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san4es73 [151]
3 years ago
5

A music concert is organized at a memorial auditorium. The first row of the auditorium has 16 seats, he second row has 24 seats,

the third row has 32 seats, and so on increasing by 8 each row for a total of 50 rows.
A) Write an equation for the nth term in the arithmetic sequence
B) Using the equation find the number of people that can be accommodated in the 16th row
Mathematics
2 answers:
olganol [36]3 years ago
5 0

Answer:

(a)  8n + 8

(b) 136

Step-by-step explanation:

No. of seats in first row = 16

No. of seats in second row = 24

no. of seats in third row = 32

Total number of rows = 50

It forms an arithmetic progression

First term = a = 16

common difference, d = 8

Number of terms, n = 50

(A) The formula for the n th term of an arithmetic progression is given by

Tn = a + (n - 1) d

Tn = 16 + (n-1) 8

Tn = 16 + 8n - 8

Tn = 8n + 8

(B) Now, n = 16

The number of seats in 16 th row is given by

T(16) = 8 x 16 + 8

T(16) = 136 seats

djyliett [7]3 years ago
4 0
A(n) = 16 + 8(n - 1)

A(16) = 16 + 8(16 - 1)
A(16) = 16 + 120
A(16) = 136 people
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Step-by-step explanation:

$25 divided by 50 = 50 cents a CD

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8 0
3 years ago
Which describes how square S could be transformed to square S prime in two steps? Assume that the center of dilation is the orig
gayaneshka [121]

Answer:

The correct option is;

A dilation by a scale factor of Two-fifths and then a translation of 3 units up

Step-by-step explanation:

Given that the coordinates of the vertices of square S are

(0, 0), (5, 0), (5, -5), (0, -5)

Given that the coordinates of the vertices of square S' are

(0, 1), (0, 3), (2, 3), (2, 1)

We have;

Length of side, s, for square S is s = √((y₂ - y₁)² + (x₂ - x₁)²)

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates of two consecutive vertices

When (x₁, y₁) = (0, 0) and (x₂, y₂) = (5, 0), we have;

s = √((y₂ - y₁)² + (x₂ - x₁)²) = s₁ = √((0 - 0)² + (5 - 0)²) = √(5)² = 5

For square S', where (x₁, y₁) = (0, 1) and (x₂, y₂) = (0, 3)

Length of side, s₂, for square S' is s₂ = √((3 - 1)² + (0 - 0)²) = √(2)² = 2

Therefore;

The transformation of square S to S' involves a dilation of s₂/s₁ = 2/5

The after the dilation (about the origin),  the coordinates of S becomes;

(0, 0) transformed to (remains at) (0, 0) ....center of dilation

(5, 0) transformed to (5×2/5, 0) = (2, 0)

(5, -5) transformed to (2, -2)

(0, -5) transformed to (0, -2)

Comparison of (0, 0), (2, 0), (2, -2), (0, -2) and (0, 1), (0, 3), (2, 3), (2, 1) shows that the orientation is the same;

For (0, 0), (2, 0), (2, -2), (0, -2) we have;

(0, 0), (2, 0) the same y-values, (∴parallel to the x-axis)

(2, -2), (0, -2) the same y-values, (∴parallel to the x-axis)

For (0, 1), (0, 3), (2, 3), (2, 1) we have;

(0, 3), (2, 3) the same y-values, (∴parallel to the x-axis)

(0, 1), (2, 1) the same y-values, (∴parallel to the x-axis)

Therefore, the lowermost point closest to the y-axis in (0, 0), (2, 0), (2, -2), (0, -2) which is (0, -2) is translated to the lowermost point closest to the y-axis in (0, 1), (0, 3), (2, 3), (2, 1) which is (0, 1)

That is (0, -2) is translated to (0, 1) which shows that the translation is T((0 - 0), (1 - (-2)) = T(0, 3) or 3 units up

The correct option is therefore a dilation by a scale factor of Two-fifths and then a translation of 3 units up.

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