Solve the vector initial-value problem for y t by integrating and using the initial conditions to find the constants of integration . y ″ t = 12 t 2 i − 2 t j , y 0 = 2 i − 4 j, y ′ 0 = 0
Solve the vector initial-value problem for y t by integrating and using the initial conditions to find the constants of integration . y ″ t = 12 t 2 i − 2 t j , y 0 = 2 i − 4 j, y ′ 0 = 0
Solve the vector initial-value problem for
y
t
by integrating and using the initial conditions to find the constants of integration.
y
″
t
=
12
t
2
i
−
2
t
j
,
y
0
=
2
i
−
4
j,
y
′
0
=
0
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
The velocity of a particle moving in the plane has components
dx
= 12t – 312 and-
dt
dy
= In(1 + (t – 4)*)
dt
At time t = 0, the position of the particle is (-13, 5). At time t= 2, the object is at point P with
x-coordinate 3.
Find the speed of the particle and its acceleration vector at t= 2.
Find the y-coordinate of P.
Write an equation for the tangent line to the curve at P.
SOLVE THE DE
Find the integrating factor for
dy — 2хy dx — х dх.
А. e1-2у
1
В.
1-2у
C. el+2y
1
D. ;
1+2y
Calculus, Single Variable: Early Transcendentals (3rd Edition)
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