Consider the inequality cos(2x)<0; period [0,5π4). Milan wants to find the solution set for the inequality. She begins by finding the zeros for cos(2x):x=π4, x=3π4 , and x=5π4. Then, she studies the intervals (0,π4), (π4,3π4), and (3π4,5π4), and determines where cos(2x)<0 or cos(2x)>0 by picking a value for x from each interval. She finds the following. cos(2x)>0 from 0 to π4 cos(2x)<0 from π4 to 3π4 cos(2x)>0 from 3π4 to 5π4 Finally, Milan concludes that cos(2x)<0 on the interval [π4,3π4]. Part A: Which answer choice shows the correct analysis of Milan’s work? Part B: What is the domain of the inequality? Part C: What is the solution set for the inequality?

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.