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3 years ago

8

A right rectangular prism has a length of 6 in., a width of 9 in., and a height of 10 in. What is the surface area of the prism?

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1 answer:

Alisiya [41]3 years ago

5 0

408 in^2
.......Hope it helps, Have a nice day:)

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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

Which triangle has hypotenuse Side B F? A cube. The top face has points G, B, C, F and the bottom face has points H, A, D, E. tr

jolli1 [7]

Answer:

ΔBFG

Step-by-step explanation:

Since top face points are

G, B, C and F

and bottom face points are

H, A, D and E

The side BF can be a hypotenuse of the triangle BFG only

This triangle is on the top face and all the rest given triangles are formed by the points that are not on the same face, therefore BF can't be a hypotenuse of those, as ether B or F is becoming a right angle of the triangles.

3 0

3 years ago

Solve the following quadratic function

Leya [2.2K]

Answer:

x = ± 10

Step-by-step explanation:

to solve the equation let y = 0 , that is

100 - x² = 0 ( add x² to both sides )

100 = x² ( take square root of both sides )

± $\sqrt{100}$ = x , that is

x = ± 10

8 0

2 years ago

Simplify the expression: (3 − 4i) + (7 − 6i). 4 − 2i 4 − 10i 13 − 2i 10 − 10i

yulyashka [42]

Equivalent expressions are expressions of equal values

The simplified expression of (3 - 4i) + (7 - 6i) is $10- 10i$

The expression is given as:

$(3 - 4i) + (7 - 6i)$

Remove brackets in the above expression

$3 - 4i + 7 - 6i$

Rewrite the expression by collecting the like terms

$3 + 7- 4i - 6i$

Next, evaluate the like terms

$10- 10i$

Hence, the simplified expression of (3 - 4i) + (7 - 6i) is $10- 10i$

Read more about equivalent expressions at:

brainly.com/question/2972832

7 0

2 years ago

arron takes his dog for a walk afer school, he walks 5 blocks east and then 4 blocks north. if he was able to take a direct rout

nlexa [21]

Hi!

We are given the information found in the picture below.

Note: The directions aren't correct, but the triangle works for this problem.

The "direct path" is the hypotenuse of this triangle.

To find this, we use the Pythagorean Theorem, where $a$ and $b$ are 2 legs of the triangle, and $c$ is the hypotenuse, aka the longest side of any triangle:

$a^2+b^2=c^2$

We know $a$ and $b$ and want $c$

$4^2+5^2=c^2$

$16+25=c^2$

$41=c^2$

Therefore, $c$ is approximately $6.403$

3 0

2 years ago