has characteristic equation
with roots at 
. Then the characteristic solution is
For the particular solution, consider the ansatz 
, whose first and second derivatives vanish. Substitute 
and its derivatives into the equation:
Then the general solution to the equation is
With 
, we have
and with 
,
Then the particular solution to the equation is
Answer:
B) 9² + 12² ≠ 18²
Step-by-step explanation:
Answer: Choice B) The expression (10-2x)(30-2x)x represents the volume of the box
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The original width is 10 inches. The width reduces to 10-2x inches after we cut off the top two corners of the rectangle. We can think of it as taking 10 and subtracting off two copies of x like so: 10-x-x = 10-2x
Similarly, the length goes from 30 inches to 30-2x inches. This time we're taking off the top and bottom corners (focus on either side it doesn't matter).
The height of the box is x inches due to this portion being folded up.
Volume of box = (width)*(length)*(height)
Volume of box = (10-2x)(30-2x)x
Note: the units for the answer are in cubic inches which can be written as "in^3" (inches cubed).
Answer:
100 times
Step-by-step explanation:
multiples of 3 on a number cube are 3 and 6
probability of rolling a '3' or '6' is 1/6 + 1/6 = 2/6 or 1/3
1/3 x 300 = 100
Answer:
Rectangular Prism - 2lw + 2lh + 2wh
Triangular prism - 2B + Ph
Pyramid - 2ll +l^2
Cylinder - 2π πrh + 2π πr^2
Cone - πrl + πr^2
Step-by-step explanation:
