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3 years ago

Simplify the following cube root

Mathematics

1 answer:

mariarad [96]3 years ago

5 0

Answer: 5 (square root) 30 over 12. (If you need help with math I suggest using an app called Photomath, I use it, it helps)

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Find the equation of a line passing through the points (3, -1) with the gradient M=2÷3

Anvisha [2.4K]

Answer:

y = $\frac{2}{3}$ x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = $\frac{2}{3}$ , thus

y = $\frac{2}{3}$ x + c ← is the partial equation

To find c substitute (3, - 1) into the partial equation

- 1 = 2 + c ⇒ c = - 1 - 2 = - 3

y = $\frac{2}{3}$ x - 3 ← equation of line

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

3 years ago

Mark spins a spinner 25 times. He spins a BLUE 12 times. How many times would he expect to get the color BLUE if he did 100 spin

lina2011 [118]

D. 48.
100 / 25 = 4
4 x 12 = 48 ! (:

8 0

3 years ago

Rewrite as a mixed number in lowest terms.

Alika [10]

Answer:

9 5/9 also 86/9

9 2/5 also 47/5

5 2/9 also 47/9

2 5/9 also 23/9

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Thanks

6 0

3 years ago

Combine like terms in the following expression:

bixtya [17]

Y+7x^2
If it isnt that then it is: y+7x^4
Hope I helped

4 0

4 years ago

Read 2 more answers

Simplify the following cube root​

Simplify the following cube root