Aparticle is moving with the given acceleration function and initial conditions. find the velocity function and the position function of this particle. a(t) = 2 sin(t) − 4 cos(t), v(0) = −3, s(0) = 5

The velocity function is the particle is .

Step-by-step explanation:

The acceleration function of a moving particle is

The initial conditions are v(0) = −3, s(0) = 5.

Integrate the acceleration function with respect to time to find the velocity function.

Use the initial condition v(0) = −3 to find the value of C₁.

So the velocity function is the particle is

Integrate the acceleration function with respect to time to find the position function.

Use the initial condition s(0) = 5 to find the value of C₂.

So, the position function is the particle is .

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.

step-by-step explanation:

a and d