The perimeter of a rectangle is 360 centimetres. If the ratio of its length to its width is 11:4, find the dimensions of the rectangle.​

Here we have a problem of maximization and quadratic equations.

The unit prize that maximizes the revenue is $1,500, and the maximum revenue is $18,000.

We know that the revenue equation is:

R(P) = - 8p^2 + 24,000p

Where the variable p is the price.

Now we want to find the value of p that maximizes the revenue.

To do it, we can see that the revenue equation is a quadratic equation with a negative leading coefficient.

This means that the arms of the graph will go downwards, then the maximum point of the graph will be at the vertex.

Remember that for an equation like:

y = a*x^2 + b*x+ c

The x-value of the vertex is at:

x = -b/(2*a)

Then for the equation:

R(P) = - 8p^2 + 24,000p

The vertex is at:

p = -(24,000)/(2*-8) = 1,500

The value of p that maximizes the revenue is p = $1,500

To get the maximum revenue, we need to evaluate the revenue equation in that p value.

R(1,500) =  - 8*(1,500)^2 + 24,000*1,500 = 18,000

And the revenue equation is in dollars, then the maximum revenue is 18,000 dollars.

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p = 1500  $    the unit price

R(p) = 18000000 $ maximum revenue

We will use two different procedures to calculate the maximum revenue.

That is equivalent to solve the problem and after that to test the solution

The first one is:

R(p) = - 8*p² + 24000*p

we realize that R(p) is a quadratic function ( a parabola) of the form:

y = a*x² + b*x + c    ( c = 0 in this case)

We also know that  as the coefficient of p² is negative the parabola opens downwards then the vertex is a maximum value for R(p), and the x coordinate of p is:

x = p =  - b/2*a   then by substitution

p = - ( 24000)/ 2 ( - 8)

p = 1500  $   and for that value of p

R(p) = - 8 ( 1500)² + 24000* (1500)  = - 18000000 + 36000000

R(p) = 18000000 $

The second procedure is solving with the help of derivatives.

R(p) =  - 8*p² + 24000*p

Tacking derivatives on both sides of the equation we get:

R´(p) = -16p  +  24000

If R´(p) = 0    then    -16p  +  24000 = 0

p = 24000/ 16         p  =  1500

if we check for the second derivative

R´´(p) = -16          -16 < 0  therefore there is a maximum value for R(p) when p = 1500, and that value is:

By substitution in R(p)

R(p) = -8 *(1500)² + 24000* 1500

R(p) =  - 18000000 + 36000000

R(p) = 18000000 $

Answer:

The function is positive when x>1

Answer:

4206 is the answer of this question

Answer:

I think it will help you a lot.

Step-by-step explanation:

A=140sq. units

Step-by-step explanation:

ABCD

A=13

B=15

C=14

D=20

C=14×14

=196sqr.units

Answer:

Step-by-step explanation:

f(x) = 4(x-3)² + 6

Up-opening parabola with vertex (3, 6)

g(x) = -2(x+1)² + 4

Down-opening parabola with vertex (-1,4)

A. True

B. True

C. False

D. True

E. False

F. False

The correct statements are:

Here we have the two quadratic functions:

The x-value of the vertex is the value of x such that the first term becomes equal to zero, so for f(x) the vertex is at x = 3, and the y-value of the vertex is:

f(3) = 0 + 6 = 6

So the vertex is (3, 6)

For g(x) we can see that the vertex is at x = -1, and:

g(-1) = 0 + 4

So the vertex is at (-1, 4)

Also, you can see that for g(x) and f(x) the leading coefficients are of different sign. Meaning that f(x) opens upwards and g(x) opens downwards.

Now that we know the two vertices, we can see that the correct options are:

"The vertex of function g is 4 units to the left of the vertex of function f."

"The vertex of function gis 2 units below the vertex of function f."

"Function gopens in the opposite direction of function f."

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Answer:

There is a   min     value of   376     located at (x,y) =   (9,7)  

============================================================

Explanation:

Solve the second equation for y

x+y = 16

y = 16-x

Then plug it into the first equation

f(x,y) = 3x^2+4y^2 - xy

g(x) = 3x^2+4(16-x)^2 - x(16-x)

g(x) = 3x^2+4(256 - 32x + x^2) - 16x + x^2

g(x) = 3x^2+1024 - 128x + 4x^2 - 16x + x^2

g(x) = 8x^2-144x+1024

The positive leading coefficient 8 tells us we have a parabola that opens upward, and produces a minimum value (aka lowest point) at the vertex.

Let's compute the derivative and set it equal to zero to solve for x.

g(x) = 8x^2-144x+1024

g ' (x) = 16x-144

16x-144 = 0

16x = 144

x = 144/16

x = 9

The min value occurs when x = 9. Let's find its paired y value.

y = 16-x

y = 16-9

y = 7

The min value occurs at (x,y) = (9,7)

Lastly, let's find the actual min value of f(x,y).

f(x,y) = 3x^2+4y^2 - xy

f(9,7) = 3(9)^2+4(7)^2 - 9*7

f(9,7) = 376

The smallest f(x,y) value is 376.

Answer:

the answer is 1/14

hope this helps you

9514 1404 393

Answer:

  (a)  1/14

Step-by-step explanation:

Fractions are multiplied by multiplying numerators and denominators. They are reduced by cancelling common factors. When a product has an even number of minus signs, it is positive.

  [tex]\left(-\dfrac{3}{7}\right)\cdot\left(-\dfrac{1}{6}\right)=\dfrac{(-3)(-1)}{7\cdot6}=\dfrac{3}{7\cdot2\cdot3}=\dfrac{1}{7\cdot2}=\boxed{\dfrac{1}{14}}[/tex]

Answer:

29

Step-by-step explanation:

As it is a list of prime number, the sequence continues with 29 being the next prime number after 23.

Answer:

c) 29

Step-by-step explanation:

they are the prime no. in sequences so, the nex one prime no. is 29 ,

so the answer will be 29

hope it's helpful to you ☺️

Answer

3y(5x+1)

Step-by-step explanation:

9*(5x+1)/3y

3(5x+1)y

Answer:

Step-by-step explanation:

sum: 5x + 1

factor: 3 which divides into 9 evenly

quotient: the answer to division: 9(5x + 1)/(3y) = 3(5x +1)/y

coefficent: this depends on what you have been told. In my day, there were two kinds of coefficents

numerical: 5 and 3

literal: x and y

first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.

here,

7. (-154) ➗ (-14) =11

11. (-40) ➗10=-4

15. 90 ➗ (-15)=-6

16. 108 ➗ (-9)=-12

17. (-48) ➗ (-6)=8

18. (-105) ➗ 7=-15

hope it helps you..........

Answer:

Step-by-step explanation: sajkdkdksskkcfd

Answer:

The inverse is x/3 -1

Step-by-step explanation:

y = 3x+3

To find the inverse, exchange x and y

x = 3y+3

Solve for y

x-3 =3y+3-3

x-3 = 3y

Divide by 3

x/3 - 3/3 = 3y/3

x/3 -1 = y

The inverse is x/3 -1

Answer:

66 2/3 %

Step-by-step explanation:

2/3

Take 2 and divide by 3

.666666(repeating)

Multiply by 100

66.6666(repeating)%

But .6666666(repeating) is 2/3

66 2/3 %

Answer:

[tex] 66.66\%[/tex]

Step-by-step explanation:

[tex] \frac{2}{3} \times 100\% \\ \frac{200}{3} \% \\ 66.66\%[/tex]

Answer:

The (y^2 ) or (y^–2) It is not clear, I solved it in both ways (y^2) and (y^-2) .^_^

[tex] - 7 {x }^{2} - 5 + {y}^{2} \\ - 7( { - 2}^{2} ) - 5 + {4}^{2} \\ - 7( - 4) - 5 + 16 \\ 28 - 5 + 16 \\ = 39[/tex]

_______o_____o_______

[tex] - 7 {x }^{2} - 5 + {y}^{ - 2} \\ - 7( { - 2}^{2} ) - 5 + {4}^{ - 2} \\ - 7( - 4) - 5 + \frac{1}{16} \\ 28 - 5 + \frac{1}{16} \\ = 23.06[/tex]

I hope I helped you^_^

Answer:

28 square units.

Step-by-step explanation:

This is a rectangle with sides (7 - (-7) and (5 - 3)

= 14 by 2

= 28 unit^2.

A number has fixed number of factors but infinite number of multiples

Ex:-

Take a number 12

It has factors 1,2,3,4,6,12

It is fixed.

But

It has multiples 12,24,36,48,60...

It is infinite

Answer:

Cube C

Step-by-step explanation:

[tex]{ \sf{because \: it \: is \: identical}}[/tex]

Step-by-step explanation:

Hi there!

Please see attached picture for your answer.

Hope it helps!

Answer:

1/5

Step-by-step explanation:

the two points are(7,5) and (2,4)

let,(x1,y1)=(7,5) and (x2,y2)=(2,4)

slope (m)=y2-y1/x2-x1

=4-5/2-7

=-1/-5

=1/5(minus ,minus are cut)

Answer:

The answer is A

Step-by-step explanation:

The answer needs to be in slope-intercept form or y=mx+b because the amount of carpet being cleaned every minute is a constant decrease of 9 square feet.

So our b value (or how much carpet cleaned at 0 minutes) is 220

And our m value (or slope or how much carpet is being cleaned every minute) is 9

So if we plug the variables with the tangible numbers we get A(t) = -9x+220 or A(t) = 220-9x.

provided by gauth math

Answer: 0.0228

Step-by-step explanation:

please check photo explanation

The probability that the sample mean will be greater than 22.2 ounces will be equal to 0.0228

Probability is calculated as the proportion of favorable events to all potential scenarios of an event. The proportion of positive results, or x, for an experiment with 'n' outcomes can be expressed.

As per the given values in the question,

[tex]\mu_x[/tex] = 22

σ(x) = σ/√n

= 1/√100

σ(x) = 0.1

P(x>22.2) = 1- P(x<22.2)

= 1- P(x × μ(x))/ σ(x) < (22.2 - 22)/0.1

1 - P (z < 2.00)

1- 0.9772

= 0.0228

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[tex]\displaystyle \int_1^3 \frac{\mathrm dx}{x^2-2x+5}[/tex]

Follow the instruction and complete the square in the denominator:

x ² - 2x + 5 = (x ² - 2x + 1) + 4 = (x - 1)² + 4

Then the integral is

[tex]\displaystyle \int_{x=1}^{x=3} \frac{\mathrm dx}{(x-1)^2+4}[/tex]

Substitute y = x - 1 and dy = dx :

[tex]\displaystyle \int_{y+1=1}^{y+1=3} \frac{\mathrm dy}{y^2+4} = \int_{y=0}^{y=2}\frac{\mathrm dy}{y^2+4}[/tex]

Substitute y = 2 tan(z) and dy = 2 sec²(z) dz :

[tex]\displaystyle \int_{2\tan(z)=0}^{2\tan(z)=2}\frac{2\sec^2(z)}{(2\tan(z))^2+4}\,\mathrm dz = \frac12 \int_{z=0}^{z=\pi/4} \frac{\sec^2(z)}{\tan^2(z)+1}\,\mathrm dz \\\\ = \frac12 \int_{z=0}^{z=\pi/4} \frac{\sec^2(z)}{\sec^2(z)}\,\mathrm dz \\\\ = \frac12 \int_{z=0}^{z=\pi/4} \mathrm dz = \frac12 z\bigg|_{z=0}^{z=\pi/4} = \frac12 \left(\frac\pi4-0\right) = \boxed{\frac\pi8}[/tex]

Answer:

i is defined as the square root of -1.

i^2 = -1

i^3 = -i

i^4 = 1

Following the pattern, we see that i^40 = 1, so i^38 is two above, or equal to -1.

So, i^38 = -1.

Let me know if this helps!

The answer is simply just a+b.

Solution:

log10^6=log10^2+log10^3

Since log10^2=a and log10^3=b,

The answer is a+b.

I think that the answer is a+b.

Answer:

10

5z+15=65

Step-by-step explanation:

5z+15=65

5(10)+15=65

Answer:

Parallel

Step-by-step explanation:

Because of interior alternate angles

Angle ARS and Angle BRS are Interior alternate angles in this case ..

Answer:

Step-by-step explanation:

P = 2(3x-20) + 2(2x+4) = (6x-40) + (4x+8) = 10x-32

The required perimeter of the playground is 10x-32.

The length of the playground measures (3x-20) metres.
The width of the playground measures (2x+4) metres.

Perimeter, is the measure of the figure on its circumference.

The Required perimeter is for the playground is given by
= 2(3x-20) + 2(2x+4)

= 10x-32

Thus the required perimeter of the playground is 10x-32.

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