Describe the curve defined by the vector function r(t) = 3 + t, 5 + 4t, −2 + 3t . solution the corresponding parametric equations are x = 3+t , y = 5 + 4t, z = −2+3t which we recognize from these equations as parametric equations of a line passing through the point (3, 5, −2) and parallel to the vector 1, 4, 3 . alternatively, we could observe that the function can be written as r = r0 + tv, where r0 = 3, 5, −2 and v = t⟨1, 4, 3⟩ , and this is the vector equation of a line as given by this equation.

c

step-by-step explanation:

c

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c

step-by-step explanation:

i think because what else can be a sample of every member

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1