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ruslelena [56]
3 years ago
10

Helppp meeee pleaseeee

Mathematics
1 answer:
borishaifa [10]3 years ago
7 0

Answer:

I'm not sure on how to help you if you need to graph the points but I would say the answers to each letter would be having letter A as (-4, 1). B as on the grid. C as (-4, -2) then just graph (-4, -2) and you're all set!

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After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is modelled by the function C(t)=8(e
Alexxx [7]

Answer:

the maximum concentration of the antibiotic during the first 12 hours is 1.185 \mu g/mL at t= 2 hours.

Step-by-step explanation:

We are given the following information:

After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is modeled by the function where the time t is measured in hours and C is measured in \mu g/mL

C(t) = 8(e^{(-0.4t)}-e^{(-0.6t)})

Thus, we are given the time interval [0,12] for t.

  • We can apply the first derivative test, to know the absolute maximum value because we have a closed interval for t.
  • The first derivative test focusing on a particular point. If the function switches or changes from increasing to decreasing at the point, then the function will achieve a highest value at that point.

First, we differentiate C(t) with respect to t, to get,

\frac{d(C(t))}{dt} = 8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)})

Equating the first derivative to zero, we get,

\frac{d(C(t))}{dt} = 0\\\\8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)}) = 0

Solving, we get,

8(-0.4e^{(-0.4t)}+ 0.6e^{(-0.6t)}) = 0\\\displaystyle\frac{e^{-0.4}}{e^{-0.6}} = \frac{0.6}{0.4}\\\\e^{0.2t} = 1.5\\\\t = \frac{ln(1.5)}{0.2}\\\\t \approx 2

At t = 0

C(0) = 8(e^{(0)}-e^{(0)}) = 0

At t = 2

C(2) = 8(e^{(-0.8)}-e^{(-1.2)}) = 1.185

At t = 12

C(12) = 8(e^{(-4.8)}-e^{(-7.2)}) = 0.059

Thus, the maximum concentration of the antibiotic during the first 12 hours is 1.185 \mu g/mL at t= 2 hours.

4 0
3 years ago
The quotient of a number p and 3 is at most 16.
serg [7]
"the quotient of a number p and 3 is at most 16"
the number is p
"the quotient of a number p and 3" is just like saying
3/p
"is at most 16" is 
\leq 16
add them together to get
\frac{3}{p}  \leq 16
multiply both sides by p to get
3 \leq 16p
divide both sides by 16 to get
p \leq  \frac{3}{16}
6 0
4 years ago
-4y=-20x+40<br> y+10=5x
mart [117]

Answer:

infinitely many solutions

Step-by-step explanation:

We want to find solution to the system:

-4y=-20x+40

y+10=5x

We make y the subject in the second equation to get;

y=5x-10

We substitute y=5x-10 into the top equation to get:

- 4(5x - 10) =  - 20x + 40

We expand to obtain;

- 20x  + 40=  - 20x + 40

This implies that:

40 = 40

Therefore the system has infinitely many solutions.

8 0
4 years ago
15 added to the product of 13 times 2
snow_tiger [21]

Answer: 41

Step-by-step explanation:

Product would be the answer to a multiplication equation. So the product of 13 times 2 would be 26. Then you add 15 to the product.

So the answer is 41

13x2=26

26+15=41

5 0
3 years ago
Read 2 more answers
HELP ASAP!!! I’m very confused and need help. I WILL MARK BRAINLIST!!!!
iren [92.7K]

Step-by-step explanation:

In ∆PQR and ∆TSU

\because\begin{cases}PQ\approx TS \\ QR\approx TU \angle \\ Q\approx \angle T\end{cases}

\therefore{∆PQR\approx ∆TSU(\because SAS)}

And

  • <Q is greater than <T
  • So SU will be less than PR(22cm)
5 0
3 years ago
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