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USPshnik [31]
3 years ago
10

An extremely large sink hole has opened up in a field just outside of the city limits. It is difficult to measure across the sin

k hole without falling in so you use congruent triangles. You have one piece of rope that is 50 ft. long and another that is 70 ft. long. You pick a point "A" on one side of the sink hole and "B" on the other side. You tie a rope to each spot and pull the rope out diagonally back away from the sink hole so that the two ropes meet at point "C" . Then you recreate the same triangle by using the distance from line "AC" and line "BC" and creating new segments CE and CD . The distance of line "DE" is 52.2 ft. 
What is the measure of angle ACB?

*I editted it because I realized I messed up a few things whoops

Mathematics
1 answer:
abruzzese [7]3 years ago
5 0
Triangle ABC and triangle DCE are congruent, so line DE = line AB

Use the cosine rule to find angle ACB
52.2^{2}= 50^{2}+  70^{2}-(2*50*70*cos(ACB))
2724.84=7400-(7000cos(ACB))
2724.84-7400=-7000cos(ACB)
-4675.16=-7000cos(ACB)
\frac{4675.16}{7000}=cos(ACB)
Angle ACB= cos^{-1} ( \frac{4675.16}{7000})
Angle ACB = 48.1°

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A Geiger counter registers a count rate of 7,600 counts per minute from a sample of a radioisotope. Eighteen minutes later, the
ra1l [238]

Answer:

9 minutes is the half life of the radioisotope.

Step-by-step explanation:

Given;

initial count rate = 7,600 counts per minute

final count rate = 1,900 counts per minute

elapsed time, t = 18 minutes

The half life of the radioisotope is calculated as;

       Time (half life) --------------------------remaining count rate

                     0  ------------------------------7,600 counts per minute

                      x ------------------------------3,800 counts per minute

                     2x----------------------------- 1,900 counts per minute

thus, 2x = 18 minutes

x = 18 / 2

x = 9 minutes

Therefore, 9 minutes is the half life of the radioisotope.

6 0
3 years ago
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Deffense [45]
<span>Luis has 5 cans of soda. He will buy more cans of soda from the store. The store has 12 cases in stock and each case contains 24 cans of soda. The store will not sell partial cases. The function that models the number of cans Luis will have after his purchase is f(c) = 24c + 5.

What is the practical domain and range of the function? 

5 is the initial number of cans Luis has on hand.  To this 5 we add 24 times c, where c represents the # of cases (not cans).   Thus, if he buys 1 case, he will have 5+24(1), or 29, cans on hand.

c represents the number of cases he buys.  He cannot buy a neg. number of cases, altho he could theoretically buy 0 cases by not going to the store.

Thus, the domain is {integers only, ranging from 1 to infinity}

The smallest number of cans this guy would have is 5, so the range is

{integers from 5 up}</span>
4 0
2 years ago
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Helga [31]

Answer:

-2

Step-by-step explanation:

To find the rate of change of a function, we are looking for it's slope.

We can find the slope of a line by seeing it's rise over run.

Basically - how much the line's y increases divided by how much the line's x increases.

We can see that the y drops from 1 to -1 in 1 x value. This means the change in y is 1 - (-1) = 2, however in this case it is -2 as we are dropping.

The change in x is 1 .

This means that the slope (rate of change) is \frac{-2}{1} = -2.

Hope this helped!

7 0
3 years ago
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BlackZzzverrR [31]

Answer:

he makes $112.50

Step-by-step explanation:

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8 0
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Volume of cube = L^3 
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4 0
3 years ago
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