Question 1155921


19.

Let first integer be {{{x}}}
Let second integer be {{{(x+1)}}}

if their product  is {{{42}}}, we have

{{{x(x+1)=42}}}

{{{x^2+x=42}}}

{{{x^2+x-42=0}}}..factor

{{{x^2+7x-6x-42=0}}}

{{{(x^2+7x)-(6x+42)=0}}}

{{{x(x+7)-6(x+7)=0}}}

{{{(x - 6) (x + 7) = 0}}}

=> solutions:

if {{{(x - 6) = 0}}}=>{{{x=6}}}
if {{{ (x + 7) = 0}}}=>{{{x=-7}}}-> disregard negative solution

so,  the two consecutive positive integers are

{{{x=6}}}
{{{x+1=7}}}



20.

the projectile height is modeled by the equation

{{{h=-16t^2+vt+s}}}

and can be written using metric units as

{{{h=-4.9t^2+vt+s}}} where the units are converted from feet to meters

so, using
 
{{{h=-4.9t^2+vt+s }}} ...plug in given {{{v=9.8 m/s}}} and {{{s=73.5m}}}, 

{{{h=-4.9t^2+9.8t+73.5 }}}

when the cannon ball reach sea level,{{{ h=0}}}

so,

{{{0 = -4.9t^2 + 9.8t + 73.5}}}

{{{0 = -4.9(t^2 - 2t - 15)}}}

{{{0 = -4.9(t - 5)(t + 3)}}}

solutions:

if {{{t - 5 = 0}}} =>{{{t=5}}}
 if {{{t + 3 = 0}}}=>{{{t=-3}}}

your solution will be:
{{{t = 5 }}}since{{{ t = -3}}} is not acceptable {{{negative}}} value 

Hence, the cannon ball will reach sea level at{{{ 5 }}}seconds.