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bogdanovich [222]

3 years ago

14

Lake Superior is the largest of the Great Lakes it covers a surface area of about 30,000 square miles. How can you show the esti

mated area of Lake Superior as a whole number multiplied by a power of ten? How can you use a pattern to find the answer?

2 answers:

Naddika [18.5K]3 years ago

7 0

3 x 10 x10 x10 x10 or 4x 10^4 power

Daniel [21]3 years ago

6 0

Answer:

The area would be,

$3\times 10^{4}\text{ square miles}$

Step-by-step explanation:

Since, a very large or very small number can be written as the product of whole number and exponent ( a power ) of ten,

If a number is very large then we move the decimal to left side so that we get a whole number then the number of shifting is the power of ten,

While when we shift the decimal to the right side then the exponent of 10 is negative.

Here, the given number,

30,000 square miles,

The number of shifting to the left so that we get a whole number is 4,

By the above statement,

30,000 = $3.0\times 10^4$

Hence, the estimated area of the lake would be $3\times 10^4$ square miles

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Determine whether the following series converge or diverge

Mars2501 [29]

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3 years ago

Mrs. Hall records the heights of 50 students in a spreadsheet. The mean height is 68 inches. After looking at the data again, sh

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7 0

3 years ago

Read 2 more answers

MARSVECTORCALC6 3.4.020. My Notes A rectangular box with no top is to have a surface area of 64 m2. Find the dimensions (in m) t

ioda

Answer:

We would have

$l =w =\frac{8\sqrt{3}}{3} \\h = \frac{8\sqrt{3}}{6}$

where " l " is length, " w" is width and "h" is height.

Step-by-step explanation:

Step 1

Remember that

Surface area for a box with no top = $lw+2lh+2wh = 64$

where " l " is length, " w" is width and "h" is height.

Step 2.

Remember as well that

Volume of the box = $l*w*h$

Step 3

We can now use lagrange multipliers. Lets say,

$F(l,w,h) = lwh$

and

$g(l,w,h) = lw+2lh+2wh = 64$

By the lagrange multipliers method we know that

$\nabla F = \lambda \nabla g$

Step 4

Remember that

$\nabla F = (wh,lh,lw)$

and

$\nabla g = (w+2h,l+2h , 2w+2l)$

So basically you will have the system of equations

$wh = \lambda (w+2h)\\lh = \lambda (l+2h)\\lw = \lambda (2w+2l)$

Now, remember that you can multiply the first eqation, by "l" the second equation by "w" and the third one by "h" and you would get

$lwh = l\lambda (w+2h)\\\\lwh = w\lambda (l+2h)\\\\lwh = h\lambda (2w+2l)$

Then you would get

$l\lambda (w+2h) = w\lambda (l+2h) = h\lambda (2w+2l)$

You can get rid of $\lambda$ from these equations and you would get

$lw+2lh = lw+2wh = 2wh+2lh$

And from those equations you would get

$l = w =2h$

Now remember the original equation

$lw+2lh+2wh = 64$

If we plug in what we just got, we would have

$l^{2} + l^{2} + l^2 = 64 \\3l^{2} = 64 \\l = w = \frac{8\sqrt{3} }{3} \\h = \frac{8\sqrt{3} }{6}$

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3 years ago