If f(x) = 4x2 – 6 and g(x) = x2 – 4x – 8, find (f – g)(x)
1 answer:
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The question is attached in the image.
1- Carlo thinks he will go to the gym 20 times this month. Calculate how much each of these options will cost Carlo for one month.
a- Pay as you go:
Total cost = 6 * 20 = $120
b- Regular deal:
Total cost = 50 + 2(20) = 50 + 40 = $90
c- All-in-one-price:
Total cost = $100
d- The least expensive for Carlo in this case would be the regular deal.
2- How many visits each month would make the cost of the Regular-Deal and the All-in-one the same?
Assume number of visits is x.
Regular deal = All in one
50 + 2x = 100
2x = 100 - 50
2x = 50
x = 25 visits
3a- It costs $300 to join the new Superfit Gym. You then pay $15 each month and $2 each time you work out. Carlo thinks he will use the gym 20 times each month for a year.
Calculate the cost of the Superfit gym for one year.
Total cost = initial payment + 15*number of month + 2*days of workout
initial payment = $300
15*number of months = 15 * 12 = $180
2*days of workout = 2*20*12 = $480
Total cost = 300 + 180 + 480 = $960
3b- How much will Carlo save during the first year if he uses the Superfit gym rather than the regular deal at the other gym?
First we will calculate the total cost of one year using the regular deal at the other gym as follows:
Total cost at other gym = monthly cost + cost of each workout
Total cost at other gym = 50(12) + 2(12)(20) = $1080
Then, we will calculate the difference to know the amount Carlo would save as follows:
Carlo would save = 1080 - 960 = $120
Hope this helps :)
1- Carlo thinks he will go to the gym 20 times this month. Calculate how much each of these options will cost Carlo for one month.
a- Pay as you go:
Total cost = 6 * 20 = $120
b- Regular deal:
Total cost = 50 + 2(20) = 50 + 40 = $90
c- All-in-one-price:
Total cost = $100
d- The least expensive for Carlo in this case would be the regular deal.
2- How many visits each month would make the cost of the Regular-Deal and the All-in-one the same?
Assume number of visits is x.
Regular deal = All in one
50 + 2x = 100
2x = 100 - 50
2x = 50
x = 25 visits
3a- It costs $300 to join the new Superfit Gym. You then pay $15 each month and $2 each time you work out. Carlo thinks he will use the gym 20 times each month for a year.
Calculate the cost of the Superfit gym for one year.
Total cost = initial payment + 15*number of month + 2*days of workout
initial payment = $300
15*number of months = 15 * 12 = $180
2*days of workout = 2*20*12 = $480
Total cost = 300 + 180 + 480 = $960
3b- How much will Carlo save during the first year if he uses the Superfit gym rather than the regular deal at the other gym?
First we will calculate the total cost of one year using the regular deal at the other gym as follows:
Total cost at other gym = monthly cost + cost of each workout
Total cost at other gym = 50(12) + 2(12)(20) = $1080
Then, we will calculate the difference to know the amount Carlo would save as follows:
Carlo would save = 1080 - 960 = $120
Hope this helps :)
Answer:
Great work!
Step-by-step explanation:
These kind of questions are calculated through Riemann Sum. You can evaluate any definite integral using the Riemann Sum. It should be in the following form:
f(x)dx on the interval [a, b], or
Now f(x) is simply y. Therefore in this example y = x^3 - 6x. We just need the sufficient amount of data to apply the Riemann Sum, including the interval [a, b] that bounds the area, and the the number of rectangles 'n' that we need to use.
Consider an easier approach to this question: (First attachment)
Graph: (Second Attachment)
