Let p=(x, y) be a point on the graph of y= 1/x. express the distanced from p to the point x (2,0) as a function of x. what is d if x=2?

D = SQRT (x^4 + 17x^2 + 64)    This is the distance as a function of x

Step-by-step explanation:

This problem uses the Pythagorean Theorem to determine the length of a hypotenuse of a right triangle.

The base of the triangle goes x distance along the x-axis, then y distance up to the point in question.  What is the distance (the hypotenuse of that triangle) as a function of x?

D = SQRT (x^2 + y^2)

D = SQRT (x^2 + (x^2+8)^2)         (substitute for y)

D = SQRT (x^2 + x^4 + 16x^2 + 64)        (expand using FOIL)

D = SQRT (x^4 + 17x^2 + 64)                (revise order, collect terms)

   This is the distance as a function of x

54 km / hours

step-by-step explanation:

we need to convert seconds to hours

60 seconds = 1 minutes

60 minutes = 1hour

15 m         60 second   60 minutes

  * *         = 54000 meters/ hour

second     1 minute             1 hour

now we need to convert meters to km

1000 m = 1 km

54000 m       1 km

*   = 54 km / hours

hour               1000m

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.

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