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3 years ago

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