A loan of $500 is to be paid with two payments of $300, one in 3 months, and another in 6 months. The compound interest charged
2 answers:
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Answer:
Step-by-step explanation:
Given
Required
Possible values of k
The general quadratic equation is:
Subtract and
Factorize:
Rewrite as:
Compare the above equation to:
For the equation to have two distinct solution, the following must be true:
So, we have:
Expand
Rewrite as:
Expand
Factorize
Factor out k + 6
Split:
or
So:
or k
To make the above inequality true, we set:
or
So, the set of values of k is:
9514 1404 393
Answer:
671 feet
Step-by-step explanation:
There are a couple of ways to figure this. One is to use a sort of shortcut equation to find the distance traveled (d) by an object when subject to some initial velocity (v) and acceleration (a). Here the acceleration due to gravity is -32 ft/s².
v² = 2ad
d = v²/(2a) = (192 ft/s)^2/(2·32 ft/s²) = 576 ft
This height is in addition to the starting height of 95 ft, so the arrow's maximum height is ...
max height = 95 ft + 576 ft = 671 ft
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Another way to work this problem is to start with the equation for ballistic motion. Filling in the given initial velocity and height, we have ...
h(t) = -16t^2 +192t +95
The time the arrow reaches the maximum height is the time representing the axis of symmetry of the parabola:
t = -(192)/(2(-16)) = 6
Then the maximum height is ...
h(6) = -16·6^2 +192·6 +95 = 671
The maximum height is 671 feet.
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<em>Additional comment</em>
For the standard-form quadratic ...
y = ax^2 +bx +c
The axis of symmetry is ...
x = -b/(2a)
