Answer:
Step-by-step explanation:
First, we apply the Pythagorean theorem to determine the distance from Manuel’s home to the resort.
S1 = √50²+20²
S1 = √2500+400
S1 = √2900
S1 = 53.85m
Next, we find the distance from Manuel's home to his friend’s residence.
S2 = √15²+10²
S2 = √225+100
S2 = √325
S2 = 18.03m
The distance between the two boys and the resort will be represented as ∆S = S2 - S1.
∆S = 53.84 - 18.03
∆S = 35.81m
1. "The limit on John's credit card is defined by the function f(x)=15,000+1.5x," indicating that if John's monthly income is $5,000, he can spend a maximum of f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22,500 (dollars). As another example, if John's monthly income is $8,000, then he can spend up to f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars). 2. If we consider the maximum amount John can spend as y, it can be represented as y=15,000+1.5x. To express x, the monthly income, in terms of y, we rearrange this equation: y=15,000+1.5x results in 1.5x = y-15,000. Therefore, in functional notation, x is a function, referred to as g, based upon y, the maximum sum. Generally, we denote the variable of a function by x, so we redefine g as: This tells us that if the maximum amount that John can spend is $50,000, then his monthly income would be $23,333. 3. If John's limit is $60,000, his monthly income equals $30,000. Note: g is deemed as the inverse function of f because it reverses the actions of f.
