Chapter 1: Quadrati END-OF-CHAPTER REVIEW EXERCISE 1
1
A curve has equation y = 2xy+ 5 and a line has equation 2x + 5y = 1.
The curve and the line intersect at the points A and B. Find the coordinates of the midpoint
of the line AB

mid point of AB (0.5 , 0)

Step-by-step explanation:

2x + 5y = 1      2x = 1 - 5y

y = 2xy+ 5 = (1 - 5y)*y + 5 = y - 5y² + 5

y-y = y - 5y² + 5 - y = - 5y² + 5

0 = - 5y² + 5

5y² = 5

y² = 1

y = 1 or y = -1

if y = 1       x = 1/2 (1 - 5) = -2   .... point A (-2 , 1)

if y = -1      x = 1/2 (1 + 5) = 3   ..... point B (3 , -1)

mid point of AB (x' , y') :  x' = 1/2 (x₁ + x₂) = 1/2 (-2 + 3) = 1/2

                                        y' =  1/2 (y₁ + y₂) = 1/2 (-1 + 1) = 0    

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.