The area of a square sports arena is 10,000 m² what are the dimensions of the sports arena on the map.

Answer:

The dimensions of the aquarium that minimize the cost of the materials:

[tex]x=y=\sqrt[3]{\frac{2V}{5}}\\z=\sqrt[3]{\frac{25V}{4}}[/tex]

Step-by-step explanation:

Let x, y and z be the dimensions of aquarium .

Surface area of an aquarium = xy+2yz+2xz

Volume of aquarium V=[tex]Length \times Breadth \times Height=xyz[/tex]  ----A

We are given that slate costs five times as much (per unit area) as glass

So, Cost function : C=5xy+2yz+2xz

Now we will use langrage multiplier to find the dimensions of the aquarium that minimize the cost of the materials.

[tex]\nabla C =\lambda \nabla V[/tex]

[tex](\frac{\partial C}{\partial x},\frac{\partial C}{\partial y},\frac{\partial C}{\partial z})= \lambda (\frac{\partial V}{\partial x},\frac{\partial V}{\partial y},\frac{\partial V}{\partial z})[/tex]

[tex](5y+2z,5x+2z,2y+2x)=\lambda(yz,xz,xy)[/tex]

So,

[tex]5y+2z=\lambda yz[/tex]   ----1

[tex]5x+2z=\lambda xz[/tex] -----2

[tex]2y+2x=\lambda xy[/tex]  ----3

Multiply 1 ,2 and 3 by x,y and z respectively.

[tex]5xy+2xz=\lambda xyz[/tex]   ----4

[tex]5xy+2yz=\lambda xyz[/tex] -----5

[tex]2yz+2xz=\lambda xyz[/tex]   ----6

Now equate 4 and 5

5xy+2xz=5xy+2yz

x=y

Substitute y=x in 5 and 6 and equate them

[tex]5x(x)+2(x)z=2(x)z+2xz\\5x^2=2xz\\5x=2z\\\frac{5}{2}x=z[/tex]

Substitute the values in A

[tex]V = xyz = x \times x \times \frac{5}{2}xV=\frac{5}{2}x^3\\\sqrt[3]{\frac{2}{5}V}=x\\x=y=\sqrt[3]{\frac{2}{5}V}\\z=\frac{5}{2}x=\frac{5}{2}(\sqrt[3]{\frac{2}{5}})=\sqrt[3]{\frac{25V}{4}}[/tex]

Hence,

The dimensions of the aquarium that minimize the cost of the materials:

[tex]x=y=\sqrt[3]{\frac{2V}{5}}\\z=\sqrt[3]{\frac{25V}{4}}[/tex]

Answer: 21 cupcakes and 33 cookies were sold.

Step-by-step explanation:

Let x= Number of cupcakes

y = Number of cookies

As per given,

x+y= 54       (i)

Cost: 2.25x+0.25y=55.50          (ii)

Multiply 0.25 to (i0, we get

0.25x+0.25y = 0.25(54)

⇒0.25x+0.25y = 13.5         (iii)

subtract (iii) from (ii), we get

2x=42

Divide both sides by 2, we get x= 21

Put this in (i) , we get 21+y =54 ⇒ y= 54-21= 33

Hence, 21 cupcakes and 33 cookies were sold.

Answer:

$9.50

Step-by-step explanation:

Answer:

y = 2x

Step-by-step explanation:

y-int = 0

slope = 2

Answer:

512 ounces

Step-by-step explanation:

Answer:

512

Step-by-step explanation:

multiply the volume value by 128

Answer:

Yes students should be confident in addition before they proceed to mulplication.This is because addition is the base of multiplication and requires mastery before you start,so It would be much easier to solve

Answer:

x=-6

Step-by-step explanation:

Answer:

i think 6

Step-by-step explanation:

2/3 divided by 1/9 then , 2 times 9 then.  3 times 9 = 18/3 if you simplifying the answer is 6  

Answer:

13  ( x  +  y ) /  6

Answer:

Plus-or-minus one-fifth, plus-or-minus1, plus-or-minus eleven-fifths, plus-or-minus11

Step-by-step explanation:

According to the Rational Root Theorem, the potential roots of f(x) = 5x² – 7x + 11 are; Plus-or-minus one-fifth, plus-or-minus1, plus-or-minus eleven-fifths, plus-or-minus11.

The given function is; f(x) = 5x² – 7x + 11

On this note; Using the rational Root Theorem while determining the root; we have;

f(x) = 0 = x² -7/5x + 11/5.

The possible roots are therefore the factors of the constant, 11/5 and are as follows;

Read more on Rational Root Theorem;

https://brainly.com/question/4251786

Answer:

Since it is a to-scale model,

the ratio of the wingspan to the length of both the airplanes must be equal

wingspan1 = 200 ft               wingspan2 = 30 cm

length1 = 240 ft                     length2 = x cm

wingspan1 / length1 = wingspan2/length2

replacing the variables

200 / 240 = 30 / x

x = 30 * 240/200

x = 36 cm

Therefore, the length of Emma's airplane is 36 cm

Answer:

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Answer:

-11.9166666667

Step-by-step explanation:

Answer:

-11.9166666667

Step-by-step explanation: I just seached it up

Answer:

if u could include a photo it may help more ..thanks

Answer:

15.51

Step-by-step explanation:

Answer:

473 tickets

Step-by-step explanation:

8,500/18=472.2222222 but, since you can’t sell only part of a ticket, you’ll round up to get 473 tickets.

Answer:

15 (50*0.3)

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

0.3*50 = 15

Answer:

B i think

Step-by-step explanation:

Answer:

1.125 or 9/8

Step-by-step explanation:

Answer:

∡BEN=122

x=17

Step-by-step explanation:

Since you know that when two sides are congruent like this then the to angles are congruent then you know that angle BNE equals 29.

Once you know that since we know that 180 is the sum of all three angles set an equation like this:

180=29+29+(11x-65)

Take off parentheses since you can't simplify in them.

180=29+29+11x-65

Combine like terms.

180=11x-7

Solve for x.

187=11x

x=17

Plug that in to (11x-65) to find angle BEN

angle BEN = 11(17)-65

angle BEN=122

Step-by-step explanation:

(1200-700)/5

=500/5

=

The expression results to 100.

Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

Given:

divide the difference between 1200 and 700 by 5

so, mathematically

(1200- 700)/5

= 500 /5

= 100

Hence, the expression results to 100.

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ5

The constant is 18

To find distance (d) you would multiply the constant by the time(t).

D = 18t

Distance is speed x time, so the given constant would be the speed of the ant.

Answer:

-8

Step-by-step explanation:

First, write it out in standard form:

2 x (-4)

Then multiply!

Answer:

-8

Step-by-step explanation:

it is basically 2 x -4 and a negative times a positive is a negative which makes it -8

Answer:

0

Step-by-step explanation:

Everything multiplied by 0 is 0.

Answer:

$22.37

Step-by-step explanation:

Answer:

$22.37

Step-by-step explanation:

6.99(3.2)

Answer:

d. x = 7

Step-by-step explanation:

32/8 = 28/x

simplify the fraction

4/1 = 28/x

cross multiply:

4x = 28

divide both sides by 4:

x = 7

Answer:

-5 yards

Step-by-step explanation:

4 - 9

= -5

in that two plays:

loss 5 yards