At the start, the tank contains
(0.02 g/L) * (1000 L) = 20 g
of chlorine. Let <em>c</em> (<em>t</em> ) denote the amount of chlorine (in grams) in the tank at time <em>t </em>.
Pure water is pumped into the tank, so no chlorine is flowing into it, but is flowing out at a rate of
(<em>c</em> (<em>t</em> )/(1000 + (10 - 25)<em>t</em> ) g/L) * (25 L/s) = 5<em>c</em> (<em>t</em> ) /(200 - 3<em>t</em> ) g/s
In case it's unclear why this is the case:
The amount of liquid in the tank at the start is 1000 L. If water is pumped in at a rate of 10 L/s, then after <em>t</em> s there will be (1000 + 10<em>t</em> ) L of liquid in the tank. But we're also removing 25 L from the tank per second, so there is a net "gain" of 10 - 25 = -15 L of liquid each second. So the volume of liquid in the tank at time <em>t</em> is (1000 - 15<em>t </em>) L. Then the concentration of chlorine per unit volume is <em>c</em> (<em>t</em> ) divided by this volume.
So the amount of chlorine in the tank changes according to
which is a linear equation. Move the non-derivative term to the left, then multiply both sides by the integrating factor 1/(200 - 5<em>t</em> )^(5/3), then integrate both sides to solve for <em>c</em> (<em>t</em> ):
There are 20 g of chlorine at the start, so <em>c</em> (0) = 20. Use this to solve for <em>C</em> :
Answer:
it is -30
Step-by-step explanation:
you would divide both sides by x,then f=2
using PEMDAS we come to -30
(-35-42-63)/7= (-140)/7=-20
Answer:
b) y = 289.815 when
Step-by-step explanation:
We are given the following information in the question:
where y is the dependent variable,
are the independent variable.
The multiple regression equation is of the form:
where,
: is the intercept of the equation and is the value of dependent variable when all the independent variable are zero.
: It is the slope coefficient of the independent variable .
: It is the slope coefficient of the independent variable .
- The regression coefficient in multiple regression is the slope of the linear relationship between the dependent and the part of a predictor variable that is independent of all other predictor variables.
Comparing the equations, we get:
- This means holding constant, a change of one in is associated with a change of 0.5906 in the dependent variable.
- This means holding constant, a change of 1 in is associated with a change of 0.4980 in the dependent variable.
b) We have to estimate the value of y
Answer:
use the trash can icon
Step-by-step explanation:I’m pretty sure it’s somewhere you can also get it baNed.