A 15-ft ladder leans against a wall. The lower end of the ladder is being pulled away from the wall at the rate of 1.5 ft/sec. Let x be the distance from the bottom of the ladder to the wall, y be the distance from the top of the ladder to the ground and l be the length of the ladder. How fast is the top of the ladder moving along the wall at the instant it is 9 feet above the ground

The top of the ladder is sliding down at a rate of 2 feet per second.

Step-by-step explanation:

Refer the image for the diagram. Consider as right angle triangle. Values of length of one side and hypotenuse is given. Value of another side is not known. So applying Pythagoras theorem,

From the given data, , and

Substituting the values,  

Since length can never be negative, so .

Now to calculate again consider following equation,  

Differentiate both sides of the equation with respect to t,  

Applying sum rule of derivative,

Applying power rule of derivative,  

Simplifying,  

Substituting the values,  

Subtracting both sides by 18,

Dividing both sides by 9,

Here, negative indicates that the ladder is sliding in downward direction.  

c. 6tan80

step-by-step explanation:

1^3 + 2^3 + 3^3 +4^3 = (1+2+3+4)^2

step-by-step explanation:

i am only able to answer the first part. i am not sure about the second part. sorry