Solve for x: 1.4x – 0.9 = 3.3

A student is deriving the quadratic formula. Her first two steps are shown. Step 1: –c = ax2 + bx Step 2: -c = a[x^2+b/ax] Which

marta [7]

Given choices:

(1) division property of equality

(2) factoring the binomial

(3)completing the square

(4)subtraction property of equality

Answer : (2) factoring the binomial

Step 1: $-c = ax^2 + bx$

Step 2: $-c = a[x^2+\frac{b}{a} x]$

In step 2, 'a' is taken out from $ax^2 + bx$ . when we take out 'a' we divide each term by 'a'. so it becomes $a[x^2+\frac{b}{a} x]$

'a' is factored out in step 2. we call it as factoring a binomial.

6 0

1 year 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

1 year ago

Mr. Lobo is building a fence rectangular around his rectangular yard. It is 16 feet long and 14 feet wide. How much feet of feet

lawyer [7]

Answer:

30

Step-by-step explanation:

14+16 1. Break it down 14 is equal to 10+4 16 is equal to 10+6 2. Add the biggest numbers together first 10+10 = 20 3. Add the smaller numbers together 6+4 = 10 4. Add all of the numbers together 20+10 = 30

4 0

2 years ago

Rewrite in polar form: x=12. I have r=12 sec theta

romanna [79]

To solve this problem you must apply the proccedure shown below:
1. You have to rewrite x=12 in polar form. Then, you have:
12=rCosθ
2. Then, you must solve for r, as following:
r=12/Cosθ
 3. You have that 1/Cosθ=Secθ, therefore:
 r=12(1/Cosθ)
 r=12Secθ
 Therefore, as you can see, the answer is: r=12Secθ

3 0

1 year ago

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Find the magnitude of wx for w(-3 5 4) and x(9 5 3)

Hatshy [7]

Answer: Magnitude of wx is $\sqrt{145}$