In the equation of a circle in the form (x-h)^2 + (y-k)^2 = r^2, (h,k) is the center and r is the radius.
So, the center of the circle is at (-4,2) with radius 6 units.
Answers:
- a) 15000 represents the starting amount
- b) The decay rate is 16%, which means the car loses 16% of its value each year.
- c) x is the number of years
- d) f(x) is the value of the car after x years have gone by
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Explanation:
We have the function f(x) = 15000(0.84)^x. If we plug in x = 0, then we get,
f(x) = 15000(0.84)^x
f(0) = 15000(0.84)^0
f(0) = 15000(1)
f(0) = 15000
In the third step, I used the idea that any nonzero value to the power of 0 is always 1. The rule is x^0 = 1 for any nonzero x.
So that's how we get the initial value of the car. The car started off at $15,000.
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The growth or decay rate depends entirely on the base of the exponential, which is 0.84; compare it to 1+r and we see that 1+r = 0.84 solves to r = -0.16 which converts to -16%. The negative indicates the value is going down each year. So we have 16% decay or the value is going down 16% per year.
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The value of x is the number of years. In the first section, x = 0 represented year 0 or the starting year. If x = 1, then one full year has passed by. For x = 2, we have two full years pass by, and so on.
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The value of f(x) is the value of the car after x years have gone by. We found that f(x) = 15000 when x = 0. In other words, at the start the car is worth $15,000. Plugging in other x values leads to other f(x) values. For example, if x = 2, then you should find that f(x) = 10584. This means the car is worth $10,584 after two years.
In this question there is nothing complicated. Only thing is to know the way fractions can be divided. Once that is known the problem would be one of the easiest to solve. Now let us get back to the problem and look at all the information's that are given in the question.
Divide 7/15 by 3/5 = (7/15)/(3/5)
= (7 * 5)/(15 * 3)
= (35/45)
Dividing the numerator and the denominator by 5 for simplifying purpose, we get
= 7/9
So from the above deduction we can easily conclude that 7/9 is the correct answer and option "B" is the correct option among all the options given in the question.
To solve this problem we can make a proportion.
6 5
-- = ---
10 x
to solve this proportion we can cross multiply and divide.
5 times 10 is 50. divided by 6 is 8.3
it will take her 8.3 minutes to run 5 laps
