Question

Question #943a4

Answer 1

`d_m=(8*d_1*d_2)/(5*d_1+3*d_2)`

Explanation:

`m_1/m_2=3/5" "color(red)(m_1=3/5m_2)`
`d_1=m_1/v_1" "color(green)(v_1=m_1/d_1)" "color(green)(v_1)=(color(red)(3/5m_2))/(color(green)(d_1))`
`d_2=m_2/v_2" "color(blue)(v_2=m_2/d_2)`

`d_m=(color(red)(m_1)+m_2)/(v_1+v_2)" density equation for mixture"`

`d_m=(3/5m_2+m_2)/((3/5 m_2)/d_1+m_2/d_2)`

`d_m=(8m_2/5)/(((3/5m_2d_2)+m_2d_1)/(d_1*d_2))`

`d_m=(8m_2/5)/(((3m_2*d_2+5m_2*d_1))/(5d_1*d_2))`

`d_m=8 cancel(m_2)/cancel(5) *(cancel(5)*d_1*d_2)/(cancel(m_2)(3*d_2+5*d_1))`

`d_m=(8*d_1*d_2)/(5*d_1+3*d_2)`