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maxonik [38]
3 years ago
12

William Arsenio is remodeling his home in order to save money he is upgrading the plumbing himself he needs 27 pieces of copper

tubing each 2/9 of a foot-long if he has a 8 foot piece of tubing will that be enough? How much more does he need or how much tubing will be left over?
Mathematics
1 answer:
Reptile [31]3 years ago
6 0

Answer:

Yes.

2 feet

Step-by-step explanation:

Pieces of copper that Arsenio needs in total = 27 pieces

Length of each piece of copper tubing that he needs = 2/9 foot

Length of available tubing = 8 foot

Since, the length of each piece is 2/9 foot, the length of 27 pieces would be:

\frac{2}{9} \times 27 = 6

This means, Arsenio needs 6 feet in total for the copper tubing. Since he got 8 feet in total, he has sufficient amount of tubing available.

After making the 27 pieces, he will be left with 8 - 6 = 2 feet of tubing.

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Part (i)

I'm going to use the notation T(n) instead of T_n

To find the first term, we plug in n = 1

T(n) = 2 - 3n

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Repeat for n = 2 to find the second term

T(n) = 2 - 3n

T(2) = 2 - 3(2)

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The second term is -4

<h3>Answers: -1, -4</h3>

==============================================

Part (ii)

Plug in T(n) = -61 and solve for n

T(n) = 2 - 3n

-61 = 2 - 3n

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-63 = -3n

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Note that plugging in n = 21 leads to T(21) = -61, similar to how we computed the items back in part (i).

<h3>Answer:  21st term</h3>

===============================================

Part (iii)

We're given that T(n) = 2 - 3n

Let's compute T(2n). We do so by replacing every copy of n with 2n like so

T(n) = 2 - 3n

T(2n) = 2 - 3(2n)

T(2n) = 2 - 6n

Now subtract T(2n) from T(n)

T(n) - T(2n) = (2-3n) - (2-6n)

T(n) - T(2n) = 2-3n - 2+6n

T(n) - T(2n) = 3n

Then set this equal to 24 and solve for n

T(n) - T(2n) = 24

3n = 24

n = 24/3

n = 8

This means 2n = 2*8 = 16. So subtracting T(8) - T(16) will get us 24.

<h3>Answer: 8</h3>
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3 years ago
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