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Norma-Jean [14]

3 years ago

14

Find C round to the nearest tenth!!!! laws of sines!!!!! please help!

1 answer:

kiruha [24]3 years ago

3 0

Answer:

c =14.9 cm

Step-by-step explanation:

<C = 180 - (150 + 12)

<C = 180 - 162

<C = 18°

Law of sines:

sin (18) / c = sin(12) / 10

0.309 / c = 0.2079 / 10

c = 0.309 * 10 / 0.2079

c =14.9

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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

2 years ago

Solve this equation 3x + 5 = 7x – 7

Mama L [17]

Add 7 to both sides
3x + 12 = 7x
Subtract 3x
12 = 4x
Divide by 4
x = 3

4 0

3 years ago

Read 2 more answers

Help! What is the average rate of change of f(x)=x^2+3x+6 over the interval -3 less-than-or-equal-to x less-than-or-equal-to 3?

Makovka662 [10]

Answer:

The average rate of change of the function over the interval is 5.

Step-by-step explanation:

Average rate of change of a function:

The average rate of change of a function f(x) over an interval [a,b] is given by:

$A = \frac{f(b)-f(a)}{b-a}$

Interval -3 less-than-or-equal-to x less-than-or-equal-to 3

This means that $a = -3, b = 3$

$f(x) = x^2 + 3x + 6$

So

$f(b) = f(3) = (3)^2 + 3(3) + 6 = 9 + 9 + 6 = 24$

$f(a) = f(-3) = (-3)^2 + 3(-3) + 6 = 9 - 9 + 6 = 6$

Average rate of change

$A = \frac{f(b)-f(a)}{b-a} = \frac{24+6}{3-(-3)} = \frac{30}{6} = 5$

The average rate of change of the function over the interval is 5.

8 0

3 years ago

People use water to cook, clean, and drink every day. An estimate of 15.5% of the water used each

Studentka2010 [4]

Answer:

260 gallons

Step-by-step explanation:

An estimate of 26.5% of the water used each day is for cleaning and a family uses 68.9 gallons of water a day for cleaning,

Percentage of water used for cleaning= 26.5%

Gallons of water used for cleaning= 68.9

Let the number of gallons used everyday be represented by g. This will give:

26.5% of g = 68.9

26.5/100 × g = 68.9

0.265 × g = 68.9

0.265g = 68.9

Divide both side by 0.265

0.265g/0.265 = 68.9/0.265

g= 260

260 gallons of water are used everyday

5 0

3 years ago

Explanation please <br><br>thank you

GrogVix [38]

300 represents the initial value or the value that you started with.
1.15 is the rate that the function increases by over t (time)

8 0

3 years ago