Answer: r = 0.8081; s = -0.07071
Explanation:
A = (150i + 270j) mm
B = (300i - 450j) mm
C = (-100i - 250j) mm
R = rA + sB + C = 0i + 0j
R = r(150i + 270j) + s(300i - 450j) + (-100i - 250j) = 0i + 0j
R = (150r + 300s - 100)i + (270r - 450s - 250)j = 0i + 0j
Equating the i and j components;
150r + 300s - 100 = 0
270r - 450s - 250 = 0
150r + 300s = 100
270r - 450s = 250
solving simultaneously,
r = 0.8081 and s = -0.07071
QED!
Answer:
(a) The number of gallons of water in the tank when it starts draining.
(b) How many minutes it takes for all of the water to drain from the tank.
Explanation:
So, basically v(t) defines the volume of tank as a function of time. When we evaluate t=0, we find the intercept with the y-axis which represent the initial water volume of the tank in gallons:
now we need to know when v(t)=0, so:
Solving for t:
This represents the amount of time in minutes required to drain all of the water from the tank, in other words v=0gal
I attached a picture where you can see the graph that represents the function:
Answer: A minimum of $242.60 and a maximum of $1,100 per month.
Explanation:
What's the difference between a fraction and a ratio? A fraction is a number that names part of a whole or part of a group. The denominator represents the total number of equal parts the whole is divided into. A ratio is a comparison of two quantities.