Last question I have

The half-life of a certain tranquilizer in the bloodstream is 22 hours. How long will it take for the drug to decay to 90% of

nasty-shy [4]

Answer:

It will take approximately 3.34 hours for the drug to decay to 90% of the original dosage

Step-by-step explanation:

As suggested, we use the formula for exponential decay:

$A(t)=A_0\,e^{-k\,t}$

From the given information, the half life of the drug in blood id 22 hours, so that means that it takes that number of hours to go from the initial value $A_0$ , to a final value equal to $A_0/2$ . Using this information we can find the decay rate "k" by solving for this parameter in the formula, and using the natural log function to bring the exponent down:

$A(t)=A_0\,e^{-k\,t}\\\frac{A_0}{2} =A_0\,e^{-k\,*22}\\\frac{A_0}{A_0*2} =e^{-k\,*22}\\\frac{1}{2} =e^{-k\,*22}\\ln(\frac{1}{2})=-k\,*22\\ k=-\frac{ln(\frac{1}{2})}{22} \\k=0.0315$

Now we use this value for the decay rate "k" to calculate how long it would take to decay to 90% of the original dose;

$A(t)=A_0\,e^{-0.0315\,t}\\0.9*A_0} =A_0\,e^{-0.0315\,t}\\\frac{0.9*A_0}{A_0} =e^{-0.0315\,t}\\0.9 =e^{-0.0315\,t}\\ln(0.9)=-0.0315\,t\\ t=-\frac{ln(0.9)}{0.0315} \\t=3.3447\,hours$

7 0

2 years ago

Solve the following system of equations by the substitution method. 2x = 10y - 8 3x + 4y + 5 = 0

Natali [406]

Answer:

x = $-\frac{41}{19}$

y = $\frac{7}{19}$

Step-by-step explanation:

2x = 10y - 8

3x + 4y + 5 = 0

2x = 10y - 8

x = 5y - 4

3x + 4y + 5 = 0

3 ( 5y - 4 ) + 4y + 5 = 0

19y - 7 = 0

19y = 7

y = $\frac{7}{19}$

x = 5y - 4

x = 5 ( $\frac{7}{19}$ ) - 4

x = $-\frac{41}{19}$

5 0

2 years ago

Please help!! law of sines and cosines related

pickupchik [31]

Answer:

as below

Step-by-step explanation:

to find the height of the pole recall the relationship of sin cos and tan to the triangle with this helpful mnemonic SOH CAH TOA

Sin = Opp / Hyp

Cos = Adj / Hyp

Tan = Opp / Adj

we will need to solve two triangles and subtract them.

one is the 15° one of the slope of the road and the other is the 57° one that is the angle of the sun. sooooo,

lets solve the 15° one first. We are told that the adj side is 75'

since we know the angle and the adj side and we want to find the Opp side let's use Tan b/c it has all of those in it :)

Tan(15) = Opp / 75

75*Tan(15) = Opp ( I'll put my calculator to work for this )

20.096 = Opp

that's the height of the road to the bottom of the flag pole along that flag pole axis into the ground

next lets solve the 57° triangle in the exact same way

Tan(57) =Opp / 75

75*Tan(57) = Opp

115.4898 = Opp

the tall triangle is the one that goes all the way into the ground, the small one is the one that is under the ground

so subtract the small one from the big one to find the height of the flag pole above the ground

115.4898-20.096 = 95.3938

so the flag pole is about 95.4 feet tall

:o that's pretty tall :

4 0

2 years ago

10 poin

BartSMP [9]

Add Four on both sides

6 0

2 years ago

Read 2 more answers

Samantha soends 45 minutes at the gym for 6 days a week. how many hours does she spend at the gym

Alexxx [7]

45 minutes * 6 days = 270 minutes at the gum

but we need to change minutes to hours

1 hours = 60 minutes

270 minutes * 1 hr/60 minutes =

270/60 hours

divide top and bottom by 10

27/6

divide top and bottom by 3

9/2

4.5 hours

7 0

2 years ago

Last question I have ​

Last question I have