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Answer: approximately 5148 feet directly north of point A
This is equivalent to 0.975 miles
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Explanation:
Check out figure 1 (attached image below) to see how the drawing is set up.
Points A and B are separated by 2 miles, or 10560 feet. Use the conversion factor 1 mile = 5280 feet.
Because sound travels at roughly 1100 feet per second (assuming all of the conditions are right), this means that after x seconds, the sound wave has traveled a total distance of 1100x feet. This is the distance from A to C. Point C is the firework location.
The distance from B to C is 1100(x+6) feet because it takes 6 more seconds for the soundwave to travel from C to B, compared from C to A.
Note that triangle ABC is a right triangle. The 90 degree angle is at point A.
We can use the pythagorean theorem to solve for x
See figure 2 in the attached images to see the steps on solving for x. The numbers get quite big, though in the end x is fairly small. We end up with x = 4.68, which is approximate due to the 1100 figure being approximate.
This means the sound wave takes about 4.68 seconds to go from point C to point A.
With this x value, we can compute the expression 1100x to get
1100*x = 1100*4.68 = 5,148 feet
To convert this to miles, divide by 5280
(5148)/(5280) = 0.975
Therefore,
5148 feet = 0.975 miles
Answer:
see explanation
Step-by-step explanation:
The figure shown has one pair of parallel sides and is a trapezium
The area (A) of a trapezium is calculated using
A = h(a + b)
where h is the height and a, b the length of the parallel sides
here h = 2w, a = w + 3 and b = 4w - 2, hence
A = × 2w(w + 3 + 4w - 2)
= w(5w + 1) = 5w² + w
<h3>Answer: (-3, 0)</h3>
Explanation:
Point N is at (1,3)
We apply the rule which will translate the point 4 units to the left and 3 units down.
The old x coordinate x = 1 becomes x-4 = 1-4 = -3
The old y coordinate y = 3 becomes y-3 = 3-3 = 0
The point N(1,3) moves to N ' (-3, 0)