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2 years ago

If 1 ƒ (x) = 3x + 5/x, what is f(a + 2)?

Mathematics

1 answer:

Nina [5.8K]2 years ago

6 0

Answer: $3a+6+\frac{5}[a+2}$

Step-by-step explanation:

$f(a+2)=3(a+2)+\frac{5}{a+2}=3a+6+\frac{5}[a+2}$

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Solve for y<br> 220-y = 29

Veseljchak [2.6K]

Answer:

y = 191

Have a great day :)

Hope this helps !

5INGH

Step-by-step explanation:

220 - y = 29

( - 220 from both sides )

- y = - 191

( × -1 on both sides )

y = 191

6 0

3 years ago

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How write an equation a graph

Lunna [17]

Answer:

So what we need to do to write the equation is to know our slope or rate of change and to know our initial value or where the line is touching the y axis the y intercept.

5 0

3 years ago

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A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like

mixas84 [53]

Answer:

a) $\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) $\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) the steady state mass of the drug is 2000 mg

d) t ≅ 153.51 minutes

Step-by-step explanation:

From the given information;

At time t= 0

an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500

The inflow rate is 0.06 L/min.

Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.

The objective of the question is to calculate the following :

a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.

From above information given :

$Rate _{(in)}= 500 \ mg/L \times 0.06 \ L/min = 30 mg/min$

$Rate _{(out)}=\dfrac{x}{4} \ mg/L \times 0.06 \ L/min = 0.015x \ mg/min$

Therefore;

$\dfrac{dx}{dt} = Rate_{(in)} - Rate_{(out)}$

with respect to x(0) = 0

$\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}$

b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.

$\dfrac{dx}{dt} = -0.015(x - 2000)$

$\dfrac{dx}{(x - 2000)} = -0.015 \times dt$

By Using Integration Method:

$ln(x - 2000) = -0.015t + C$

$x -2000 = Ce^{(-0.015t)$

$x = 2000 + Ce^{(-0.015t)}$

However; if x(0) = 0 ;

Then

C = -2000

Therefore

$\mathbf{x = 2000 - 2000e^{-0.015t}}$

c) What is the steady-state mass of the drug in the blood?

the steady-state mass of the drug in the blood when t = infinity

$\mathbf{x = 2000 - 2000e^{-0.015 \times \infty }}$

x = 2000 - 0

x = 2000

Thus; the steady state mass of the drug is 2000 mg

d) After how many minutes does the drug mass reach 90% of its stead-state level?

After 90% of its steady state level; the mas of the drug is 90% × 2000

= 0.9 × 2000

= 1800

Hence;

$\mathbf{1800 = 2000 - 2000e^{(-0.015t)}}$

$0.1 = e^{(-0.015t)$

$ln(0.1) = -0.015t$

$t = -\dfrac{In(0.1)}{0.015}$

t = 153.5056729

t ≅ 153.51 minutes

4 0

3 years ago

Burka [1]

Answer:

Step-by-step explanation:

$F \alpha \frac{1}{d^{2} }$

$F = \frac{K}{d^{2} }$

When F = 18; d = 2

$18 = \frac{K}{2^{2} }$

$18 = \frac{K}{4}$

Cross multiply;

18 x 4 = K

72 = K

There the equation connecting F and $d^{2}$ is

$F = \frac{72}{d}$

Now, Find F when d = 6

All you do is to substitute d = 6 in to $F = \frac{72}{d}$

$F = \frac{72}{6}$

Therefore;

F = 12

Please mark me brainiest if correct.

6 0

3 years ago

Find the missing side.<br><br> Need help please.<br> I need explanation for the answer please

DochEvi [55]

Answer:

x ≈ 11.1

Step-by-step explanation:

Using the sine ratio in the right triangle

sin59° = $\frac{opposite}{hypotenuse}$ = $\frac{x}{13}$ ( multiply both sides by 13 )

13 × sin59° = x , then

x ≈ 11.1 ( to the nearest tenth )

6 0

3 years ago

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