(Inscribed Angles)<br> Find m

Use the law of cosines to find the indicated missing side

max2010maxim [7]

Answer:

19.08

Step-by-step explanation:

c² = a² + b² - 2ab×cos(C)

a=10

b=22

C=60

cos(60) = 0.5

c² = 10² + 22² - 2×10×22×cos(60) =

= 100 + 484 - 20×22×0.5 = 584 - 20×11 = 584 - 220 =

= 364

c = sqrt(364) ≈ 19.08

7 0

3 years ago

What value of x makes this proportion true? 36/48 = x/24

ruslelena [56]

Answer:

18

Step-by-step explanation:

18/24 is a 1/2 reduction from 36/48.

3/4 is simplest form.

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,

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