Let
= amount of salt (in pounds) in the tank at time
(in minutes). Then
.
Salt flows in at a rate

and flows out at a rate

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.
Then the net rate of salt flow is given by the differential equation

which I'll solve with the integrating factor method.



Integrate both sides. By the fundamental theorem of calculus,





After 1 hour = 60 minutes, the tank will contain

pounds of salt.
Answer:
- 321 adult tickets
- 227 child tickets
Step-by-step explanation:
This sort of problem is easily solved by defining a variable to be the quantity of the higher-value contributor. Here, we can let x represent the number of adult tickets. Then total revenue is ...
6.50x +3.50(548-x) = 2881
3x +1918 = 2881 . . . . . . . . . . . . eliminate parentheses, collect terms
3x = 963 . . . . . . . . . . . . . . . . . . subtract 1918
x = 321 . . . . . . . . . . . . . . . . . . . . divide by 3
548-x = 548 -321 = 227 . . . . . .number of child tickets
321 adult tickets and 227 child tickets were sold.
If you mean the price is now 120% of the original, $<span>4.74 (3.95 * 0.8) is the new price.
If you mean the price is now 80% of the original, $3.16 (3.95 * 1.2) is the new price.</span>
Turn phrases into mathmatical expressions:
"<span>one side(s) twice the length of the shortest side(x)" = 2x
"</span><span>the third side(t) is 30 feet more than the length of the shortest side " = x+30
</span>Shortest side= x
Perimeter= side1+ side 2 + side 3
138ft= x+2x+x+30
138= 4x+30
108=4x
x= 27 feet
Answer:
The shortest side is 27ft. The middle side 2x= 2(27)= 54ft. The longest side being x+30= 27+30= 57ft.