Answer:
Here's what I get.
Step-by-step explanation:
Assume the diagram is like the one below.
Segments AB, BC, and CH are transversals to the sides of the pool table.
BC is also a transversal to AB and CH.
a. Angles we can be sure about
∠ABC — interior opposite angles of transversal BC
∠CBH — interior opposite angles of transversal BC
∠BHC — interior angles of triangle BHC
∠ABK — alternate exterior angles of transversal BC
∠CHG — complementary to ∠CGH
b. Sets of congruent angles
∠ABC ≅ ∠BCH = 66° — interior opposite angles of transversal BC
∠CBH ≅ ∠BCE = 57° — interior opposite angles of transversal BC
∠BHC ≅ ∠GCH = 57° — interior opposite angles of transversal CH
∠ABK ≅ ∠GCH = 57° — alternate exterior angles of transversal BC
One set of congruent angles is {∠ABC, ∠BCH}
Another set is {∠ABK, ∠BCE, ∠BHC, ∠CBH, ∠GCH}
c. Alternate interior angles
Alternate interior angles are a pair of angles on the inner sides of the parallel lines but on opposite sides of the transversal.
The sets of alternate interior angles are {∠ABC, ∠BCH}, {∠ ABC, ∠BCD} {∠BCE, ∠CBH}, {∠CHJ, ∠GCH}
d. Corresponding angles
Corresponding angles are a pair of angles on the same side of parallel lines and on the same side of the transversal.
The diagram has no corresponding angles.
Using the washer method, the volume is given by the integral
where 3 - 1 = 2 is the distance from <em>y</em> = 3 to the axis of revolution, and similarly (1 + sec(<em>x</em>)) - 1 = sec(<em>x</em>) is the distance from <em>y</em> = 1 + sec(<em>x</em>) to the axis. The integrand is symmetric about <em>x</em> = 0, so the integral "folds" in on itself, and the integral from -π/3 to π/3 is twice the integral from 0 to π/3.
So the volume is
Answer:
$280 dollars
Step-by-step explanation:
When they were leaving
When they returned home, they brought 196 Euros.
They brought back $280 dollars to the United States.