Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position. a(t) = 2 i + 6t j + 12t2 k, v(0) = i, r(0) = 7 j − 4 k

v(t) = (2t + 1)i + 3t²j + 4t³k

r(t) = (t² + t)i + (t³ + 7)j + (t⁴ - 4)k

Explanation:

a(t) = 2i + 6tj + 12t²k

v(t) = ∫a(t)dt

     = ∫(2i + 6tj + 12t²k)dt

     = 2ti + (6t²/2)j + (12t³/3)k + c

     = 2ti + 3t²j + 4t³k + c

v(0) = i

    i = 0i + 0j + 0k + c

    c = i

∴ v(t) = 2ti + 3t²j + 4t³k + i

v(t) = (2t + 1)i + 3t²j + 4t³k

r(t) = ∫ v(t)dt

    = i ∫ (2t + 1)dt + 3j ∫ t²dt + 4k ∫ t³dt

    = i (2t²/2 + t) + 3j(t³/3) + 4k(t⁴/4) + d

    = i (t² + t) + jt³ + t⁴k + d

r(0) = 7j - 4k

0i + 0j + 0k + d = 7j - 4k

d = 7j - 4k

∴ r(t) = (t² + t)i + t³j + t⁴k + 7j - 4k

r(t) = (t² + t)i + (t³ + 7)j + (t⁴ - 4)k

hi,

henry is an economist and wants to understand the relationship between inflation and consumer spending habits. for his research, he needs the consumer price index for 2014 and the inflation rate. based on the prices of goods given, what will he find to be the cpi and inflation rate for 2014? assume that a consumer’s basket for three consecutive years consists of the following:

you dont privide answer choices.

answer - 15% of a inflatation rate is 15% less in cpi

answer; customers within the organization