7.) find the equation of the curve that passes through the point (4, 5) if its slope is given by the following equation.

Rearranging and integrating, you have

... y = ∫(4x-7)dx = 2x² -7x +c

Applying the boundary condition, you have

... 5 = 2·4² -7·4 +c

... 5 - 4 = c = 1

Then the equation of the curve is

... y = 2x² -7x +1

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

13cm

step-by-step explanation:

(apex)