A. 25 = (.5 * 22) + (2 * x)
B. 25 = (.5 * 22) + (2 * x)
25 = 11 + 2x
14 = 2x
7 = x
C. 7
At the start, the tank contains
(0.25 lb/gal) * (100 gal) = 25 lb
of sugar. Let
be the amount of sugar in the tank at time
. Then
.
Sugar is added to the tank at a rate of <em>P</em> lb/min, and removed at a rate of

and so the amount of sugar in the tank changes at a net rate according to the separable differential equation,

Separate variables, integrate, and solve for <em>S</em>.







Use the initial value to solve for <em>C</em> :


The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

has passed. At this time, we want the tank to contain
(0.5 lb/gal) * (5 gal) = 2.5 lb
of sugar, so we pick <em>P</em> such that

-21/5 is the closest!!!
Hope this helps.
If you want me to explain why, just ask! :)
Just solve for , then substitute back into either expression and calculate either BC or AD. The other one is then the same amount.
The one about the square is the same thing except you don't care how the figure is named because all 4 sides are equal anyway. Just set the two expressions equal to one another and then solve for
Answer: We can find angle BAC by using (1) SinA = 9.8/12
(2) CosA = 6.9/12
(3) TanA = 9.8/6.9
Step-by-step explanation: The question indicates that we have a right angled triangle ABC with the right angle at point C (that is, angle ACB is the right angle). Also the three sides have been labeled as AB equals 12 cm, CB equals 9.8 cm and AC equals 6.9 cm. Line AB has been identified as the hypotenuse and angle A (that is, BAC) is the reference angle. If angle A is the reference angle, then line CB facing angle A shall be the opposite side, while line AC is the adjacent (which lies between the reference angle and the right angle). Please see the attached diagram for details.
Having these details available, we can actually find angle A by using any of the three trigonometric ratios, since all three sides are given. Hence,
SinA = opposite/hypotenuse
SinA = 9.8/12
SinA = 0.8167
Checking with your calculator or table of values, A = 54.76 (approximately 55)
Also CosA = adjacent/hypotenuse
CosA = 6.9/12
CosA = 0.5750
Checking with your calculator or table of values A = 54.90 (approximately 55).
Finally TanA = opposite/adjacent
TanA = 9.8/6.9
TanA = 1.4203
Checking with your calculator or table of values A = 54.83 (approximately 55).