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3 years ago

What is the ratio of 5-10-15

Mathematics

1 answer:

Sedbober [7]3 years ago

5 0

1:2:3 is the answer mark as brain linear pls

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A rectangular box without a lid is to be made from 48 m2 of cardboard. Find the maximum volume of such a box. SOLUTION We let x,

tatiyna

Answer:

The maximum volume of such box is 32m^3

V = x×y×z = 32 m^3

Step-by-step explanation:

Given;

Total surface area S = 48m^2

Volume of a rectangular box V = length×width×height

V = xyz ......1

Total surface area of a rectangular box without a lid is

S = xy + 2xz + 2yz = 48 .....2

To be able to maximize the volume, we need to reduce the number of variables.

Let assume the rectangular box has a square base,that means; length = width

x = y

Substituting y with x in equation 1 and 2;

V = x^2(z) ....3

x^2 + 4xz = 48 .....4

Making z the subject of formula in equation 4

4xz = 48 - x^2

z = (48 - x^2)/4x .......5

To be able to maximize V, we need to reduce the number of variables to 1, by substituting equation 5 into equation 3

V = x^2 × (48 - x^2)/4x

V = (48x - x^3)/4

differentiating V with respect to x;

V' = (48 - 3x^2)/4

At the maximum point V' = 0

V' = (48 - 3x^2)/4 = 0

Solving for x;

3x^2 = 48

x = √(48/3)

x = √(16)

x = 4

Since x = y

y = 4

From equation 5;

z = (48 - x^2)/4x

z = (48 - 4^2)/4(4)

z = 32/16

z = 2

The maximum volume can be derived by substituting x,y,z into equation 1;

V = xyz = 4×4×2 = 32 m^3

7 0

4 years ago

3/4 times the amount of 20

klio [65]

Answer:

$= { \rm{ \frac{3}{4} \times 20}} \\ \\ = { \rm{ \frac{60}{4} }} \\ \\ = { \boxed{ \tt{ \: \: 15 \: \: }}}$

8 0

3 years ago

Read 2 more answers

The tape diagram represents an equation.

elena-s [515]

Answer:1.75 = 5n

Step-by-step explanation:

5 0

3 years ago

What is the standard form of the function F? f(x)=4(x+6)^2+5

pashok25 [27]

Answer:

$f(x) = 4x^2+24x+149$

Step-by-step explanation:

Expand the binomial and collect terms.

3 0

3 years ago

A salesperson is paid a base salary of $1700 per month plus a 4.25% commission on sales. How much sales must he generate in orde

iren [92.7K]

Salesperson must generate a sales of $ 26280 in order to earn $2,816.90 per month in total compensation

Solution:

Given that,

A salesperson is paid a base salary of $1700 per month plus a 4.25% commission on sales

Therefore,

Total salary = 1700 + 4.25 % commission on sales

How much sales must he generate in order to earn $2,816.90 per month in total compensation?

Therefore, let us first subtract the basic salary

2816.90 - 1700 = 1116.9

We have to find the sales he must generate

Let "x" be the sales he must generate

4.25 % of x = 1116.9

Therefore,

$4.25 \% \times x = 1116.9\\\\\frac{4.25}{100} \times x = 1116.9\\\\0.0425x = 1116.9\\\\x = \frac{1116.9}{0.0425}\\\\x = 26280$

Thus he must generate a sales of $ 26280 in order to earn $2,816.90 per month in total compensation

8 0

3 years ago