Acertain theatre is shaped so that the first row has 23 seats and, moving towards the back, each successive row has 2 seats more than the previous row. if the last row contains 81 seats and the total number of seats in the theatre is 1560, how many rows are there?

There are rows in the theater.

Step-by-step explanation:

Given terms.

Seats in order will form an Arithmetic progression.

As the common difference ,same for three consecutive terms so this an AP.

Now accordingly we can put the AP terms.

Total number of seats

Seats in the first row

Seats in the last row

Summation of terms in AP

OR

Using the second equation.

So the number of rows (n) in the theater

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)

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step-by-step explanation: