Which of the following is an asymptote of y = csc(x)? x= -pi x=-pi/3 x=pi/4 x= pi/2

x = -π

Step-by-step explanation:

The asymptote occur when the y value does not exist.  We know that the y value doesnt exist when the denominator of a function equals zero.

csc(x) can be written as 1/sin(x)

So to find the asymptote we just need to know where sin(x) = 0, because it is illegal to divide by zero.  

sin(x) = 0 at 0, π, 2π, and so on

So an asymptote of the function would be pi times any whole number.  x=-π is the only answer that multiplied π by a whole number, so it is the only asymptote.

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.