In the
plane, we have
everywhere. So in the equation of the sphere, we have
![25=(x-2)^2+(y+10)^2+(-3)^2\implies(x-2)^2+(y+10)^2=16=4^2](https://tex.z-dn.net/?f=25%3D%28x-2%29%5E2%2B%28y%2B10%29%5E2%2B%28-3%29%5E2%5Cimplies%28x-2%29%5E2%2B%28y%2B10%29%5E2%3D16%3D4%5E2)
which is a circle centered at (2, -10, 0) of radius 4.
In the
plane, we have
, which gives
![25=(x-2)^2+10^2+(z-3)^2\implies(x-2)^2+(z-3)^2=-75](https://tex.z-dn.net/?f=25%3D%28x-2%29%5E2%2B10%5E2%2B%28z-3%29%5E2%5Cimplies%28x-2%29%5E2%2B%28z-3%29%5E2%3D-75)
But any squared real quantity is positive, so there is no intersection between the sphere and this plane.
In the
plane,
, so
![25=(-2)^2+(y+10)^2+(z-3)^2\implies(y+10)^2+(z-3)^2=21=(\sqrt{21})^2](https://tex.z-dn.net/?f=25%3D%28-2%29%5E2%2B%28y%2B10%29%5E2%2B%28z-3%29%5E2%5Cimplies%28y%2B10%29%5E2%2B%28z-3%29%5E2%3D21%3D%28%5Csqrt%7B21%7D%29%5E2)
which is a circle centered at (0, -10, 3) of radius
.
I have 5 bags of Totino Pizza Rolls. There are 3 pieces per bag. 1/3 of each bag is burnt.
If she runs 7 miles every hour and runs a total of 11.2 miles, we can set this up as:
![11.2=7x](https://tex.z-dn.net/?f=11.2%3D7x)
Where x represents the # of hours she ran for. Let's solve for x:
![x = \frac{11.2}{7} = 1.6](https://tex.z-dn.net/?f=x%20%3D%20%20%20%5Cfrac%7B11.2%7D%7B7%7D%20%20%3D%201.6)
So, she ran for a total of 1.6 hours.
Answer:
the first time 4 and 6 intersent is 24
so 24 days after september 5th
september 29th
Hope This Helps!!!
Answer:
= 1/x^2
Step-by-step explanation:
Possible derivation:
d/dx(-16 - 1/x + y)
Differentiate the sum term by term and factor out constants:
= d/dx(-16) - d/dx(1/x) + d/dx(y)
The derivative of -16 is zero:
= -(d/dx(1/x)) + d/dx(y) + 0
Simplify the expression:
= -(d/dx(1/x)) + d/dx(y)
Use the power rule, d/dx(x^n) = n x^(n - 1), where n = -1.
d/dx(1/x) = d/dx(x^(-1)) = -x^(-2):
= d/dx(y) - -1/x^2
Simplify the expression:
= 1/x^2 + d/dx(y)
The derivative of y is zero:
= 1/x^2 + 0
Simplify the expression:
Answer: = 1/x^2