Two hundred liters of a 75% acid solution is obtained by mixing a 90% solution with a 50% solution. how many liters of each?

There would be 125 liters of 90% solution and 75 liters of 50% solution.

Step-by-step explanation:

Let x represent 90% of solution and y represent 50% of solution.

We have been given that there is 200 liters of the solution. We can represent this information in an equation as:  

We are also told that two hundred liters of a 75% acid solution is obtained by mixing a 90% solution with a 50% solution. We can represent this information in an equation as:  

From equation (1), we will get:

Upon substituting this value in equation (2), we will get:

Let us solve for x.

Therefore, there would be 125 liters of 90% solution.

Upon substituting in equation (1), we will get:

Therefore, there would be 55 liters of 50% solution.

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

7,24

step-by-step explanation: