On monday, harry had 75\%75% as many toys as teddy did. on tuesday, after harry acquired 3232 more toys and teddy acquired 15\%15% more than he had on monday, harry had as many toys as teddy did. how many toys did harry have on monday?

Let the number of toys Teddy has on Monday = x

On Monday Harry has = 75% of x or 0.75x

As given, On Tuesday, after Harry acquired 32 more toys and Teddy acquired 15% more than he had on Monday, Harry had as many toys as Teddy did.

Toys Teddy has =

= = 1.15x   .... (i)

Toys Harry has = 0.75x+32   ...... (ii)

As both have equal toys now, so equation (i) equals equation (ii)

x=80

Hence, Teddy had 80 toys on Monday.

And Harry had 75% of 80 toys = 60 toys on Monday.

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