Answer:
cot theta = -√3
Step-by-step explanation:
we are given that cos theta = - √3/2 within the range 180° < theta < 270° and
since cos theta = adj/hyp
adj = - √3
hyp = 2
Get the opposite using the pythagoras theorem
hyp^2 = opp^2 + adj^2
2² = opp² + (-√3)²
4 = opp² + 3
opp² = 4-3
opp² = 1
opp = 1
tan theta = opp/adj
tan theta = - 1/√3
Recall that cot theta = 1/tan theta
cot theta = 1/(-1/√3)
cot theta = -√3
Answer:
-5.875
Step-by-step explanation:
To check if a piecewise defined function is continuous, you need to check how the pieces "glue" together when you step from one domain to the other.
So, the question is: what happens at x=3? If you reach x=3 from values slightly smaller than 3, you obey the rule f(x)=log(3x). So, as you approach 3, you get values closer and closer to

Similarly, if you reach x=3 from values slightly greater than 3, you obey the rule f(x)=(4-x)log(9). So, as you approach 3, you get values closer and closer to

So, the function is continuous at x=3, because both pieces approach log(9) as x approaches 3.
I think it would be the first answer.
Cheetah ran 300 feet in 2.92 seconds.
Average speed in miles per hour.
Converting 300 feet to mile.
5280 feet = 1 mile
1 feet = (1/5280) mile
300 feet = (1/5280) * 300 = (300/5280) = (30/528) = (10/176) mile.
2.92 seconds to hour.
3600 seconds = 1 hour
1 second = (1/3600) hour
2.92 seconds = 2.92 * (1/3600) = (2.92/3600) hour.
Speed of Cheetah in miles per hour = (10/176) mile / (2.92/3600) hour
= 70.05 miles/hour