Answer:
33 1/3 L of the 40% solution, 16 2/3 L of the 25% solution
Step-by-step explanation:
Set up two equations...
Let x represent the number of Liters of the 40% solution
Let y represent the number of Liters of the 25% solution
We need 50 liters total, so
x + y = 50
and we need the 50 L to be 35% solution, so
0.4x = 0.25y = 0.35(50)
Solve the first equation for one variable...
x = 50 - y (subtract y from both sides in equation 1)
Now substitute that value into the second equation...
0.4(50 - y) + 0.25y = 17.5 (x becomes 50 - y, 0.35(50) = 17.5)
Now solve for y...
20 - 0.4y + 0.25y = 17.5
-0.15y = -2.5
y = 16.66666667
y = 16 2/3 L
So we need to plug that into the first equation to find 'x'
x + 16 2/3 = 50
x = 50 - 16 2/3
x = 33 1/3
Answer:
Point slope formula: (y + 4) = 2(x - 5)
Slope intercept formula: y = 2x - 14
Step-by-step explanation:
Point slope formula: (y + 4) = 2(x - 5)
Slope intercept formula: y = 2x + b, -4 = 10 + b, b = -14
y = 2x - 14
If we let
x as the distance traveled by the boat
y as the distance between the boat and the lighthouse.
Then, we have:
tan 18°33' = 200 / (x + y)
and
tan 51°33' = 200 / y
Solving for y in the second equation:
y = 200 / tan 51°33'
Rearranging the first equation and substituting y
x = 200 / tan 18°33' - 200 / tan 55°33'
x = 458.81 ft
Therefore, the boat traveled 458.81 ft before it stopped.
Let 
. The gradient of 
at the point (1, 0, 0) is the normal vector to the surface, which is also orthogonal to the tangent plane at this point.
So the tangent plane has equation
Compute the gradient:
Evaluate the gradient at the given point:
Then the equation of the tangent plane is
The volume of this container is 5990 feet³.
<h3>How to calculate the volume?</h3>
Volume of a cylinder = πr²h
π = 3.14
r = radius = 17.5/2 = 8.75
h = 24.5
The volume will be:
= πr²h
= 3.14 × 8.75² × 24.5
= 5990 ft³
Therefore, the volume of this container is 5990 feet³.
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