Answer:
4,200 liters
Step-by-step explanation:
The flow rate is given by:
Integrating the flow rate expression from t=0 to t=30 minutes, yields the total volume that flows out of the tank during that period:
4,200 liters of water flow from the tank during the first 30 minutes.
Answer:
Graph B
Step-by-step explanation:
The solutions to a quadratic equation are the points on which we have the graph of the curve touching the x-axis
Now the first thing we will do here is to solve the quadratic equation graph;
x^2 + 4x -12 = 0
x^2 +6x - 2x -12 = 0
x (x + 6) -2(x + 6) = 0
(x-2)(x + 6) = 0
x = 2 or -6
So the graph that touches the x-axis at the points x = 2 and x = -6 is the solution to the quadratic equation
Graph B is the closest to what we have as answer
Let's start b writing down coordinates of all points:
A(0,0,0)
B(0,5,0)
C(3,5,0)
D(3,0,0)
E(3,0,4)
F(0,0,4)
G(0,5,4)
H(3,5,4)
a.) When we reflect over xz plane x and z coordinates stay same, y coordinate changes to same numerical value but opposite sign. Moving front-back is moving over x-axis, moving left-right is moving over y-axis, moving up-down is moving over z-axis.
A(0,0,0)
Reflecting
A(0,0,0)
B(0,5,0)
Reflecting
B(0,-5,0)
C(3,5,0)
Reflecting
C(3,-5,0)
D(3,0,0)
Reflecting
D(3,0,0)
b.)
A(0,0,0)
Moving
A(-2,-3,1)
B(0,-5,0)
Moving
B(-2,-8,1)
C(3,-5,0)
Moving
C(1,-8,1)
D(3,0,0)
Moving
D(1,-3,1)