What are the removable discontinuities of the following function? f (x) = StartFraction x squared minus 36 Over x cubed minus 36 x EndFraction

the removable discontinuities are at x = 6 and at x = -6

Step-by-step explanation:

Notice that the function has common binomial factor in numerator and denominator:

therefore, the removable discontinuities are those at x= 6 and x = -6 that correspond to zeros common in numerator and denominator, and therefore those associated with the (x + 6) factor, with the (x - 6) factor.

There is a non-removable discontinuity at x = 0.

The discontinuities can be removed by re-assigning the value of f(x) at x=6 (as 1/6), and at x = -6 (as -1/6)

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~

christopher is 272,195 year old

step-by-step explanation: