Find the missing side of the triangle

Mathematics

1 answer:

slamgirl [31]2 years ago

4 0

Answer:

the answer would be 11.62

Step-by-step explanation:

16^2 -11^2= 11.62^2

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Solve the equations

Minchanka [31]

Answer:

#1 - All real numbers are solutions.

#2 - All real numbers are solutions.

Step-by-step explanation:

#1 -

Let's solve your equation step-by-step.

12(6t−4)=3t−2

Step 1: Simplify both sides of the equation.

12(6t−4)=3t−2

(12)(6t)+(12)(−4)=3t+−2(Distribute)

3t+−2=3t+−2

3t−2=3t−2

Step 2: Subtract 3t from both sides.

3t−2−3t=3t−2−3t

−2=−2

Step 3: Add 2 to both sides.

−2+2=−2+2

0=0

Same for #2

8 0

2 years ago

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,

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