Find the point in the first quadrant where the line y=4x intersects a circle of radius 4 centered at the origin.

point:

give exact values or give decimal values accurate to at least 3 decimal places

the point is : (1 ; 4 )

Step-by-step explanation:

an equation for this circle is : x²+y² = 16

you have the system : x²+y² = 16 (1)

                                      y = 4x (2)

Substitute y = 4x into (1) and solve for x :

x² + (4x)² = 16

x² +16x² = 16

17x² = 16

x² = 16/17

x = 4/√17   or x = - 4/√17 ( refused) because the point in the first quadrant where  : x ≥0

 x = 4/√17 ≅ 0.970

exact values or give decimal values accurate to at least 3 decimal places

is : x =1

Substitute  x = 1 into (2) : y =4    the point is : (1 ; 4 )

answer: given that the roller coaster can accommodate 1600 riders per hour, thus the roller coaster can accomodate 1600 / 60 = 26.67 riders per minute.

given that there are 345 people in the line, the number of minutes it will take for the 345 persons to get into the roller coaster is given by 345 / 26.67 = 12.94 minutes.

therefore, it will take you 12.94 minutes to get to the front of the line.

step-by-step explanation:

ruth is 6 years old

step-by-step explanation:

6 + 24 = 30,   so 6/30 = .2  

if you do 1/5 it also equals .2, so that is the answer.