Ask question

Ask question

All categories

3 years ago

14

Frank has a sheet of paper which is 1/624 inch thick. If the sheet is folded in half, the total thickness will be 1/312 inch A s

econd fold will produce a total thickness of 1/156 inch. What will be the thickness of the sheet if Frank folds it 8 times?

2 answers:

netineya [11]3 years ago

8 0

Answer:

The thickness of the sheet will be 16/39 inch after folded 8 times

Step-by-step explanation:

* Lets explain how to solve the problem

- Frank has a sheet of paper of 1/624 inch thick

- The sheet is folded in half, the total thickness is 1/312 inch

- The sheet folded in half again and the total thickness is 1/156 inch

- We need to know the thickness of the sheet after folded 8 times

∵ The 1st thickness is 1/624 inches

∵ The 2nd thickness is 1/312 inch ⇒ after 1st fold

∵ The 3rd thickness is 1/156 inch⇒ after 2nd fold

∵ 1/312 ÷ 1/624 = 2

∵ 1/156 ÷ 1/312 = 2

∴ There is a common ratio 2 between each two fold

∴ The thicknesses of the sheet after each fold formed a

geometric series

∵ Any term of the geometric series is $a_{n}=a(r)^{n-1}$ , where

a is the first term, r is the ratio between each two consecutive

terms and n is the position of the term

∵ a = 1/312 because it is the thickness of the 1st fold

∵ r = 2 , n = 8

∴ $a_{8}=\frac{1}{312}(2)^{8-1}=\frac{16}{39}$

∴ The thickness of the sheet will be 16/39 inch after fold 8 times

Leya [2.2K]3 years ago

6 0

Answer:0.41 in

Step-by-step explanation:

You might be interested in

Help please! Thank you!

Stolb23 [73]

Because a rectangular pyramid's base is square, the cross section would be as well

4 0

2 years ago

A rancher wishes to build a fence to enclose a rectangular pen having area 24 square yards. Along one side the fence is to be ma

Gnoma [55]

Answer:

The value is $C \approx \$76$

Step-by-step explanation:

From the question we are told that

The area of the rectangular pen is $A = 24 \ yard^2$

The cost of material used to make one side is $z = \$ 6$

The cost of material used to make the other sides is $r = \$ 3$

Now , the fence to be build around the rectangular pen has four sides, the first opposite sides are equal, let assume each of the to be x yard and the other opposite sides are also equal as well let assume of the to be y yard

So the cost is mathematically represented as

$C = zx + r (x + 2y )$

=> $C = 6x + 3(x + 2y)$

=> $C = 9x + 6y$

Now the area of the fence is mathematically represented as

$A = x* y = 24$

=> $y = \frac{24}{x}$

=> $C = 9x + 6[\frac{24}{x} ]$

=> $C = 9x + [\frac{144}{x} ]$

Now differentiating

$C' = 9 + 144* (-2) x^{-2}$

$C' = 9 - 288x^{-2}$

At minimum $C' = 0$

So

$9 - 288x^{-2} = 0$

$x^{-2} = 0.03125$

$x = \sqrt{\frac{1}{0.03125} }$

$x = 5.66$

Now substituting for x in the equation above to obtain minimum cost

$C = 9(5.66) + [\frac{144}{5.66} ]$

$C \approx \$76$

8 0

2 years ago

The degree of a polynomial is

scoundrel [369]

The degree of a polynomial is<span> the highest </span>degree<span> of its terms when the </span>polynomial is<span> expressed in its canonical form consisting of a linear combination of monomials.</span>The degree<span> of a term is the sum of the exponents of the variables that appear in it.</span>

5 0

2 years ago

A rectangle has a perimeter of 30 inches.

erastova [34]

The new perimeter would be 60. because the width and the height are doubled.

8 0

2 years ago

Which expression is equivalent to V-80?<br> -455<br> O -4.5;<br> O 4.5;<br> O 415

steposvetlana [31]

Answer:

v-12

Step-by-step explanation:

1Nonly_n8thanfull

4 0

1 year ago

Read 2 more answers