Simplify the following equation completely. Write your answer in only positive exponents.
1 answer:
Answer:
Appears to be A with a typo.
Should be
Step-by-step explanation:
To evaluate or simplify expressions with exponents, we use exponent rules.
1. An exponent is only a short cut for multiplication. It simplifies how we write the expression.
2. When we multiply terms with the same bases, we add exponents.
3. When we divide terms with the same bases, we subtract exponents.
4. When we have a base to the exponent of 0, it is 1.
5. A negative exponent creates a fraction.
6. When we raise an exponent to an exponent, we multiply exponents.
7. When we have exponents with parenthesis, we apply it to everything in the parenthesis.
We will use these rules to simplify.
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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