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3 years ago

Find the slope and y-intercept of 3y - 4x = 39

Mathematics

2 answers:

Alisiya [41]3 years ago

8 0

Slope
4/3
Y- intercept:13

Alexus [3.1K]3 years ago

3 0

<h2>Greetings!</h2><h3>Firstly, the slope is found by rearranging the formula:</h3>

3y = 4x + 39

y = $\frac{4x}{3}$ + $\frac{39}{3}$

When x is 0, y = 0(x) + $\frac{39}{3}$ , so the y intercept is $\frac{39}{3}$

<h3>Next, the slope is simply the number in front of the x, </h3>

So $\frac{4x}{3}$ can be rearranged to $\frac{4}{3}x$ , so the slope would be $\frac{4}{3}$ .

<h2>Hope this helps!</h2>

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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,

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