Aparticle is moving with the given data. find the position of the particle. a(t) = 13 sin(t) + 4 cos(t), s(0) = 0, s(2π) = 10

OK so we need to find the function v(t) which will tell us where the particle is at any given time.

We know that the derivative of distance is speed and the derivative of speed is acceleration.

In this case we need to work backwords and find the integrals.

a(t) = 13 sin(t) + 4 cos(t)

s(t)= integral of above = 13(-cos(t)) + 4(sin(t)) + C

v(t)= integral of above = -13sin(t) -4cos(t) +Ct + D

Now I believe you have incorrect initial conditions

s(0) = 0, s(2π) = 10

As cos and sin functions have the same value at 0 and 2Pi the above cannot be true.

My guess is that one is s(0) and the other is v(2Pi) or the other way round.

These initial conditions will determine the value of the two constants: C and D.

Hope this helps.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)