Aladder 25 feet long is leaning against the wall of a building. initially, the foot of the ladder is 7 feet from the wall. the foot of the ladder begins to slide at a rate of 2 ft/sec, causing the top of the ladder to slide down the wall. the location of the foot of the ladder at time t seconds is given by the parametric equations (7+2t,0).

The location of the foot of the ladder at time t is

Step-by-step explanation:

The wall, ladder and the ground makes a right angled triangle. Let the ground be x and the wall be y.

Then, by Pythagorean theorem, we have,

Also, given that the ladder is sliding at a rate of 2ft/sec.

The location of the foot of the ladder at time t is given by the parametric equations and thus, . Substituting these values in the equation , we get,

Subtracting on both sides,

Taking square root on both sides, we get,

Thus, the location of the foot of the ladder at time t is

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

$5.41

step-by-step explanation:

$20 - $14.51 = $5.49.