Peter's suitcase weighs 14 2/5 pounds, and he adds 3/5 pounds each minute. william's suitcase weighs 48 pounds, and he removes 4/5 pounds each minute. after how many minutes will the weight of both suitcases be the same?

After 25 minutes both bags of Peter's suitcase will have same weights.

Solution:

Given, Peter's suitcase weighs

And he adds pounds each minute.

Then, series of his bag weights will be

This forms an Arithmetic progression

William's suitcase weighs 48 = pounds, and he removes pounds each minute.

Then, series of bag weights will be

This forms an A.P

After how many minutes will the weight of both suitcases be the same?

So, now we have to equate nth terms of above two series to get the answer.

Then, nth term of peters series = nth term of Williams series

nth term = a + (n – 1)d

Hence after 25 minutes both bags will have same weights.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2