The definition of the piece-wise function is:
.
<h3>What is a piece-wise function?</h3>
A piece-wise function is a function that has different definitions, depending on the input.
In this problem, for inputs between -2 and 2, the function is a line that goes through (-2,-4) and (2,6). The slope is:
m = (6 - (-4))/(2 - (-2)) = 2.5.
The y-intercept is of b = 1, hence the rule is:
For x greater than 2 and less than 6, the function is constant at -3, hence the rule is:
.
More can be learned about piece-wise functions at brainly.com/question/27262465
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Factors of 24: 1,2,3,4,6,8,12,24
factors of 30: 1,2,3,5,6,10,15,30
factors of 42: 1,2,3,6,14,21,42
Answer:
Step-by-step explanation:
Using the exact values of the given trig functions, then
sin45° × sin30° × cos60°
= 
× 
× =
Answer:
819
Step-by-step explanation:
Givens
Formula
Sum = a(1 - r^n) / ( 1 - r)
Sum = -1(1 - (-4)^6 / (1 - -4)
Sum = -1 (1 - 4096) / 5
Sum = -1 (- 4095 ) / 5
Sum = 819
Answer:
Step-by-step explanation:
Let the base camp is point A and boats' locations after two hours are points B and C.
By connecting the three points together we get a triangle ABC with sides:
- AB = 50*2 = 100 km
- AC = 70*2 = 140 km
The angle between AB and AC is:
- 60 + 50 = 110 degrees (opposite directions from south)
We are looking for the distance BC, which can be found by using the law of cosines:
- BC² = AB² + AC² - 2AB*AC*cos ∠BAC
- BC² = 100² + 140² - 2*100*140*cos 110°
- BC² = 39176.56 (rounded)
- BC = √39176.56 = 197.93 km (rounded)
The distance between the boats is 197.93 km.
