1. The velocity "v" in feet per second of a freely falling object that has fallen h feet can be represented by v = 8h^1/2. Find the distance that an object has fallen if its velocity is 96 feet per second.2. The relationship of the current, the power, and the resistance in an appliance can be modeled by IR^1/2 = √P, where I is the current in amperes, P is the power in watts, and R is the resistance in ohms. Find the power that an appliance is using if the current is 2.5 amps and the resistance is 16 ohms.
In your answer, please explain and show your work to the best of your ability. I want to know how you got your answer. It will help me a lot! :)
Note: These questions are from 7-3 Practice: Rational Exponents from Glencoe Algebra 1.
Good luck! :)
Answers
(1) To solve for h, we manipulate the variable such that it becomes,
h = √(v / 8)
Substituting the given,
h = √ (96 / 8) = √12 ft
(2) To solve for P in this problem, we raise both sides of the equation to exponent 2,
P = I²R
Substituting,
P = (2.5 amps)² x (16 ohms)
P = 100 watts
Final answer:
To find the distance fallen, substitute the given velocity into the equation and solve for h. To find the power being used, substitute the given current and resistance into the equation and solve for P.
Explanation:
1. To find the distance that an object has fallen if its velocity is 96 feet per second, we need to use the given equation v = 8h^(1/2). We'll substitute 96 for v in the equation and solve for h:
96 = 8h^(1/2)
To isolate h, we'll divide both sides of the equation by 8:
12 = h^(1/2)
To get rid of the exponent, we'll square both sides of the equation:
144 = h
Therefore, the object has fallen a distance of 144 feet.
2. The equation IR^(1/2) = √P represents the relationship between current (I), power (P), and resistance (R). We're given that I = 2.5 amps and R = 16 ohms. We'll substitute these values into the equation and solve for P:
(2.5)(16)^(1/2) = √P
(2.5)(4) = √P
10 = √P
To isolate P, we'll square both sides of the equation:
100 = P
Therefore, the appliance is using 100 watts of power.
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We can do this by converting 20% to a fraction or decimal. We'll do fraction because I think it is easier to see.
20% = 20/100 = 2/10 = 1/5
So we need to find 1/5th of 30,000
1/5 x 30,000 = 30,000/5 = 6,000
Therefore, Peter has $6,000 to spend on expenses.
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Steps to solve (Please note, steps will be in numerical order.)
1.To start off you have to find the lCD of
2. Now, rewrite the fraction
3. You only have to add
4. First, add the numerators 3+4 which is 7. Remember when adding fractions the denominator stays the same.
5. In conclusion, you're final answer should be
Hope This Helped :)
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Since this is a linear function, the domain and range are both all real number.