Step-by-step explanation:
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This is a value next to a variable what is it called
1 answer:
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Answer:
Giovanni was 0.5 miles from the finish line
Step-by-step explanation:
This is a problem of movement with constant velocity.
For this kind of problems, generally it is enough to remember the definition of average velocity v:
Where x is the change in position that took place in an interval t.
First, find the time that Jean, who cycled at 24 miles per hour, spent on the race:
Isolating t from the last equation,
, and replacing the data for Jean movement:
Second, find what was the distance that Giovanni had cycled when Jean crossed the line:
When Jean crossed the line he had cycled 120 miles, and Giovanni 119.5; so Giovanni was 0.5 miles from the finish line.
Answer: Line AC = 24 units and line BC = 12 units.
Step-by-step explanation: Please refer to the diagram attached for more details.
The right angled triangle ABC has been drawn with angle A measuring 30 degrees and line AB measuring 12√3. To calculate the other two unknown sides AC labelled b, and BC labelled a, we shall use the trigonometric ratios. However, in this scenario, we shall apply the special values of each trigonometric ratio. These are shown in the box on the top right in the picture. The proof is given in the second right angled triangle at the bottom part of the attached picture.
Assume an equilateral triangle with lengths 2 units on all sides and 60 degrees at all angles. Drawing a line perpendicular to the bottom line would divide the top angle into two equal halves (30 degrees each), and the bottom line also would be divided into two equal halves (1 unit each). So the hypotenuse will measure 2 units and the line at the base would measure 1 unit. By using the Pythagoras' theorem, we derive the third side to be √3 <u>(that is x² = 2² - 1², and then x² = 4 - 1, and then x² = 3 and finally x = √3).</u>
Therefore, in triangle ABC, using angle 30 as the reference angle, to calculate side AC;
Cos 30 = Adjacent/Hypotenuse
Cos 30 = (12√3)/b
b = (12√3)/Cos 30
Where Cos 30 is √3/2
b = (12√3)/√3/2
b = (12√3) * 2/√3
b = 12 * 2
b = 24
To calculate side BC;
Tan 30 = Opposite/Adjacent
Tan 30 = a/(12√3)
Tan 30 * 12√3 = a
Where Tan 30 = 1/√3
(1/√3) * 12√3 = a
12 = a
Therefore, the missing lengths in the right triangle are
AC = 24 units and BC = 12 units
