1/4=2/8
7/8-2/8=5/8
so 5/8 foot of the board is left
D. 2744 cm^3
Soultion no. 1
If you put the figure sideways you get a prism (with the two dark triangles as bases) and the formula for the volume is
V = BH (where B is the area of the base and H is the height, 49)
The area of the triangle is
P = (8*14)/2 (half the area of a rectangle with sides 8 and 12) which is:
P = 8*7 = 57
The volume is:
V = 57 * 49 = 2744
Solution no. 2
The figure has half the volume of a rectangular prism with sides 8, 14 and 49
Which is:
V = (8*14*49)/2 = 2744
angle A = 30
(2x-9) = (2x+21)
+9 +9
2x=2x+30
-2x -2x
=30
The equations (2) and (3) you referred to are unavailable, but it is clear that you are trying to show that two set of solutions y1 and y2, to a (second-order) differential equation are solutions, and form a fundamental set. This will be explained.
Answer:
SOLUTION OF A DIFFERENTIAL EQUATION.
Two functions y1 and y2 are set to be solutions to a differential equation if they both satisfy the said differential equation.
Suppose we have a differential equation
y'' + py' + qy = r
If y1 satisfies this differential equation, then
y1'' + py1' + qy1 = r
FUNDAMENTAL SET OF DIFFERENTIAL EQUATION.
Two functions y1 and y2 are said to form a fundamental set of solutions to a second-order differential equation if they are linearly independent. The functions are linearly independent if their Wronskian is different from zero.
If W(y1, y2) ≠ 0
Then solutions y1 and y2 form a fundamental set of the given differential equation.
1. sixty three 2.63 3. 60+3 4. 50+13
