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2 years ago

Which of the following values for m proves that 2m + 2m is not equivalent to 4m2?

Mathematics

2 answers:

Mashutka [201]2 years ago

6 0

M=0 i am not sure it is right

max2010maxim [7]2 years ago

4 0

When m=0 ,

2m+2m=2(0)+2(0)= 0

$4m^{2}.=4(0^{2})=0$

When m=1 ,

2m+2m=2(1)+2(1)=2+2=4.

$4m^{2}. =4(1)^{2}.=4.$

When m=2

2m+2m=2(2)+2(2)=4+4=8.

$4m^{2}.=4(2)^{2}.=4(4)=16.$

Both expressions are not equivalent when m=2.

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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

2 years ago

Sue played four games of golf for these games her modal score was 98 and her mean score was 100 her range of score was 10 what w

earnstyle [38]

Answer : Remaining two observation becomes 97 and 107.

Explanation :

Since we have given that

Mean = 100

Modal value = 98

Range = 10

As we know that ,

Range = Highest-Lowest

Let highest observation be x

Let lowest observation be y

So equation becomes x-y=10 ----equation 1

So, observation becomes

x,98,98,y

Now, we use the formula of mean i.e.

Mean = $\frac{\text{Sum of observation}}{\text{N.of observaton}}$

So, mean = $\frac{x=98=98+y}{4}=400\\\frac{196+x+y}{4}=100\\x+y=400-196\\x-y=204$

So our 2nd equation becomes

x+y=204

On using elimination method of system of linear equation on these two equation we get,

x=97

and

$x+y=204\\y=204-x\\y=204-97\\y=107$

Hence , remaining two observation becomes 97 and 107.

8 0

2 years ago

The lines shown below are parallel if the green line has a slope of 8 what is the slope of the redline?

Advocard [28]

Answer:

Option D

Step-by-step explanation:

If these lines are parallel, they should have the same slope. How so? Well slope is the change in axis, y / x more specifically. If the lines are parallel they should change at a similar rate so that they don't intersect, and hence are, by definition, ║;

$Green Line's Slope = Red Line's Slope,\\8 = Red Line's Slope,\\Red Line's Slope = 8 units\\\\Solution - Option D$

Hope that helps!

7 0

2 years ago

Find an explicit formula for the arithmetic sequence 12, 5, -2, -9,...12,5,−2,−9,...12, comma, 5, comma, minus, 2, comma, minus,

Andrew [12]

Answer:

A(n) = 19 - 7n

Step-by-step explanation:

12, 5, -2, -9,...

First term, a = 12

Common difference, d = a2 - a1

a2 = 5

a1 = 12

Common difference, d = a2 - a1

= 5 - 12

= -7

d = -7

A(n) = a + (n - 1)d

A(n) = 12 + (n - 1) -7

= 12 + (-7n + 7)

= 12 - 7n + 7

= 12 + 7 - 7n

= 19 - 7n

A(n) = 19 - 7n

5 0

2 years ago

Read 2 more answers

The ordered pairs model an exponential function, where w is the function name and t is the input variable. {(1, 60), (2, 240), (

alexandr1967 [171]

We are given the set of points
{(1, 60), (2, 240), (3, 960), (4, 3840)}{(1, 60), (2, 240), (3, 960), (4, 3840)}
If w is the function name and t is the input variable, then the equation has the form
w = k a^t
Plugging in any two of the points to solve for k and a
Choosing (1, 60) and (2, 240)
60 = k a
k = 60 / a

240 = k a^2

Substituting
240 = 60/a (a^2)
a = 4
and
k = 60 / 4 = 15

The function is
w = 15 (4^t)

3 0

2 years ago

Read 2 more answers