Answer:
(x,y) => (x+3, y+4)
Step-by-step explanation:
Given a triangle DEF, D(4,2), E(3,3), F(2,1).
Centroid of the area (and the vertices) equals the mean of the coordinates, namely ( (4+3+2)/3, (2+3+1)/3 ) = (3,2)
To translate (3,2) to (6,6), we need the rule
(x,y) => x+(6-3), y+(6-2), or
(x,y) => (x+3, y+4)
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:
3.71 cm
Step-by-step explanation:
Hi there!
Area of a circle equation: 
where r is the radius
Plug in the area 43.25 cm²
Divide both sides by π to isolate r²
Take the square root of both sides to isolate r
Therefore, the length of the radius rounded to 2 decimal points is 3.71 cm.
I hope this helps!
To calculate to volume of a rectangular prism you use the formula l × w × h = V
l, w, and h are the sides, and V is the volume
So... 24 × 10 × h = 2,880
h = 2,880 / 240
h = 12
