Answers
Evaluating the piecewise function we will get:
g(-1) = -2
g(2) = 0
g(3) = 1/2
How to evaluate the piecewise function?To evaluate the piecewise function we need to use the correct part depending on the domains.
g(-1), here x = -1, then we need to use the second part of the function:
g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2
For the second one x = 2, we use the last part:
g(2) = (1/2)*2 - 1 = 0
For the last one, we have x = 3, again we need to use the last part:
g(3) = (1/2)*3 - 1 = 3/2 - 2/2 = 1/2
These are the 3 values.
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Related Questions
Two aircrafts travel from the position P(30°N, 130°W) to Q (50°N, 170°E) all leaving at 0845hrs and at the same speed of 500km/hr. Aircraft A travels due north to the position (50°N, 130°W) and then along a parallel of latitude using the shortest route. Aircraft B travels along a parallel of latitude (30°N, 170°E) and then due north.
(a) If a third aircraft C had left a point R (30°N, 10°W) at the same time as the two above aircrafts left P and flew via the shortest possible distance to point Q, calculate its position when the aircraft A was passing the longitude 180°W. (b) Calculate the arrival local time of the two aircrafts. (5mks) (5mks)
Answers
(a) The time taken by aircraft C to travel the distance from R to the longitude 180°W is 25.92 hours
(b) Since aircraft A departed at 08:45 hrs, the arrival time would be:
Arrival time is 13:14 hrs
Aircraft A would arrive at approximately 13:14 hrs, and aircraft B would arrive at approximately 21:01 hrs local time.
To calculate the position of aircraft C when aircraft A was passing the longitude 180°W, we need to determine the distance and direction between R (30°N, 10°W) and Q (50°N, 170°E) via the shortest route.
Distance between R and Q:
The latitude difference between R and Q is 50°N - 30°N = 20°. As each degree of latitude is approximately 111 km, the distance in terms of latitude is 20° × 111 km = 2,220 km.
The longitude difference between R and Q is 170°E - 10°W = 180°.
At the latitude of 40°N (midpoint between 30°N and 50°N), each degree of longitude is approximately cos(40°) × 111 km = 70.7 km.
The distance in terms of longitude is 180° × 70.7 km = 12,726 km.
Using the Pythagorean , the shortest distance between R and Q is:
Distance = √((2,220 km)² + (12,726 km)²)
≈ 12,960 km
Speed of aircraft C is 500 km/hr.
The time taken by aircraft C to travel the distance from R to the longitude 180°W is:
Time = Distance / Speed
= 12,960 km / 500 km/hr
≈ 25.92 hours
Since the aircraft A and aircraft C departed at the same time, when aircraft A was passing the longitude 180°W, aircraft C would also be at the same longitude, assuming they maintained a constant speed.
(b) To calculate the arrival local time of the two aircraft, we need to consider the time taken for each leg of their respective routes.
For aircraft A:
Distance from P to (50°N, 130°W) = (50°N - 30°N) × 111 km/degree
= 2,220 km
Time taken = Distance / Speed
= 2,220 km / 500 km/hr
= 4.44 hours
Since aircraft A departed at 08:45 hrs, the arrival time would be:
Arrival time = Departure time + Time taken
= 08:45 + 4.44 hours
≈ 13:14 hrs
For aircraft B:
Distance from (30°N, 170°E) to Q = (170°E - 130°W) × cos(40°) × 111 km/degree = 6,282 km
Time taken = Distance / Speed
= 6,282 km / 500 km/hr
= 12.564 hours
Since aircraft B departed at 08:45 hrs, the arrival time would be:
Arrival time = Departure time + Time taken
= 08:45 + 12.564 hours
≈ 21:01 hrs
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if 30 is divided by .06 the result is ? what are the steps to solve it by hand
Answers
Answer:
30/.06 =500
Step-by-step explanation:
30÷6/100
==>
30*100/6
=500
Camila has 6 bags of candy. She can pour 1/3 of a bag of candy into a bowl. How many bowls of candy can Camila make in all?
Answers
Answer:
18 Bowls of Candy
Step-by-step explanation:
Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.
Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.
Now, we can calculate the total number of bowls of candy:
Total bowls of candy = (Number of bags) x (Bowls per bag)
Total bowls of candy = 6 bags x 3 bowls per bag
Total bowls of candy = 18 bowls
Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.
help i have no clue what this is
Answers
The value of angle x is determined as 40 degrees.
The value of angle y is determined as 180 degrees.
What is the value of the missing angles?
The value of the missing angles is calculated by applying intersecting chord theorem which states that the angle at tangent is half of the arc angle of the two intersecting chords.
The value of angle x is calculated as follows;
50 = ¹/₂ (140 - x ) (exterior angle of intersecting secants)
2(50) = 140 - x
100 = 140 - x
x = 140 - 100
x = 40
The value of angle y is calculated as follows;
The value of angle y is equal to the value of the remaining arc.
y = 360 - (40 + 140 ) ( sum of angles in a circle)
Simplify further as follows;
y = 360 - 180
y = 180⁰
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Slope of Linear Equations
Which description best compares the graph given by the following equations:
5x-3y = -5
2x-y = 8
parallel
perpendicular
intersecting but not perpendicular
Answers
5x - 3y = -5
2x - y = 8
is "intersecting but not perpendicular."
Solve the system with elimination.
-2x + 7y =10
x - 3y = -3
Answers
Answer:
x = 9 and y = 4
Step-by-step explanation:
-2x + 7y = 10 (call this equation '1')
x - 3y = -3 (call this '2')
multiply '2' by 2:
2x - 6y = -6 (call this '3')
add '1' and '3':
(-2x + 7y = 10) + (2x - 6y = -6)
0x + y = 4
y = 4
sub that back into '1':
-2x + 7y = 10
-2x + 7(4) = 10
-2x + 28 = 10
-2x = 10 - 28 = -18
x = -18/-2 = 9
sub both y = 4 and x =9 into '2' to check if everything adds up:
x - 3y = -3
9 - 3(4) = 9 - 12 = -3
so x = 9 and y = 4
Calculate the area of the composite figure please help me with the total area and shape part especially the solve for area please
Answers
a. Shape 1 = 24cm²
Shape 2 = 14.1cm²]
Total area = 38.1cm²
b. Shape 1 = 50ft²
Shape 2 = 24ft²
Total area = 74ft²
How to determine the valuesThe formula for calculating area of a triangle is;
A = 1/2bh
Substitute the values
A = 1/2 × 8 × 6
Multiply the values
A = 24cm²
Area of a semicircle =3. 14 × 3²/2 = 14.1cm²
Total area = 38.1cm²
2. Area of the trapezoid is;
A = a +b/2h
A = 20/2(5) = 50ft²
Area of the triangle;
A = 1/2 × 6 × 8
A = 24ft²
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Which table was created using the equation y = 4x-1?
A
C
Input (x) Output (y)
3
11
4
15
27
31
35
39
5
6
7
8
Input (x) Output (y)
3
42
43
45
47
48
49
4
5
7
8
B
D
Input (x) Output (y)
3
11
15
19
23
27
31
4
5
6
7
8
Input (x) Output (y)
3
42
4
43
44
45
46
47
5
6
7
8
Answers
Answer:
Table B was created using the equation y = 4x-1.
Explanation:
The equation y = 4x-1 means that for any given value of x, the corresponding value of y can be found by multiplying x by 4 and then subtracting 1.
Table B shows input values of x and output values of y that are consistent with this equation. For example, when x = 3, y = 11 (4 * 3 - 1), and when x = 4, y = 15 (4 * 4 - 1), and so on.
Therefore, we can conclude that Table B was created using the equation y = 4x-1.
