Answer:
First we need to find the slope. This is (7 - 3) / (4 - 2) = 2. Since we know the slope, we can use point-slope form. I'm using the point (2, 3).
y - 3 = 2(x - 2)
y - 3 = 2x - 4
y = 2x - 1
Answer:
x = -2
y = 3
Step-by-step explanation:
from above equation we get ,
=》y = 3x + 9
now ,
by second equation,
=》2x + 3y = 5
=》2x + 3 × ( 3x + 9 ) = 5
( since, y = 3x + 9 , by equation 1 )
=》2x + 9x + 27 = 5
=》11x = -22
=》x = -2
putting value of x in equation 1 ;
=》 y = 3x + 9
=》 y = 3 × ( -2 ) + 9
=》 y = -6 + 9
=》 y = 3
Answer:
78 i believe
Step-by-step explanation:
Well a double negative makes a positive so it is just thirty two. But if you arent supposed to change it it is negative parenthesis negative thirty two parenthesis.
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
