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Firlakuza [10]
3 years ago
6

A large company increased its sales from last year to this year by 34%.

Mathematics
1 answer:
AlexFokin [52]3 years ago
8 0

Given:

The last year sales = $288,000,000

Company increased its sales from last year to this year by 34%.

To find:

The this year's sales to the nearest million dollars.

Solution:

We have,

The last year sales = $288 million

The company increased its sales from last year to this year by 34%. So,

This year's sales =288+288\times \dfrac{34}{100}

                            =288+97.92

                            =385.92

                            \approx 386

Therefore, this year's sales were 386 million dollars or $386,000,000.

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The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much
Y_Kistochka [10]

Answer:

x = ∛ 2*V/5  

y = ∛ 2*V/5

h  = V/ ∛ 4*V²/25

Step-by-step explanation:

Dimensions of the aquarium base is  x*y

We call c₁ cost per unit area of the sides, then cost per unit area of slate is equal 5c₁.

let call h the height of the aquarium then volume of the aquarium is:

V = x*y*h      where   h =  V / x*y

As the base is a rectangular one there are 2 sides x*h .  and 2 sides  y*h

According to this:

Ct (cost of aquarium )  = cost of the base  + cost of the sides

cₐ  ( cost of the base) = 5*c₁*x*y

c₆ (cost of the sides ) = c₁*2*x*h   +   c₁*2*y*h

C(t)  =  5*c₁*x*y +2* c₁*x* V/x*y  +  2* c₁*y* V/x*y    or

C(t)  =  5*c₁*x*y  + 2*c₁*V/y   *2*c₁* V/x

Taking partial derivatives en x and y we have:

C´(x)  =  5*c₁*y - 2*c₁*V/x²

C´(y)  =  5*c₁*x - 2*c₁*V/y²

C´(x)  = C´(y)        ⇒  5*c₁*y - 2*c₁*V/x²  =   5*c₁*x - 2*c₁*V/y²

or    5*y - 2*V/x²  =   5*x - 2*V/y²

(5*y*x² - 2*V)/x²  = ( 5*y²x - 2*V) /y²

(5*y*x² - 2*V)*y²  = ( 5*y²x - 2*V)*x²

5*y³*x² - 2*V*y²  =  5*y²x³  - 2*V*x²

5*y³*x² - 5*y²x³  =  2*V * ( y² - x²)

by symmetry  x =  y

Then using x = y  and plugging that value on the derivatives

C´(x) =  5*c₁*y - 2*c₁*V/x²

C´(x) =  5*c₁*x - 2*c₁*V/x²

C´(x) = 0          ⇒     5*c₁*x - 2*c₁*V/x²  = 0

5*x  - 2*V/x² = 0      ⇒  5*x³ - 2*V = 0   ⇒   5*x³  = 2*V  ⇒ x³ = 2*V/5

x = ∛ 2*V/5       and   y = ∛ 2*V/5    and   h  =  V/ x*y    h  = V/ ∛ 4*V²/25

7 0
3 years ago
Percy said that any real number for k would cause the system of equations to have no solution. Explain the error in Percy’s stat
MatroZZZ [7]

Answer:

Except k=7, any real number for k would cause the system of equations to have no solution.

Step-by-step explanation:

In general a system of equations can be represented as ax+by=c and dx+ey=f. In order this system of equations to have NO SOLUTIONS a/d=b/a≠c/f. In our example a=6, b=4, c=14, d=3, e=2 and f=k. To apply the formula above, 6/3=4/2≠14/k. Hence k≠7. It can be concluded that except k=7, any real number for k would cause the system of equations to have no solutions.

Just for information, if k=7 the system will have infinitely many solutions.

5 0
2 years ago
Read 2 more answers
Bruce drew a scale drawing of a restaurant. The scale he used was 1 millimeter 10 meters The restaurant's kitchen is 3 millimete
Burka [1]

Answer:

answer=30

Step-by-step explanation:

by taking the length as x

1 millimetre = 10 metres

3 millimetres = x

10×3= 30 metres

HOPE THIS HELPS

8 0
2 years ago
A circular race track has a radius of 200 feet a car drives 50 laps around the track approximately how many miles does the car t
bazaltina [42]

Answer:

  11.9 miles

Step-by-step explanation:

The length of the track is ...

  C = 2πr = 2π(200 ft) = 400π ft

Then the length of 50 laps will be ...

  50C = 50·(400π ft) = 20,000π ft ≈ 62,831.9 ft

The number of miles (m) this is can be found from ...

  m(5280 ft) = 62,831.9 ft

  m = 62,831.9/5280 ≈ 11.90 . . . . miles

50 laps is about 11.9 miles.

4 0
2 years ago
What is the area of a circle with a radius of 21 feet?
lidiya [134]

Answer:

Area is about 1520.53

Step-by-step explanation:

A=\pi r^{2}

A = \pi 21^{2}

A ≈ 1520.53

6 0
3 years ago
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