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guajiro [1.7K]
2 years ago
5

An unknown radioactive element decays into non-radioactive substances. In 180 days the radioactivity of a sample decreases by 73

percent.
(a) What is the half-life of the element? (in days)
(b) How long will it take for a sample of 100 mg to decay to 60 mg? (in days)

Mathematics
1 answer:
BigorU [14]2 years ago
8 0

Answer:

  • half-life: 95.3 days
  • 60% life: 70.2 days

Step-by-step explanation:

a) The proportion remaining (p) after d days can be described by ...

  p = (1 -0.73)^(d/180) = 0.27^(d/180)

Then p=1/2 when ...

  0.50 = 0.27^(d/180)

  log(0.50) = (d/180)log(0.27)

  180(log(0.50)/log(0.27) = d ≈ 95.3

The half-life is about 95.3 days.

__

b) For the proportion remaining to be 60/100, we can use the same solution process. In the end, 0.50 will be replaced by 0.60, and we have ...

  d = 180(log(0.60)/log(0.27) ≈ 70.2 . . . days

60 mg will remain of a 100 mg sample after 70.2 days.

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2. Find the number of distinct triangles with c=11,b=7,B=18 a.0 b.1 c.2 d. cannot be determined
jok3333 [9.3K]
Answer: Choice C) 2

----------------------------------------------

Explanation:

Using the law of sines, we get
sin(B)/b = sin(C)/c
sin(18)/7 = sin(C)/11
0.0441452849107 = sin(C)/11
11*0.0441452849107 = sin(C)
0.4855981340177 = sin(C)
sin(C) = 0.4855981340177
C = arcsin(0.4855981340177) or C = 180-arcsin(0.4855981340177)
C = 29.0516679549861 or C = 150.948332045013
There are two possibilities for angle C because of something like sin(30) = sin(150) = 1/2 = 0.5

Those approximate values of C round to
C = 29.05 and C = 150.95

If C = 29.05, then angle A is
A = 180-B-C
A = 180-18-29.05
A = 132.95
Making this triangle possible since angle A is a positive number

If C = 150.95, then angle A is 
A = 180-B-C
A = 180-18-150.95
A = 11.05
making this triangle possible since angle A is a positive number

There are two distinct triangles that can be formed. 
One triangle is with the angles: A = 132.95, B = 18, C = 29.05
The other triangle is with the angles: A = 11.05, B = 18, C = 150.95
The decimal values are approximate
7 0
3 years ago
Parmesan cheese was on sale for $13.60 per pound. Wesley bought a piece of the Parmesan cheese that weighed 1 1/8 pounds. How mu
sweet [91]
He payed $15.30 is you divide 13.60 by 8 you get 1.70then you just add 13.60+1.70 because he also bought a pound
4 0
2 years ago
Read 2 more answers
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Alexandra [31]

Answer:

Step-by-step explanation:

1) Number of white chocolate bars = x

Number of dark chocolate bars = y

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x + y = 15 --------------(I)

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20x + 25y = 340 ----------------(II)

2)  We can use elimination method to solve this equations.

Multiply equation (I) by (-20) and then add the equations.

(I)* (-20)          -20x  -20y = - 300

(II)                    <u>20x + 25y = 340 </u>     {Now add and x will be eliminated}

                                  5y = 40

                                    y = 40/5

y = 8

Substitute y = 8 in equation (I)

x + 8 = 15

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4 0
3 years ago
12+98=<br> really confused on this one
kipiarov [429]

Answer:

12+98=110

Step-by-step explanation:

7 0
3 years ago
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F the radius of a flying disc is 7.6 centimeters, what is the approximate area of the disc?
hoa [83]

Answer:

3.14x7.6=23.864 because raidus is the disctance around  one circle

Step-by-step explanation:

8 0
3 years ago
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