Tutors Answer Your Questions about Equations (FREE)
Question 988976: In consider the function 1/x
Find the slope of the line L tangent to the graph of (3,f(3))
I know to find the slope of the tangent I use: lim h->0 f(x+h)-f(x)/h
why does this switch from that to (1/(x+h))-(1/x)/(h)?
I thought since we have x and y values (3,f(3)) I can just somehow plug those values in. Why does x+h become 1/(x+h)
Do we first have to alter the limit definition of a derivative (tangent slope) first given the graph shape? then do some rearranging and factoring? Because I know it gets to be lim h->0 1/x^2 which makes the slope m = -1/9
what I also don't get is why do y become y=1/3 when the original points were (3,f(3))
Confused so much about all this.
Please help
Thank you
Click here to see answer by rothauserc(4718)   |
Question 989231: A train leaves the station at noon. The train is 180 miles from its destination at 12:45 P.M and 90 miles from it's destination at 2:15 P.M.
Write an equation and solve for each.
1. How far is the station from the destination?
2. At what time will the train reach its destination?
Click here to see answer by stanbon(75887) |
Question 989231: A train leaves the station at noon. The train is 180 miles from its destination at 12:45 P.M and 90 miles from it's destination at 2:15 P.M.
Write an equation and solve for each.
1. How far is the station from the destination?
2. At what time will the train reach its destination?
Click here to see answer by solver91311(24713)  |
Question 989301: The height of a ball above the ground at time t is h(t), and the ball bounces on a concrete floor at time t = 4 (seconds). Consider the following two one-sided limits:
i. lim t->4^- 
ii. lim t->4^+
(a). Which of the one-sided limits should be negative, and which positive? Explain your answer in a complete sentence.
(b). What would it mean physically for the absolute value of the two limits to be the same?
Please explain these in detail I am very confused.
Thank you
Click here to see answer by jim_thompson5910(35256) |
Question 989350: Basic question. What exactly does it mean when you have say x≤y≤z idk why but this confuses me what exactly does it mean to have something set up in this formation? of two ≤ symbols. Maybe it would be better with numbers but this all confuses me.
Click here to see answer by josgarithmetic(39616) |
Question 989359: If x≤y≤z.
And x≤y is saying x is less than y
and y≤z is saying y is less than z
then y is either between the two values.
But what if I am trying to isolate only y and understand it specifically. Isn't there something to where I could take out x and y and make it so that y≥x? so to say that y is greater than on equal to x. I forget the name of this rule.
Thanks
Click here to see answer by josgarithmetic(39616) |
Question 989359: If x≤y≤z.
And x≤y is saying x is less than y
and y≤z is saying y is less than z
then y is either between the two values.
But what if I am trying to isolate only y and understand it specifically. Isn't there something to where I could take out x and y and make it so that y≥x? so to say that y is greater than on equal to x. I forget the name of this rule.
Thanks
Click here to see answer by solver91311(24713) |
Question 989338: Certain chemotherapy dosages depend on a patient's surface area. According to the Mosteller model
S = √(h*M) / 6
where h is the patient's height in m, M is the patient's mass in kg and S is the patient's approximate surface area in m^2. Assume that the patient's height is a constant 187 cm but he is on a diet. If a patient loses 3.1 kg per month, how fast is his surface area changing (in m^2/month) at the instant his mass is 71 kg?
Give your answer correct to 4 decimal places.
Note. You may be wondering why we have referred to the patient's mass here, rather than his weight. Technically, a person's weight is a force (recall: F = Ma, where F is the force, M is the mass, and a is the acceleration, which in this case is g, the acceleration due to gravity). Force (and therefore weight) is measured in Newtons, not kilograms. Scientists, and you are one, should know that. (In orbit, an astronaut experiences weightlessness, not masslessness.)
I am so confused!
Initial = S = √(187*71) / 6 = 19.2043
After One month = S = √(187*69.7) / 6 = 19.0277
I am not sure how to put these together?
THANK YOU
Click here to see answer by solver91311(24713) |
Question 989789: During summer, you work 30 hours per week at a gas station and earn $8.75 per hour. You also work as a landscaper for $11 per hour and can work as many hours as you want. You want to earn a total of $400 per week. How many hours must you work as a landscaper?
Click here to see answer by solver91311(24713) |
Question 989706: During summer, you work 30 hours per week at a gas station and earn $8.75 per hour. You also work as a landscaper for $11 per hour and can work as many hours as you want. You want to earn a total of $400 per week. How many hours must you work as a landscaper?
Click here to see answer by macston(5194)  |
Question 989731: Write an equation and solve.
One Saturday Omar collected from his newspaper customers twice as many dollar bills as fives and one fewer ten than fives. If Omar collected $58,how many tens,fives, and ones did he get?
Click here to see answer by macston(5194) |
Question 989736: Write an equation and solve.
Josef has a jar of dimes,nickels, and pennies. He has one dime more than five times the number of nickels and four times as many pennies as nickels. How many of each coin does he have if their total value is $7.77?
Click here to see answer by macston(5194) |
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