step explanation:

if u write 4/20 simplify it which becomes 1/5

u can write in percentage or in decimal depending on what the question wants

The coordinates of point P that lies on the line segment MQ is P(-11/4 , 9/2).

Given:

M(-5, 3), Q(4, 9), and partition the segment at a ratio of 1 : 3.

(x1,y1) and (x2,y2) in the ratio m:n then,

(x,y) = (mx2+nx1 / m+n , my2+ny1 / m+n)

= (1*4+3*-5 / 1+3 , 1*9+3*3 / 1+3

= (4 - 15 / 4 , 9 + 9 / 4)

= (-11/4 , 18/4)

= (-11/4 , 9/2)

Therefore the coordinates of point P that lies on the line segment MQ is P(-11/4 , 9/2).

Learn more about the coordinates point here:

https://brainly.com/question/21950350

#SPJ1

Answer:

  x < 0

Step-by-step explanation:

You want an inequality that represents the number line graph with an open circle at 0 and shading to the left.

The end point of an interval on a number line graph is indicated by either an open circle or a filled circle (dot). The circle is open if that end point is not included in the set being graphed. If the end point is included, then the circle is filled to become a solid dot.

The circle at x=0 on this graph is an open circle, so x=0 is not part of the solution set.

The shading on the number line indicates the values that are included in the solution set. Here, shading is to the left of x=0, so includes all values less than 0. This is written as the inequality ...

  x < 0

__

Additional comment

If you write number-line intervals using the left-pointing symbols < or ≤, then the location of x relative to the symbol is the same as the location of the shading relative to the end point.

Here, shading is to the left of 0, so we can write the inequality ...

  x < 0

where x is to the left of 0 in the inequality expression. (As we said above, we use < for the open circle. ≤ is used for a filled dot.)

The equation of the number of pages is y = 40 + 10x and for 9 days, you read 130 pages

From the question, we have

Initial number of pages = 40

Rate per day = 10 pages per day

The equation of the number of pages is then represented as

y = Initial number of pages + Rate per day x Number of days

Substitute the known values in the above equation, so, we have the following representation

y = 40 +10 * x

Evaluate

y = 40 + 10x

For 9 days, we have

x = 10

This gives

y = 40 +10 * 9

Evaluate

y = 130

Hence, the number of pages is 130

Read more about linear equations at

https://brainly.com/question/13738662

#SPJ1

The appropriate fraction produced by the expression is -32/9.

Any function that can be expressed as a rational fraction, which is an algebraic fraction in which both the numerator and the denominator are polynomials, is referred to as a rational function.

Given the function below:

6x-5/3 = 5x + 9

Cross multiply

6x - 5 = 3(5x + 9)

Expand to have:

6x - 5 = 3(5x) + 3(9)

6x - 5 = 15x + 27

6x - 15x = 27 + 5

-9x = 32

Divide both sides by -9

-9x/-9 = 32/-9
x = -32/9

Hence the result of the expression as an improper fraction is -32/9.

Learn more on rational fraction here: https://brainly.com/question/19044037

#SPJ1

Answer:

[tex] G [/tex]eometric.

Step-by-step explanation:

To get the common ratio in a Geometric Progression (GP), T2/a(T1). a(T1) = 1000, T2 = 500.

So, 500/1000 = 1/2. Therefore, common ratio = 1/2

Now, multiply by the the given term to find the next term i.e

1/2 × 1000 = 500, 1/2 × 500 = 250, 1/2 × 250 = 125, 1/2 × 125 = 62.5, etc.

Parking 11,000 automobiles at the venue and 4,600 in satellites will bring in total $166,500.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream.

Given,

If an arena charges $7. 50 to park in satellite parking and $12. 00 to park in an arena lot,

Multiplying:

$7.5 x 4,600 = satellite parking

$34,500 = satellite parking

The next step is to determine how much it will cost to park in the arena lot.

$11,000 ×12 = arena lot

$32,000 = arena lot

Let's now calculate the entire revenue from parking.

Total earnings equal $132,000 + $34,500.

Amount made in total is $166,500.

In conclusion Parking 11,000 automobiles at the venue and 4,600 in total satellites will bring in $166,500.

To learn more about multiplication, visit:

https://brainly.com/question/23354835

#SPJ4