Answer:
The expected mass of the sample in the year 2009 is approximately 60 miligrams.
Step-by-step explanation:
The mass of radioactive isotopes decays exponentially in time, the equation that represents this phenomenon is presented below:
[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex] (1)
Where:
[tex]m(t)[/tex] - Current mass of the radioactive isotope, in miligrams.
[tex]m_{o}[/tex] - Initial mass of the radioactive isotope, in miligrams.
[tex]t[/tex] - Time, in years.
[tex]\tau[/tex] - Time constant, in years.
First, we must find the time constant associated to the decay of the radioactive isotope by clearing the respective term in (1):
[tex]-\frac{t}{\tau} = \ln \frac{m(t)}{m_{o}}[/tex]
[tex]\tau = -\frac{t}{\ln \frac{m(t)}{m_{o}} }[/tex]
If we know that [tex]t = 5\,y[/tex], [tex]m(t) = 190\,mg[/tex] and [tex]m_{o} = 800\,mg[/tex], then the time constant is:
[tex]\tau = -\frac{t}{\ln \frac{m(t)}{m_{o}} }[/tex]
[tex]\tau = -\frac{5\,y}{\ln \frac{190\,mg}{800\,mg} }[/tex]
[tex]\tau \approx 3.478\,y[/tex]
Now, we calculate the mass of the radioactive isotope in 2009 ([tex]t = 9\,y[/tex]). If we know that [tex]t = 9\,y[/tex], [tex]\tau \approx 3.478\,y[/tex] and [tex]m_{o} = 800\,mg[/tex], then the mass of the radioactive isotope is:
[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex]
[tex]m(9\,y) = (800\,mg)\cdot e^{-\frac{9\,y}{3.478\,y} }[/tex]
[tex]m(9\,y) \approx 60.155\,mg[/tex]
The expected mass of the sample in the year 2009 is approximately 60 miligrams.
Look at this graph: What is the equation of the axis of symmetry?
9514 1404 393
Answer:
x = -6
Step-by-step explanation:
The curve is symmetrical about the vertical line through the minimum point. That minimum is 6 grid squares left of the y-axis, so the equation is ...
x = -6
In circle A as shown below, segment DC is tangent to circle A at D. Also, DC = 4 and BC = 2
Find the length of the radius of circle A
A. 3
B. 5
C. 6
D. 12
please help!!!
Answer:6
Step-by-step explanation:
for khan academy math please answer, thank you!
Answer:
7pi/theta = radius
Step-by-step explanation:
So we are using the arc length, central angle(in radians), and radius.
We know arc length, which is 7pi.
We don't know theta, which does not matter.
And finally, we don;t know radius, which is what we are looking for.
To find radius, we use:
arc length/theta=radius
Lets plug in our values:
7pi/theta=radius.
So the answer to the khan acadamy question is
7pi/∅
Here are some othr things that may help:
Radian * Radius = arc length
This solves for arc length
Here is another one:
Arc length/radius= radian
This solves for radians
Hope these help! :)
HELP asap now lol lorf
Answer:
[tex]22\ km[/tex]
Step-by-step explanation:
One is given the following information:
[tex]10\frac{1}{1}[/tex] km were covered on Thursday[tex]10\frac{1}{1}[/tex] km were covered on FridayOne is asked to find the total distance covered on both of these days. In order to do so, one must remember in a fraction, any number over (1) is equal to the numerator (number over the fraction bar). Thus one can form the following equation:
[tex](Thursday)+(Friday) = Total\ distance[/tex]
Substitute,
[tex](Thursday)+(Friday) = Total\ distance[/tex]
[tex](10\frac{1}{1})+(10\frac{1}{1}) = Total\ distance[/tex]
Simplify,
[tex](10\frac{1}{1})+(10\frac{1}{1}) = Total\ distance[/tex]
[tex](10+1)+(10+1) = Total\ distance[/tex]
[tex](11)+(11)=Total\ distance[/tex]
[tex]11+11=Total\ distance[/tex]
[tex]22=Total\ distance[/tex]
Find an expression which represents the sum of (-8x+7y)(−8x+7y) and (2x-2y)(2x−2y) in simplest terms.
Answer:
Step-by-step explanation:
(-8x+7y)(-8x+7y)+(2x-2y)(2x-2y)
=64x²-56xy-56xy+49y²+(4x²-4xy-4xy+4y²)
=64x²-112xy+49y²+4x²-8xy+4y²
=68x²-120xy+53y²
(x + 6)² + (y - 2)² = 100. What is the center of the circle? What is the radius of the circle?
Answer:
Step-by-step explanation:
"100" or any constant at the end of the equation is r² (radius squared). So, the radius is 10.
the center of the circle is (-6, 2)
the equation template of a circle is (x -h)² + (y - k)² = c
(h,k) is the center of the cirlce.
Mhanifa can answer this only
I don't understand
8x + 2y = 104
Is that possible, and if so, prove it pls
Mhanifa is the best user on Brainly
So, if I attract him, I will die
Answer:
Implicit Form: 4x + y - 52 = 0
Step-by-step explanation:
8x + 2y = 104 => Move constant to the left and change the sign
8x + 2y - 104 = 0 => Divide both sides of the equation by 2
4x + y - 52 = 0
Hope this helps!
Iva del 21% de 150=
Por favor diganme cuanto es
malia and her sister walk at a constant rate of 4 miles per hour how far can malia and her sister walk in 1.5 hours
please i need help now.
Can someone help me?
Answer:
0 h= 0 mi
1 h = 60 mi
2 h = 120 mi
3 h = 180 mi
Area of parts of circles
You might need: Calculator
2
Find the area of the semicircle.
Either enter an exact answer in terms of or use 3.14 for T and enter your answer as a decimal.
units
What do the three red tiles in the model of the equation below represent?
=
1
-3
3
ОООО
-Зх
Step-by-step explanation:
There are 3 times of -x
which means the total of those x
=
[tex]3 \times ( - x) \\ = - 3x[/tex]
Series:
Use the Arithmetic Series formula to calculate the sum:
-6+(-3)+0+ • • • + 162
(Hint: how many numbers are being added?)
Answer:
Step-by-step explanation:
The common difference is 3.
nth term = -6+(n-1)3
-6+(n-1)3 = 162
(n-1)3 = 168
n-1 = 56
n = 57
162 is the 57th term.
S₅₇ = 57×(a_1+a_{57})/2
= 57×(-6+162)/2
= 57×156/2
= 57×78
= 57×(-6+162)/2
= 4446
Please help with this question!!!!!
I keep getting this wrong. I got f(x)=1/2^x
Answer:
Try that....
[tex]f(x) = \frac{1}{ {5}^{x} } [/tex]
Step-by-step explanation:
I hope that is useful for you :)
A square mirror has an area of 25 square feet. How long is each edge of the mirror?
A running track has two semi-circular ends with radius 25m and two straights of length 87.6m as shown.
Calculate the total distance around the track rounded to 1 DP.
The total distance around the track is 332.2 meters
How to calculate the total distance?The complete question is in the attached image
The given parameters are:
Radius, r = 25 m
Length, l = 87.6 m
Start by calculating the circumference of the two semi-circular ends using:
[tex]C = 2\pi r[/tex]
So, we have:
C = 2* 3.14 * 25
Evaluate
C = 157
The total distance around the track is then calculated as:
Total = 2l + C
This gives
Total = 2 * 87.6 + 157
Evaluate
Total = 332.2
Hence, the total distance around the track is 332.2 meters
Read more about perimeter at:
https://brainly.com/question/24571594
#SPJ1
How many times larger is the value of 42.38 compared to 4.238
Answer:
10 times larger
Solve for x
2 (x + 1) = -200 x= 66
2x + (-3) = = (-23) x=
X - 3 = (-9) x=
(-3x) - 5 = 16 x=
-4 (y - 2) = 12 x=
4x = (-28) x=
2x + 9 = (-15) x=
X + 5 = 18
3 (x+ 5) = 18
3x + 5 = 18
2 (x + 5) = 16
3 (y + 200) = 3000
20.8 = 4 (z + 1.1)
3 (x + 4.5) = 36
9 = 3 (x + 2)
2x + 16 = 50
14 = 2 (x + 3)
5x + 2 = 17
Answer:
---------
Step-by-step explanation:
x-3= -9
x= -9/ 3
x= -3
( -3x)-5 =16
-3x = 16+5
×= 21/-3
x = -7
In ABC with the right angle at vertex C, sin(b)= (26)/8. What is sin(a)?
Answer:
We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts.
Step-by-step explanation:
Pythagorean theorem: a2 + b2 = c2.
Sines: sin A = a/c, sin B = b/c.
Cosines: cos A = b/c, cos B = a/c.
Tangents: tan A = a/b, tan B = b/a.
Which of the following is the surface area of the right cylinder below?
O A. 480pi units2
O B. 204pi units2
O c. 408pi units2
O D. 240pi units2
Answer:
The answer is D.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
there are 45 students In a class if 60% of them are girls and 40% of them are boys find the number of girls and boys
Answer:
27 girls and 18 boys
Step-by-step explanation:
you need to divide the 45 pupils into 60 and 40 percent to
use a ratio to compare this quantity 25mm : 2cm
What is the value of 3/4
Answer:
0.75
0.25 less than 1
Step-by-step explanation:
i dont get it
Answer:
0.75 is the answer
2 (-3x-4) >16
Solve the inquality for X
Answer:
x < -4
Step-by-step explanation:
2(-3x - 4) > 16
-6x - 8 > 16
-6x > 16 + 8
-6x > 24
-x > 4
x < -4
Answer:
x < -4
Step-by-step explanation:
2(-3x - 4) > 16
Distribute.
-6x - 8 > 16
Add 8 to both sides.
-6x > 24
Divide by -6. When dividing by a negative, flip the sign.
x < -4.
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
18/999
Step-by-step explanation:
Answer:
2/111 = 18/999
write an explicit formula for an, the nth term of the sequence 11,2,-7
Answer:
[tex]a_{n}[/tex] = 20 - 9n
Step-by-step explanation:
There is a common difference d between consecutive terms, that is
d = 2 - 11 = - 7 - 2 = - 9
This indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 11 and d = - 9 , then
[tex]a_{n}[/tex] = 11 - 9(n - 1) = 11 - 9n + 9 = 20 - 9n
What’s the answer for this question
Answer:
dvdvsdv
Step-by-step explanation:
dsvfvdfvdv
A drawing of a house is 8.5 inches tall. Enter the height of the house in feet.
HELP PLSSSS I REALLY APPRECIATE IT!
Answer:
.70833
Step-by-step explanation:
Divide 8.5 by 12 since there are 12 inches in 1 foot
Answer:
.71 feet
Step-by-step explanation:
If you need an explanation then let me know in comments
plss help i’ll give brainliest thank you!
Answer:
p
Step-by-step explanation:
Absolute value cancels negative so the greatest would be P.
have a nice day and i hope this helps! <3