In a previous section we looked at mixing problems in which the volume of fluid remained constant and saw that such problems giv
e rise to separable equations. (See example.) If the rates of flow into and out of the system are different, then the volume is not constant and the resulting differential equation is linear but not separable. A tank contains 25 L of water. A solution with a salt concentration of 0.4 kg/L is added at a rate of 5 L/min. The solution is kept mixed and is drained from the tank at a rate of 3 L/min. If y(t) is the amount of salt (in kilograms) after t minutes, show that y satisfies the differential equation dy dt = 2 − 3y 25 + 2t . Solve this equation and find the concentration after 20 minutes. (Round your answer to four decimal places.)
1 answer:
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Answer:
The inequality for is:
Step-by-step explanation:
Given:
Width of rectangle = 3 ft
Height or length of rectangle = ft
Perimeter is at least 300 ft
To write an inequality for .
Solution:
Perimeter of a rectangle is given as:
⇒
where represents length of the rectangle and
represents the width of the rectangle.
Plugging in the given values in the formula, the perimeter can be given as:
⇒
Using distribution:
⇒
Simplifying.
⇒
The perimeter is at lest 300 ft. So, the inequality can be given as:
⇒
Solving for
Subtracting both sides by 16.
⇒
⇒
Dividing both sides by 2.
⇒
⇒ (Answer)
Answer:
4th option
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x - 6 ← is in slope- intercept form
with slope m =
Given a line with slope m then the slope of a line perpendicular to it is
= -
= -
= -
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - and (a, b ) = (- 2, 5 ) , then
y - 5 = - (x - (- 2) ) , that is
y - 5 = - (x + 2)