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2 years ago

Write a function rule for "The output is four more than the input." Let x represent the input and let y represent the output.

Mathematics

1 answer:

vodka [1.7K]2 years ago

7 0

Answer:

y(x) = x + 4

Step-by-step explanation:

A function rule is nothing more than a process that correlates changes in input to changes in output. If y is the output and x is the input, the function must be of the form y(x). Since "The output is four more than the input", the value of y is always 4 units greater than the value of x. The function rule is:

$y(x) = x + 4$

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It is desired to pile some logs in layers so that the top layer contains one log, the next layer contains two logs, the next lay

Hitman42 [59]

Answer:

Yes all of the logs can be used in such a grouping.

We'll have <u>19 logs</u> in the bottom row (and have 19 rows)

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

Explanation:

Let n be the number of layers. Let T(n) represent how many logs there are total.

If you have 1 layer, then you have 1 log. So we can say that T(1) = 1.
If there are n = 2 layers, then we have 1 log on top of two other logs, which leads to 1+2 = 3 logs total. This shows that T(2) = 3.
If there are n = 3 layers, then we have 1 log on top of 2 which are on top of 3 at the very bottom. We have 1+2+3 = 6 logs total. So T(3) = 6.
Having n = 4 layers gives 1+2+3+4 = 10 logs. So T(4) = 10
Having n = 5 layers gives 1+2+3+4+5 = 15 logs. So T(5) = 15

This process continues for however long you like. The sequence 1,3,6,10,15 is the set of triangular numbers, since the logs form a triangular or pyramid shape when stacked this way. To get the nth value in the triangular number sequence, use this formula

T(n) = 0.5*n*(n+1)

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For example, let's say we wanted to find how many logs there were in the fifth layer

T(n) = 0.5*n*(n+1)

T(5) = 0.5*5*(5+1)

T(5) = 15

This matches from earlier.

The purpose of bringing in a formula is to see if we can get T(n) = 190 for some integer n.

-------------------

T(n) = 0.5*n*(n+1)

190 = 0.5*n*(n+1)

190*2 = n(n+1)

380 = n^2+n

0 = n^2+n-380

n^2+n-180 = 0

Applying the quadratic formula will lead to the two solutions: n = -20 and n = 19. We ignore the negative value of n as we can't have a negative number of rows. Therefore, n = 19 is the only valid solution here.

If we wanted to stack 190 logs in this triangular pyramid fashion, then we'll need to have 19 rows. The bottom row will have 19 logs.

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Check:

1+2+3+4+5+6+7+8+9+10 = 55

11+12+13+14+15+16+17+18+19 = 135

55+135 = 190

Or you could say,

T(n) = 0.5*n*(n+1)

T(19) = 0.5*19*(19+1)

T(19) = 190

Either way, the answer is confirmed.

8 0

2 years ago

Help with 7 and 8 please <br> ASAP !!! Thanks

lukranit [14]

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2 years ago

Read 2 more answers

Find x (btw if you answer this randomly just to get the point I'm reporting ur acc

NNADVOKAT [17]

Answer:

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2 years ago

The volume of this regular pentagonal pyramid is 82.5 cubic meters. What is the height of the pyramid?

a_sh-v [17]

the height of the pentagonal pyramid is 5. 70 meters