There are 450 seats in the lower level of a concert hall with b balcony seats in the upper level. So far, 170 tickets have been
1 answer:
There are 400 balcony seats in the concert hall.
<u>Step-by-step explanation</u>:
Step 1 :
- The number of lower seats = 450 seats
Total seats = Lower seats + balcony seats
Step 2 :
- Tickets sold = 170 tickets
- Total tickets = x
Tickets sold = 1/5 of total tickets.
⇒ 170 = (1/5)x
⇒ x = 5170
⇒ x = 850 tickets
∴ Total seats in the concert hall is 850.
Step 3 :
Total seats = 450 + balcony seats
850 - 450 = balcony seats
∴ balcony seats = 400
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When the railroad expands, it makes an isosceles triangle at the center of the rail.
The base of the triangle is 6 kilometers while each leg of the triangle is given by (6 + 10/100,000) / 2 = 6.0001 / 2 = 3.00005 kilometers.
[recall that 100,000 centimeters gives 1 kilometers, thus 10 centimetres gives 10/100,000 kilometers]
Taking one half of the isoceles triangle, we have a right triangle with one of the leg as 6 / 2 = 3 kilometers and the hypothenus = 3.00005 kilometers.
Thus, using the Pythagoras theorem, we find the other leg (height) of the right triangle as follows.
Let the other leg of the right triangle be h, then
Thus, the center of the rail will rise 0.01732058 kilometers above the ground.
But, there are 1,000 meters in 1 kilometers, therefore, </span><span><span>the center of the rail will rise 0.01732058 x 1,000 = 17.32 meters above the ground.</span></span>
When the railroad expands, it makes an isosceles triangle at the center of the rail.
The base of the triangle is 6 kilometers while each leg of the triangle is given by (6 + 10/100,000) / 2 = 6.0001 / 2 = 3.00005 kilometers.
[recall that 100,000 centimeters gives 1 kilometers, thus 10 centimetres gives 10/100,000 kilometers]
Taking one half of the isoceles triangle, we have a right triangle with one of the leg as 6 / 2 = 3 kilometers and the hypothenus = 3.00005 kilometers.
Thus, using the Pythagoras theorem, we find the other leg (height) of the right triangle as follows.
Let the other leg of the right triangle be h, then
Thus, the center of the rail will rise 0.01732058 kilometers above the ground.
But, there are 1,000 meters in 1 kilometers, therefore, </span><span><span>the center of the rail will rise 0.01732058 x 1,000 = 17.32 meters above the ground.</span></span>