Taking
and differentiating both sides with respect to
yields
![\dfrac{\mathrm d}{\mathrm dx}\bigg[3x^2+y^2\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[7\bigg]\implies 6x+2y\dfrac{\mathrm dy}{\mathrm dx}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B3x%5E2%2By%5E2%5Cbigg%5D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B7%5Cbigg%5D%5Cimplies%206x%2B2y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D0)
Solving for the first derivative, we have
Differentiating again gives
![\dfrac{\mathrm d}{\mathrm dx}\bigg[6x+2y\dfrac{\mathrm dy}{\mathrm dx}\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[0\bigg]\implies 6+2\left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2+2y\dfrac{\mathrm d^2y}{\mathrm dx^2}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B6x%2B2y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B0%5Cbigg%5D%5Cimplies%206%2B2%5Cleft%28%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cright%29%5E2%2B2y%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dx%5E2%7D%3D0)
Solving for the second derivative, we have
Now, when
and
, we have
Answer:
a) -3/13
b) -1/8
Step-by-step explanation:
a) - (21 / 7) / (91 / 7) = 3/13
b) (32 / 32 ) / - (256 / 32) = -1/8
Answer:
= 8p
Step-by-step explanation:
Steps
2p · 4
Remove parentheses: (a) = a
= 2p · 4
Multiply the numbers: 2 · 4 = 8
= 8p
Inches
Centimeters
Centimeters are more accurate.
Answer:
Fraction of bread used in the recipe is 3/12 which can be further simplified into 1/4
Explanation:
The original loaf of bread is 100% complete (no fraction is taken from it yet). This means that the value of the original loaf is 12/12
Now, assume that the fraction used in the recipe is x
We know that:
2/12 of the loaf was used in making a sandwich
7/12 of the oaf was put in the refrigerator
Therefore:
complete loaf = fraction used in making a sandwich + fraction used in making recipe + fraction put in refrigerator
12/12 = x + 2/12 + 7/12
12/12 = x + 9/12
x = 12/12 - 9/12
x = 3/12
Hope this helps :)
