What is 2.5 in expanded and word form?

A rectangular storage container with an open top is to have avolume

IRINA_888 [86]

Answer:

Dimensions of the container:

x = 3 m

y = 6 m

h = 1.1 m

C(min) = 270 $

Step-by-step explanation:

Volume of storage container

V = 20 m³

Let "y" be the length and "x" the width then y = 2*x

V = x*y*h ⇒ V = 2*x²*h ⇒ 20 = 2*x²+h ⇒ h = 10/ x²

Costs:

Total cost = cost of base ( 5*2*x² ) + cost of side with base x ( 2*9*x*h) +

cost of side witn base y =2x (2*9*2x*h)

C(t) = 10*x² + 18*x*h + 36*x*h

C(x) = 10x² + 54*x*10/x² ⇒ C(x) 10*x² + 540 /x

Taking derivatives on both sides of the equation we get:

C´(x) = 20*x - 540/x²

C´(x) = 0 ⇒ 20*x - 540/x² = 0 ⇒ 2x - 54/x² = 0

2x³ - 54 = 0

x³ = 27 x = 3 m

Then y = 2*x ⇒ y = 2*3 y = 6 and h = 10 / x² h = 1.1 m

And the minimum cost is

C (min) = 10*x² + 540/x ⇒ C (min) = 90 + 180

C(min) = 270 $

5 0

4 years ago

Placing numbers in order

blagie [28]

Answer:

Step-by-step explanation:The largest number is 10,080,000 then 1,224,000 the smallest number is 1,215,678

6 0

3 years ago

5-6. Find the constant of proportionality (unit rate) for each set of values. Then use the constant of proportionality to write

kakasveta [241]

5. The constant of proportionality is 1.5

The equation is p = 1.5×s

6. The constant of proportionality is 1.99

The equation is p = 1.99 × a

7. The variables Number of Pens and Cost are not proportional

Please find attached the required graph

8. The variables Number of minutes and Words Typed are not proportional

Please find attached the required graph

The procedure for finding the answers are as follows;

5. The given data are presented as follows;

$\begin{array}{ccc}Shirts \ (s)&&Profit \ (p)\\5&&7.50\\10&&15.00\\15&&22.50\end{array}$

Where two variables, s and p are proportional, we get;

p ∝ s

Therefore;

p = C × s

C = p/s

Where;

C = The constant of proportionality

Therefore, the constant of proportionality, C, of the given variables, (number of shirts, s, and profit, p, is found as follows;

C = 7.50/5 = 15.00/10 = 22.50/15 = 1.5

The constant of proportionality, C = 1.5

The equation that relates the two values is p = 1.5×s

6. For the apples to price relationship, we have;

$\begin{array}{ccc}Apples \ (a)&&Price\ (p)\\4&&7.96\\5&&9.95\\6&&11.94\end{array}$

Therefore;

p ∝ a

p = C × a

C = p/a

Plugging in the values gives;

C = 7.96/4 = 9.95/5 = 11.94/6 = 1.99

The constant of proportionality, C = 1.99

Therefore, the equation relating the two values is p = 1.99 × a

7. The given data is presented in a tabular form as follows;

$\begin{array}{ccc}Number \ of \ pens &&Cost\ \\1&&52\\2&&54\\3&&56\\4&&58\end{array}$

A set of data is proportional or has a proportional relationship if their x, and therefore, y-intercept is (0, 0)

From the graph of the data, created with MS Excel, the y-intercept is 50 which is not equal to zero, therefore, the relationship between the data is not a proportional relationship

8. The given data is presented in a tabular form as follows;

$\begin{array}{ccc}Number \ of \ Minutes&&Words \ Typed\ \\1&&50\\2&&90\\3&&140\\4&&180\end{array}$

From the graph of the data, we have that the y-intercept of the line of best fir is 5, therefore, the relationship is not a proportional relationship

Learn more about proportional relationships here;

brainly.com/question/24289972.