Answer:
There are 3,628,800 different ways for the runners to finish.
Step-by-step explanation:
Arrangments of x elements:
The number of possible arrangments of x elements is given by the following formula:
In this question:
10 different runners, which means that the number of different ways that there are for the runners to finish is an arrangment of 10 elements. So
There are 3,628,800 different ways for the runners to finish.
Answer:
x = π/2 + πk
Step-by-step explanation:
cot² x csc² x + 2 csc² x − cot² x = 2
Multiply both sides by sin² x:
cot² x + 2 − cos² x = 2 sin² x
Add cos² x to both sides:
cot² x + 2 = 2 sin² x + cos² x
Pythagorean identity:
cot² x + 2 = sin² x + 1
Subtract 1 from both sides:
cot² x + 1 = sin² x
Pythagorean identity:
csc² x = sin² x
Multiply both sides by sin² x:
1 = sin⁴ x
Take the fourth root:
sin x = ±1
Solve for x:
x = π/2 + 2πk, 3π/2 + 2πk
Which simplifies to:
x = π/2 + πk
Answer:
(x, g(x)) = {(-2, -2), (0, 0), (2, 2), (4, -3), (6, -3)}
Step-by-step explanation:
The first three values of x in the table are all less than or equal to 2, so the first part of the function definition applies. The y-value is equal to the x-value. The ordered pairs are ...
(-2, -2), (0, 0), (2, 2)
The last two values of x in the table are more than 2, so the last part of the function definition applies. For those values of x, the y-value is -3. The ordered pairs are ...
(4, -3), (6, -3)
Answer:
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