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photoshop1234 [79]
3 years ago
12

Suppose that two people standing 2 miles apart both see the burst from a fireworks display. After a period of​ time, the first p

erson standing at point A hears the burst. Six seconds ​later, the second person standing at point B hears the burst. If the person at point B is due west of the person at point A and if the display is known to occur due north of the person at point​ A, where did the fireworks display​ occur? Note that sound travels at 1100 feet per second.

Mathematics
1 answer:
Usimov [2.4K]3 years ago
6 0

Answer: approximately 5148 feet directly north of point A

This is equivalent to 0.975 miles

==============================================================

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

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Answer:

20

Step-by-step explanation:

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40 times $16400= $656,000

Now, lets find how much money she had for the cheap calculators.

$774,000- $656,000=$118000

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Triangles ABD and ACE are similar right triangles. which ratio best explains why the slope of AB is the same as the slope of AC
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B. AC/EA = AB/DA because theyre equal slopes just different sizes
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3 years ago
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Emily needs enough Fabric for 3 1/2 hats. Since she has half a hat done. If each bag requires 1 2/7 ft of Fabric, how much fabri
kow [346]

first off let's convert the mixed fractions to improper fractions.

\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} ~\hfill \stackrel{mixed}{1\frac{2}{7}}\implies \cfrac{1\cdot 7+2}{7}\implies \stackrel{improper}{\cfrac{9}{7}}

she already did half a hat, so we can say   \cfrac{7}{2}-\cfrac{1}{2}\implies \cfrac{7-1}{2}\implies 3

so she only needs enough fabric to make 3 more full hats, we know each one uses 9/7 ft, so

3\cdot \cfrac{9}{7}\implies \cfrac{27}{7}\implies 3\frac{6}{7}

5 0
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Step-by-step explanation:

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6 0
2 years ago
Bubbles bakery has 24 oatmeal cookies, 36 vanilla bean cookies, 42 chocolate chip cookies. What is the greatest common factor bu
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Answer:6

Step-by-step explanation:

We have three groups of cookies as follows:

24   oatmeal

36   vanilla bean

42  chocolate chip

If we breack down into factors we get

24    2       24 = 2³ * 3        36    2   36 = 2²*3³         42   2   42 = 2*3*7

12     2                                 18    2                              21   3

6      2                                   9    3                                7   7

3      3                                   3    3                                1

1                                             1

Fom where we can get that biggest common factor is 6

24 ÷  6      =  4

36 ÷  6      =  6

42 ÷  6      =  7

Then Bakery will have  4 groups of oatmeal cookies, 6 of vanilla bean, and 7 chocolate chip

7 0
3 years ago
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