Find the length of the segment ab if points a and b are the intersection points of the parabolas with equations y=−x^2+9 and y=2x^2−3 .

The length of the segment AB is √48

Step-by-step explanation:

Given the two equations, the idea is to find the solution to the system

y = x² + 9

y = 2x² - 3

you can use the equality method to find the "x" and "y" of the solution.

x² + 9 = 2x² - 3 ⇒ x² - 2x² = -3 - 9 ⇒ -x² = -12 ⇒ x² = 12 ⇒ x = ±√12.

With this value we return to the original equations and replace it to find "y" values.

y = (±√12)² + 9 ⇒ y = 21

The solutions to the system are (-√12, 21) and (√12, 21). Now you need to find the distance between this points.

d= √[(x2-x1)² + (y2-y1)²] ⇒ d = √48.

The length of the segment AB is √48.

24

step-by-step explanation:

the graph shows 30% of students walk. 80 students were questioned, so the number that said they walk is

30% × 80 = 0.30 × 80 = 24

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92