At Niagra High, Mr. Borton bought 4 student tickets and 2 adult tickets for the high school musical which cost $64. then Mrs. Ge
1 answer:
Answer:
Each student ticket costs $8.33
Each adult ticket costs $15.34
Step-by-step explanation:
At Niagra High, Mr. Borton bought 4 student tickets and 2 adult tickets for the high school musical which cost $64. then Mrs. Gelvoria bought 3 student tickets and 3 adult tickets for the show and it cost her $72. How much are each type of tickets?
s = cost of each student ticket
a = cost of adult ticket
Our system of equations:
4s + 2a = 64
3s + 3a = 71
-3(4s + 2a = 64) ==> -12s - 6a = -192
2(3s + 3a = 71) ==> 6s + 6a = 142
-12s - 6a = -192
6s + 6a = 142
-6s = -50
/-6 /-6
s = $8.33 (the cost of each student ticket)
Now, let's find the cost of each adult ticket:
4s + 2a = 64
4(8.33) + 2a = 64
33.32 + 2a = 64
-33.32 -33.32
2a = 30.68
/2 /2
a = 15.34 (the cost of each adult ticket)
(x, y) ==> (8.33, 15.34)
Check your answer:
4s + 2a = 64
4(8.33) + 2(15.34) = 64
33.32 + 30.68 = 64
64 = 64
This statement is true
Hope this helps!
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When the motion is traveling on a straight line, we say that it travels at a certain linear speed or velocity. But when it is in circular motion, the distance it travels is angular. So, this time, we say that it travels at a certain angular speed or velocity. The relationship between linear velocity and angular velocity is:
V = rω
where
V is the linear velocity
r is the radius of the circle
ω is the angular velocity
The final answer should be in miles per hour. To be consistent, let's transform all distances to miles and time to hour.
Brett's distance:
19 ft + 12 in = 19 ft + 12 in (1 ft/12 in) = 20 ft
1 foot is equal to 0.000189394 mile
20 ft * 0.000189394 = 0.00378788 miles
Will's distance:
12 ft + 3 in = 12 ft + 3(1ft/12in) = 12.25 ft
12.25 ft * 0.000189394 = 0.00232 miles
Next, we convert ω from revolution per minute to radians per minute. One revolution is equal to 2π radians, and 60 minutes is equal to 1 hour:
ω = 2.2 rev/min * (2π rad/1 rev) * (60 min/1 hr)
ω = 264π rad/hour
Now, we can determine the linear velocities of Brett and Will:
Brett's linear velocity = (0.00378788 miles)(264π rad/hour)
Brett's linear velocity = 3.142 miles/h
Will's linear velocity = (0.00232 miles)(264π rad/hour)
Will's linear velocity = 1.924 miles/h
V = rω
where
V is the linear velocity
r is the radius of the circle
ω is the angular velocity
The final answer should be in miles per hour. To be consistent, let's transform all distances to miles and time to hour.
Brett's distance:
19 ft + 12 in = 19 ft + 12 in (1 ft/12 in) = 20 ft
1 foot is equal to 0.000189394 mile
20 ft * 0.000189394 = 0.00378788 miles
Will's distance:
12 ft + 3 in = 12 ft + 3(1ft/12in) = 12.25 ft
12.25 ft * 0.000189394 = 0.00232 miles
Next, we convert ω from revolution per minute to radians per minute. One revolution is equal to 2π radians, and 60 minutes is equal to 1 hour:
ω = 2.2 rev/min * (2π rad/1 rev) * (60 min/1 hr)
ω = 264π rad/hour
Now, we can determine the linear velocities of Brett and Will:
Brett's linear velocity = (0.00378788 miles)(264π rad/hour)
Brett's linear velocity = 3.142 miles/h
Will's linear velocity = (0.00232 miles)(264π rad/hour)
Will's linear velocity = 1.924 miles/h