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:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean =

also, median= , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean =  

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)