+97 A sphere with radius 7 has its center at the origin of the 3D cartesian grid shown on the left. Consider only the top half of the sphere:
Calculate the value of z, the slope in the x-direction and the slope in the y-direction at the two points where (x,y) are (2.3,-0.8) and (-0.5,1.4).
z (2.3, -0.8)= correct answer is 6.56
x ('''''''''''''')= correct answer is -0.35
y ('''''''''''''')= correct answer is 0.12
z(-0.5, 1.4)= correct answer is 6.84
x ('''''''''''''')= correct answer is 0.07
y ('''''''''''''')=correct answer is -0.20.
Thanks guys. This is the full question.
+33616 The general equation for a sphere, centred at (0,0,0) is x2 + y2 + z2 = r2
Rearrange this as z = (r2 - x2 - y2)1/2
The slope of z with respect to x is given by
∂z/∂x = -x/ (r2 - x2 - y2)1/2
The slope of z with respect to y is given by
∂z/∂y = -y/ (r2 - x2 - y2)1/2
You have the values of x, y and r, so I'll leave you to plug them into these formulae.
+33616 The general equation for a sphere, centred at (0,0,0) is x2 + y2 + z2 = r2
Rearrange this as z = (r2 - x2 - y2)1/2
The slope of z with respect to x is given by
∂z/∂x = -x/ (r2 - x2 - y2)1/2
The slope of z with respect to y is given by
∂z/∂y = -y/ (r2 - x2 - y2)1/2
You have the values of x, y and r, so I'll leave you to plug them into these formulae.
