Answer:
Volume required = 100mL
Step-by-step explanation:
Let the volume of 30% solution required be = V mL
Amount of solute in V mL of solution = 30% of V = 0.3V...............(i)
This amount is also present in 150 mL of 20% solution
For 150 mL of 20% solution we have amount of solute = 150 mL X 20%
= 30..............(ii)
Thus equating i and ii we get
0.3V = 30
Thus V =100 mL
Answer:
Step-by-step explanation:
We have the equations
4x + 3y = 18 where x = the side of the square and y = the side of the triangle
For the areas:
A = x^2 + √3y/2* y/2
A = x^2 + √3y^2/4
From the first equation x = (18 - 3y)/4
So substituting in the area equation:
A = [ (18 - 3y)/4]^2 + √3y^2/4
A = (18 - 3y)^2 / 16 + √3y^2/4
Now for maximum / minimum area the derivative = 0 so we have
A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0
-3/8 (18 - 3y) + √3 y /2 = 0
-27/4 + 9y/8 + √3y /2 = 0
-54 + 9y + 4√3y = 0
y = 54 / 15.93
= 3.39 metres
So x = (18-3(3.39) / 4 = 1.96.
This is a minimum value for x.
So the total length of wire the square for minimum total area is 4 * 1.96
= 7.84 m
There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.
1/4 x 24 is 6.
Your welcome
there are 60 minutes per hour
24/60 = 0.4 miles per minute
0.4*5 = 2
they will ride 2 miles in 5 minutes
