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2 years ago

What is 60,978 in expanded form

Mathematics

1 answer:

lana66690 [7]2 years ago

7 0

Expanded Notation Form: 60,978= 60,000 +0 +900 +70 +8

Expanded Factors Form: 60,978= 6 × 10,000 +0 × 1,000 +9 × 100 +7 × 10 +8 × 1

Expanded Exponential Form: 60,978 = 6 × 104+0 × 103+9 × 102+7 × 101+8 × 100

Word Form:60,978 =sixty thousand nine hundred seventy-eight

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A cylindrical can without a top is made to contain 25 3 cm of liquid. What are the dimensions of the can that will minimize the

Basile [38]

Answer:

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

Step-by-step explanation:

Given that, the volume of cylindrical can with out top is 25 cm³.

Consider the height of the can be h and radius be r.

The volume of the can is V= $\pi r^2h$

According to the problem,

$\pi r^2 h=25$

$\Rightarrow h=\frac{25}{\pi r^2}$

The surface area of the base of the can is = $\pi r^2$

The metal for the bottom will cost $2.00 per cm²

The metal cost for the base is =$(2.00× $\pi r^2$ )

The lateral surface area of the can is = $2\pi rh$

The metal for the side will cost $1.25 per cm²

The metal cost for the base is =$(1.25× $2\pi rh$ )

$=\$2.5 \pi r h$

Total cost of metal is C= 2.00 $\pi r^2$ + $2.5 \pi r h$

Putting $h=\frac{25}{\pi r^2}$

$\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}$

$\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}$

Differentiating with respect to r

$C'=4\pi r- \frac{62.5}{ r^2}$

Again differentiating with respect to r

$C''=4\pi + \frac{125}{ r^3}$

To find the minimize cost, we set C'=0

$4\pi r- \frac{62.5}{ r^2}=0$

$\Rightarrow 4\pi r=\frac{62.5}{ r^2}$

$\Rightarrow r^3=\frac{62.5}{ 4\pi}$

⇒r=1.71

Now,

$\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0$

When r=1.71 cm, the metal cost will be minimum.

Therefore,

$h=\frac{25}{\pi\times 1.71^2}$

⇒h=2.72 cm

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

6 0

2 years ago

Which of the following is not a case of direct variation?a Number of sheets of some kind and increased when their total weight i

VladimirAG [237]

Answer:

Step-by-step explanation:

If two variables, x and y have a direct variation, it means that an increase in x would lead to a corresponding increase in y. A decrease on x would lead to a corresponding decrease in y.

Therefore, we would compare the scenarios to determine which is not a direct variation. The correct option is

d) Time taken will be less if number of workers are increased to complete the same work.

The rest are direct variation scenarios

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2 years ago

Solve y = x^2 +11 <br> for x.

lisabon 2012 [21]

Answer:

x = ± $\sqrt{y-11}$

Step-by-step explanation:

Given

y = x² + 11 ( subtract 11 from both sides )

y - 11 = x² ( take the square root of both sides )

± $\sqrt{y-11}$ = $\sqrt{x^2}$ , hence

x = ± $\sqrt{y-11}$

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3 years ago

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The width of a box is two inches less than twice the height. The length is 4 inches less than three times the height. The volume

Mrac [35]

Answer:

Dimensions are 8 Inches by 14 inches by 20 inches

Step-by-step explanation:

The volume of the box is 2240. This means:

lbh = 2240

Where b is the width.

Width is two inches less than twice the height

b = 2h - 2

length is 4 inches less than 3 times the height

l = 3h - 4

Substituting these parameters into the lbh equation will yield the following:

h * (3h - 4) * (2h - 2) = 2240

h[6h^2-14h+8] = 2240

6h^3 -14h^2 + 8h - 2240= 0

Solving this cubic equation will yield one of the values to be 8. The other two values are complex numbers.

b = 2h - 2

l = 3h - 4

b = 2(8) - 2 = 14

l = 3(8) - 4 = 20

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2 years ago

The answer to this question.

mariarad [96]

Answer:

Number 3

Step-by-step explanation:

there are 4 multiplication terms that requires you to multiply then add them so its number 3

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