All categories

2 years ago

Can someone help me on question 14. Please show steps

Mathematics

1 answer:

zavuch27 [327]2 years ago

5 0

Answer:

$0.5a+7.5b^2$

Step-by-step explanation:

$4b^2+3.5a-2a+3.5b^2-a$

Group similar terms together:

$3.5a-2a-a+4b^2+3.5b^2$

Add the term $b^2$ :

$3.5a-2a-a+7.5b^2$

Subtract the term a:

$0.5a+7.5b^2$

You might be interested in

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

What is the value of h in the figure below? In this diagram BAD~CBD

liberstina [14]

Answer:

The correct option is E. 8

The value of h is 8 unit.

Step-by-step explanation:

Given:

Δ BAD ~ Δ CBD

AC = 20

DC = 4

∴ $AD = AC - DC=20-4=16$

To Find:

h = ?

Solution:

Δ BAD ~ Δ CBD ................Given

If two triangles are similar then their sides are in proportion.

$\frac{BD}{CD} =\frac{AD}{BD} =\frac{BA}{CB}\ \textrm{corresponding sides of similar triangles are in proportion}\\$

On substituting the given values we get

$\dfrac{BD}{CD} =\dfrac{AD}{BD}$

$\dfrac{h}{4} =\dfrac{16}{h}\\\therefore h^{2}=64\\\therefore h=8\ unit$

The value of h is 8 unit.

8 0

2 years ago

Read 2 more answers

PROBLEM SOLVING Scientists conducted aerial surveys of a seal sanctuary and recorded the number x of seals they observed during

Akimi4 [234]

Answer:

Probability that at most 50 seals were observed during a randomly chosen survey is 0.0516.

Step-by-step explanation:

We are given that Scientists conducted aerial surveys of a seal sanctuary and recorded the number x of seals they observed during each survey.

The numbers of seals observed were normally distributed with a mean of 73 seals and a standard deviation of 14.1 seals.

Let X = numbers of seals observed

The z score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean numbers of seals = 73

$\sigma$ = standard deviation = 14.1

Now, the probability that at most 50 seals were observed during a randomly chosen survey is given by = P(X $\leq$ 50 seals)

P(X $\leq$ 50) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{50-73}{14.1}$ ) = P(Z $\leq$ -1.63) = 1 - P(Z < 1.63)

= 1 - 0.94845 = 0.0516

The above probability is calculated by looking at the value of x = 1.63 in the z table which has an area of 0.94845.

4 0

2 years ago

FWML is a parallelogram. Find the values of x and y. Solve for the value of z, if z=x−y.

Ganezh [65]

Answer:

x = 5, y = 8, z = -3

Step-by-step explanation:

Opposite sides of a parallelogram are congruent so to find x:

x + 7 = 3x - 3

-2x = -10

x = 5

To find y:

y + 2 = 2y - 6

-y = -8

y = 8

Therefore, z = x - y = 5 - 8 = -3.

4 0

2 years ago

Arrange the circles (represented by their equations in general form) in ascending order of their radius lengths. Tiles x2 + y2 −

sashaice [31]

When doing this, we would have to first straight them all out, and as we see above, they are just all over the place, and then, we would have to set them up as a sequence.

$\left[\begin{array}{ccc}5x2 + 5y2 - 20x + 30y + 40 = 0\end{array}\right]$ would be our first step in this problem mainly because it contains the most terms in this aspect.

Then we would then $x2 + y2 - 2x + 2y -1 = 0$ , then, $2x2 + 2y2 - 28x - 32y - 8 = 0$ .

These would only be our first 3 part of the sequence in this aspect.

The others would then be the following:

$\boxed{x2 + y2 + 12x - 2y - 9 = 0 } \ then \ , \boxed{x2 + y2 - 4x + 4y - 10 = 0} \\ \\ then \ \boxed{x2 + y2 - 8x - 6y -20 = 0}$

Thus, as we would have one more afterward, our last part of the sequence would then be the following.

$\boxed{\boxed{4x2 + 4y2 + 16x + 24y - 40 = 0}}$

I hope this was found helpful!

3 0

2 years ago

Read 2 more answers