The differential of

is

where the partial derivatives are

So the differential d<em>w</em> is

Company A: y = 50x + 15
Company B: y = 130x + 55
Set the equations equal to each other and solve for x (number of weeks).
50x + 15 = 130x + 55
Subtract 50x from both sides:
15 = 80x + 55
Subtract 55 from both sides:
-40 = 80x
Did you have a typo? The companies will never have the same cost because company B costs so much more and weeks cannot be negative.
Answer:
x=-7,1
Step-by-step explanation:
Answer:
Work done in stretching the spring = 7.56 lb-ft.
Step-by-step explanation:
Normal length of the spring = 8 in or
ft
=
ft
If the spring has been stretched to 11 inch then the stretched length of the spring is = 11 in
=
ft
Force applied to stretch the spring = 12 lb
By Hook's law,
F = kx [where k is the spring constant and x = length by which the spring is stretched]
12 = k(
)
k = 18
Work done (W) to stretch the spring by
ft will be
W = 
= 
= ![18[\frac{x^{2}}{2}]^{\frac{11}{12}}_0](https://tex.z-dn.net/?f=18%5B%5Cfrac%7Bx%5E%7B2%7D%7D%7B2%7D%5D%5E%7B%5Cfrac%7B11%7D%7B12%7D%7D_0)
= 9(
)²
= 7.56 lb-ft