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lilavasa [31]
3 years ago
8

A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third row from the top, and so

on, until there are 200 logs in the bottom row. ​ Is the pattern an arithmetic sequence?​ Identify a and d.​ Write the 50th term of the sequence.​ Find the total number of logs in the first 10 rows.​
Mathematics
1 answer:
mamaluj [8]3 years ago
7 0

Answer:

1) Is the pattern an arithmetic sequence?​

Yes it is

2)Identify a and d.​

a = First term = 2

d = Common difference = 2

3) Write the 50th term of the sequence.​

50th term = 100

4) Find the total number of logs in the first 10 rows.​

= 1010 logs

Step-by-step explanation:

Is the pattern an arithmetic sequence?​

Yes it is

2) Identify a and d.​

A pyramid of logs has 2 logs in the top row, 4 logs in the second row from the top, 6 logs in the third row from the top, and so on,

The formula for arithmetic sequence =

an = a+ (n - 1)d

a = First term

d = Common difference

For the above question:

a = 2

d = Second term - First term

= 4 - 2

d = 2

3) Write the 50th term of the sequence.​

Using the formula for arithmetic sequence

an = a+ (n - 1)d

a = 2

n = 50

d = 2

a50 = 2 + (50 - 1)2

= 2 + (49)2

= 2 + 98

= 100

The 50th term = 100

4)Find the total number of logs in the first 10 rows.​

Sum of first n terms = n/2(a + l)

n = 10

a = first term = 2

We are told that there are 200 logs in the bottom row, hence:

l = last term = 200 logs

Hence,

Sn = 10/2×[ (2 + 200

= 5(202)

= 1010 logs

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3 years ago
Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, select the st
notka56 [123]

Options

  • (A)g(5) = 12
  • (B)g(1) = -2
  • (C)g(2) = 4
  • (D)g(3) = 18

Answer:

(D)g(3) = 18

Step-by-step explanation:

Given that the function, g, has a domain of -1 ≤ x ≤ 4 and a range of                       0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8

Then the following properties must hold

  1. The value(s) of x must be between -1 and 4
  2. The values of g(x) must be between 0 and 18.
  3. g(-1)=2
  4. g(2)=9

We consider the options and state why they are true or otherwise.

<u>Option A: g(5)=12</u>

The value of x=5. This contradicts property 1 stated above. Therefore, it is not true.

<u>Option B: g(1) = -2 </u>

The value of g(x)=-2. This contradicts property 2 stated above. Therefore, it is not true.

<u>Option C: g(2) = 4 </u>

The value of g(2)=4. However by property 4 stated above, g(2)=9. Therefore, it is not true.

<u>Option D: g(3) = 18</u>

This statement can be true as its domain is in between -1 and 4 and its range is in between 0 and 18.

Therefore, Option D could be true.

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Total number of people sharing muffin = 8

Muffins each person will receive = Total number of muffins
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7 0
3 years ago
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What are the endpoint coordinates for the midsegment of △BCD that is parallel to BC?
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Answer:

<em>The endpoint coordinates for the mid-segment are:  (-2,-1) and (1,0)</em>

Step-by-step explanation:

According to the given diagram, the coordinates of the vertices of \triangle BCD are:   B(-3,1), C(3,3) and D(-1,-3)

Now, the endpoints of the mid-segment of \triangle BCD which is parallel to BC will be the mid-points of sides BD and CD.

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and the mid-point of CD will be:  (\frac{3-1}{2},\frac{3-3}{2})=(\frac{2}{2},\frac{0}{2})=(1,0)

Thus, the endpoint coordinates for the mid-segment of \triangle BCD that is parallel to BC are  (-2,-1) and (1,0)

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