Once Kate's kite reaches a height of 50 ft (above her hands), it rises no higher but drifts due east in a wind blowing 7 ft divided by s. How fast is the string running through Kate's hands at the moment that she has released 107 ft of string?

dz  = 7.136 (answer)

Explanation:

given height  for kate's kite   = 50 ft  (say y)

due to drift it move towards east =  dx = 7 ft  

string maximum length          = 107 ft ( say z)

we have to find change in z  

that is  dz

it will form a right angle triangle for x , y and z  where x is base y is height and z is hypotenuse

so we get according to Pythagoras Theorem

...............(i)

by derivative both side  consider y as constant

from (i)  equation

now put the value and find dz

after solving these  we get

 

dz  = 7.136 (answer)

The correct answer is
A. Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity on the object.

In fact, mass is an intrinsic property of any object: it does not depend on external conditions, and it gives a measure of the amount of matter in the object.
Weight, instead, is the measure of the force of gravity on the object. Weight is related to the mass by the equation:

where
W is the weight
m is the mass
g is the gravitational acceleration

From the formula, we see that the weight is proportional to the mass, but it also depends on strength of the gravitational field g, which is not constant (for instance, g is different if we are on another planet, or very far from Earth's surface).