If the length of the major axis of an ellipse is 28 units and the foci are located 3.5 units away from the center, what is the e
2 answers:
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Answer: The time at which the distance between the two is 150 miles is 1.3 hr.
Step-by-step explanation:
Step 1: Sketch the problem as shown in the attached image.
The problem can be solved using Pythagoras theorem since the sketch is a right angled triangle.
It follows the equation x² + y² = 15².
The distance covered by Greg is given by <em>x mi</em>, and that of Erin is given by <em>y mi</em>.
Step 2: To derive the distance covered by Erin and Greg, we use the formula <em>Speed = distance ÷ time.</em>
Which by cross-multiplying gives <em>distance = speed × time</em>.
Let time taken to cover the distance be <em>t h</em>.
Given that Speed of Erin is 9 mph and that of Greg is 7 mph.
Hence, distance covered by Greg, x = 7 × t = 7t.
Distance covered by Erin, y = 9 × t = 9t.
Step 3: Insert the terms x and y into the Pythagoras equation x² + y² = 15² and solve for <em>time t.</em>
(7t)² + (9t)² = 15²
49t² + 81t² = 225
(49 + 81)t² = 225
t² = 225/(49 + 81)
t² = 225/130
t² = 1.730769231
t = √1.730769231
t = 1.315587029
t = 1.3hr
Hence the time at which the distance between the two is 150 miles is 1.3 hr.
Answer:
The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:
Step-by-step explanation:
Value of the car:
Constant rate of change, so the value of the car in t years after 2012 is given by:
In which f(0) is the initial value and r is the decay rate, as a decimal.
In 2012 your car was worth $10,000.
This means that , thus:
2014 your car was worth $8,850.
2014 - 2012 = 2, so:
We use this to find 1 - r.
Thus