<u>Solution-</u>
As given in △ABC,

As from the properties of trigonometry we know that, the greater the angle is, the greater is the value of its sine. i.e

According to the sine law,

In order to make the ratio same, even though m∠A>m∠B>m∠C, a must be greater than b and b must be greater than c.

Also given that its perimeter is 30. Now we have to find out whose side length is 7. So we have 3 cases.
Case-1. Length of a is 7
As a must be the greatest, so b and c must be less than 7. Which leads to a condition where its perimeter won't be 30. As no 3 numbers less than 7 can add up to 30.
Case-2. Length of b is 7
As b is greater than c, so c must 6 or less than 6. But in this case the formation of triangle is impossible. Because the triangle inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. If b is 7 and c is 6, then a must be 17. So no 2 numbers below 7 can add up to 17.
Case-3. Length of c is 7
As this is the last case, this must be true.
Therefore, by taking the aid of process of elimination, we can deduce that side c may have length 7.
X1+X2 Y1+Y2
--------- , ---------
2 2
Thats the equation. You write that (the equation above) in parentheses.
Answer:
The length and width of the rectangle are 20 feet and 31.25 feet, respectively.
Step-by-step explanation:
Let the scale be
and the dimensions of the rectangle being 4 inches and 5 inches, respectively. The scale (
), measured in inches per feet, is equivalent to the following rational number:

We can convert each length by dividing it by scale factor. That is:
Length


Width


The length and width of the rectangle are 20 feet and 31.25 feet, respectively.
Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of
(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min
and flows out at a rate of
(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min
Then the net flow rate is governed by the differential equation

Solve for S(t):


The left side is the derivative of a product:
![\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dt%7D%5Cleft%5Be%5E%7Bt%2F800%7DS%28t%29%5Cright%5D%3D%5Cdfrac8%7B100%7De%5E%7Bt%2F800%7D)
Integrate both sides:



There's no sugar in the water at the start, so (a) S(0) = 0, which gives

and so (b) the amount of sugar in the tank at time t is

As
, the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.
X=-1/3 and x=4 are the positive and negative x intercepts