All categories

3 years ago

How to solve. -3(4r-8)= -36

Mathematics

1 answer:

maks197457 [2]3 years ago

8 0

$-3(4r-8)=-36 \\ \\ (-3*4r)+(-3*-8)=-36 \\ \\ -12r+24=-36 \\ \\ -12r=-60 \\ \\ r=5$

You might be interested in

1. A baseball pitcher has pitched 12 2/3 innings.

bagirrra123 [75]

What is the rest of the question?

8 0

2 years ago

* 1. Find the two roots X7 and x2 of the quadratic equation x2 – 8x + 12 = 0. Enter y

dezoksy [38]

9514 1404 393

Answer:

x = 2, x = 6

Step-by-step explanation:

The quadratic can be factored as ...

x^2 -8x +12 = 0

(x -2)(x -6) = 0

Solutions are the values of x that make these factors zero:

x -2 = 0 ⇒ x = 2

x -6 = 0 ⇒ x = 6

8 0

2 years ago

This is an easy question for people who want points

Valentin [98]

Answer:

5.33 or 5 $\frac{1}{3}$

Step-by-step explanation:

Assuming you don't want the answer in decimals, this is the process to find the answer in fractions:

1 $\frac{2}{5}$ + (3 $\frac{1}{3}$ + $\frac{3}{5}$ )

= $\frac{7}{5}$ + $\frac{10}{3}$ + $\frac{3}{5}$ → convert into mixed fractions

= $\frac{21}{15}$ + $\frac{50}{15}$ + $\frac{9}{15}$ → find the least common denominator to make them the same

= $\frac{80}{15}$ = 5 $\frac{5}{15}$ = 5 $\frac{1}{3}$ → = add and simplify

4 0

3 years ago

We measure temperature using a scale that has both positive and negative numbers. On the Celsius

Vadim26 [7]

Answer:

22 degrees

Step-by-step explanation:

3 0

3 years ago

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

2 years ago