math

posted by .

Can you please check my work.

A particle is moving with the given data. Find the position of the particle.
a(t) = cos(t) + sin(t)
s(0) = 2
v(0) = 6

a(t) = cos(t) + sin(t)
v(t) = sin(t) - cos(t) + C
s(t) = -cos(t) - sin(t) + Cx + D

6 = v(0) = sin(0) -cos(0) + C
C=7

2= s(0) = -cos(0) - sin(0) + 7 (0) + D
D= 3

s(t) = -cos(t) - sin(t) + 7t + 3

  • math -

    All correct.

    We can check backwards:
    assume given:
    s(t) = -cos(t) - sin(t) + 7t + 3

    v(t)=s'(t)=sin(t)-cos(t)+7
    a(t)=v'(t)=cos(t)+sin(t)
    v(0)=sin(0)-cos(0)+7=0-1+7=6
    s(0)=-cos(0)-sin(0) + 7(0) + 3 =-1+0+0+3=2
    All correct!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. tigonometry

    expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) …
  2. Trig

    Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos …
  3. algebra

    Can someone please help me do this problem?
  4. Mathematics - Trigonometric Identities

    Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y …
  5. TRIG!

    Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
  6. calc

    i did this problem and it isn't working out, so i think i'm either making a dumb mistake or misunderstanding what it's asking. A particle moves along the x axis so that its velocity at any time t greater than or equal to 0 is given …
  7. calculus

    A particel is moving with the given data. Find the position of the particle. v(t)= sin t - cos t , s(0)= 0
  8. Calculus 12th grade (double check my work please)

    1.)Find dy/dx when y= Ln (sinh 2x) my answer >> 2coth 2x. 2.)Find dy/dx when sinh 3y=cos 2x A.-2 sin 2x B.-2 sin 2x / sinh 3y C.-2/3tan (2x/3y) D.-2sin2x / 3 cosh 3yz...>> my answer. 2).Find the derivative of y=cos(x^2) …
  9. Calculus (Related Rates)

    The position of a particle moving in a straight line is given by s(t) = (e^(-t))(cos(5t)) for t>0, where t is in seconds. If the particle changes direction at time T seconds, then T must satisfy the equation: cos(5T) = 0 5T = arctan(-1/5) …
  10. calculus

    A particle moves so that its position is given by ⟨cos(t),sin(t),cos(6t)⟩. Find the maximum and minimum speeds of the particle.

More Similar Questions