A hotel offers a reward program based on the number of night stayed. The function f(x) represents the number of free nights earn
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The average velocity of the object after during the first three seconds is: 48m/s
The time at which the instantaneous velocity equals the average velocity within the first three seconds is 1.5 seconds.
<h3>What is instantaneous and average velocities?</h3>Instantaneous velocity is the speed of an object at a particular point in time.
Average velocity is the velocity of an object after covering a certain distance for a period of time
Analysis:
Given
initial height = 600 feet
Height with respect to time = f(t) = -16 + 600
a) Height at t = 0 = 600 feet
Height at t = 3 seconds = f(3) = -16 + 600 = 456 feet
Distance travelled = 600 - 456 = 144 feet
Average velocity = distance travelled/time taken = 144/3 = 48 feet/seconds
b) instantaneous velocity at time t = =
= -32t
when instantaneous velocity equal average velocity
-32t = -48
t = 1.5 seconds
In conclusion, the Average velocity after 3 seconds is 48 feet per seconds and the time taken for the average velocity to equal the instantaneous velocity is 1.5 seconds.
Learn more about instantaneous and Average velocity: brainly.com/question/13372043
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Option A : is the solution of the equation.
Explanation:
The equation is
To determine the value of x, let us simplify the equation.
Subtracting 5 from both sides of the equation, we have,
Simplifying, we get,
Now , dividing both sides of the equation by 8, we get,
Using the logarithmic definition that if then
Thus, rewriting the above expression using the logarithmic definition, we have,
⇒
Substituting the value of , we get,
Rounding off the answer to two decimal places, we get,
Hence, the solution of the equation is
Therefore, Option A is the correct answer.