500L tank initially has 200L saltwater with 250g salt dissolved. In flows 4L/min saltwater with [salt]=5g/L, Outflow of the mixture at [salt]=Q/V has rate 6L/min. Write the IVP for Q(t)= quantity of salt in the mixing tank. dQ 250 6Q 500-t dt dQ 20 3Q dt 100-t dQ dt 6Q 200+2t 20 3Q 250+t dQ 200 dt dQ dt 3Q 50-t 200 search Inser prt sc F10 home F11 end F12 F9 DII F4 F7 F8 F5 F6 F3 F2 F1 *- %23 2$ 7 8. 2 3 4
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
![500L tank initially has 200L saltwater with 250g salt dissolved. In flows 4L/min
saltwater with [salt]=5g/L, Outflow of the mixture at [salt]=Q/V has rate 6L/min.
Write the IVP for Q(t)= quantity of salt in the mixing tank.
dQ
250
6Q
500-t
dt
dQ
20
3Q
%3|
dt
100-t
dQ
6Q
200+2t
20
dt
dQ
3Q
250+t
200
dt
3Q
dQ
dt
200
50-t
search
Inser
prt sc
F10
home
F11
end
F12
F9
DII
F4
F7
F8
F6
F5
F3
F2
F1
*-
2#
24
7
8.
4
2
P
E
R
T
Y
W](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F521df3ae-8e5f-4edb-bcc7-9453c7ca96c5%2Febce0085-6fee-4c20-9cb7-9af610263e38%2F44kvuo_processed.jpeg&w=3840&q=75)
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