Find the point on the circle x^2+y^2 = 16900 which is closest to the interior point (30,40)

Answer-

(78,104) is the closest to the interior point.

Solution-

The equation of the circle,

As the point will be on the circle, so the coordinate of the point will be,

The distance "d' between the point and (30,40) is,

Now, we have to calculate x for which d is minimum. d will be minimum when    will be minimum.

Let,

Finding the critical values,

Then,

f''(x) is positive, so f(x) will be minimum at x=78

For x = 78, y will be

Therefore, the point is (78,104)

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.

~

x = 12

y = 1

for the points!