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2 years ago

Which is the best approximation for the solution of the system of equations?

Mathematics

1 answer:

Olenka [21]2 years ago

4 0

Answer:

see explanation

Step-by-step explanation:

2. y=3x-2

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Pregnant women metabolize some drugs at a slower rate than the rest of the population. The half-life of caffeine is about 4 hour

UkoKoshka [18]

Answer:

Husband:

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Woman:

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

Step-by-step explanation:

The amount of caffeine in the body can be modeled by the following equation:

$C(t) = C(0)e^{rt}$

In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.

110 mg of caffeine at 8 am,

So $C(0) = 110$

Husband

Half life of 4 hours. So

$C(4) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{4r}$

$e^{4r} = 0.5$

Applying ln to both sides

$\ln{e^{4r}} = \ln{0.5}$

$4r = \ln{0.5}$

$r = \frac{\ln{0.5}}{4}$

$r = -0.1733$

So for the husband

$C(t) = 110e^{-0.1733t}$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.1733t}$

$C(11) = 110e^{-0.1733*11} = 16.35$

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Pregnant woman

Half life of 10 hours. So

$C(10) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{10}$

$e^{10r} = 0.5$

Applying ln to both sides

$\ln{e^{10r}} = \ln{0.5}$

$10r = \ln{0.5}$

$r = \frac{\ln{0.5}}{10}$

$r = -0.0693$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.0693t}$

$C(11) = 110e^{-0.0693*11} = 51.33$

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

7 0

3 years ago

Find a complex number a+ ????????????????, with aand ???????? positive real numbers, such that (a+ ????????????????)3 = i.

stepan [7]

Answer:

The complex number is 0+i/3.

Step-by-step explanation:

Let the imaginary part be x.

The complex number will be a+xi

Given:

real part =a

(a+xi)*3=i...............(i)

To find:

imaginary part

Solution:

3a + 3xi=i.............(ii)

Comparing real and imaginary parts of eq(ii).

3a=0 and 3x=1

a=0

x=1/3.

6 0

3 years ago

The game of roulette involves spinning a wheel with 38 slots: 18 red, 18 black, and 2 green. A ball is spun onto the wheel and w

Zigmanuir [339]

Answer:b

Step-by-step explanation:

8 0

3 years ago

CONVERT TO STANDARD FORM <br>7.43 x 10^5 <br>CONVERT TO SCIENTIFIC NOTATION <br>1,200,000,000

denis23 [38]

Answer:

743000

1.2×10^9

hope it helps;)

6 0

3 years ago

1: A square has an area of 144cm, What is the length of each side

agasfer [191]

1. Area of square = s*s
144=s*s
S=12 cm

2. Perimeter of a square=4*s
32=4s
S=32/4=8cm

3 0

3 years ago