T is less then or equal to 10 equals 100
The solution to the given differential equation is yp=−14xcos(2x)
The characteristic equation for this differential equation is:
P(s)=s2+4
The roots of the characteristic equation are:
s=±2i
Therefore, the homogeneous solution is:
yh=c1sin(2x)+c2cos(2x)
Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:
yp=Axsin(2x)+Bxcos(2x)
If you take the second derivative of the equation above for yp , and then substitute that result, y′′p , along with equation for yp above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side, sin(2x) , you will find:
A=0
B=−14
Therefore,
yp=−14xcos(2x)
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Answer:
29 m
Step-by-step explanation:
The dashes mean that the lines are equal in length, so from this we can determine that the area marked 441 m² is a square.
Area of a square = x², where x is the length of 1 side.
Therefore, x = √441 = 21 m
Now we have a right-angled triangle with two legs of 20 m and 21 m. We need to find the hypotenuse (labelled ?). To do this, use Pythagoras' Theorem a² + b² = c², where a and b are the legs and c is the hypotenuse.
Therefore,
20² + 21² = c²
⇒ 400 + 441 = c²
⇒ 841 = c²
⇒ c = √841
⇒ c = 29
So the side marked ? on the diagram is 29
Answer: Wall 1 & 2 : 26 ft by 9 ft
Wall 3 : 18 ft by 9 ft
Area 1 : 26 ft x 9 ft = 234 ft²
Area 2 : 26 ft x 9 ft = 234 ft²
Area 3 : 18 ft x 9 ft = 162 ft²
Total Area : 234 ft² + 234 ft² + 162 ft² = 630 ft²
1 Gallon = 250 ft²
630 ft² ÷ 250 ft² per gallon = 2.52 gallons
