answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Evgesh-ka [11]
1 year ago
8

There is an integer n such that 2n2 − 5n + 2 is prime. To prove the statement it suffices to find a value of n such that (n, 2n2

− 5n + 2) satisfies the property "2n2 − 5n + 2 is prime." Show that you can do this by entering appropriate values for n and 2n2 − 5n + 2.
Mathematics
1 answer:
fomenos1 year ago
7 0

Answer:

n = 0 or 3

Step-by-step explanation:

2n² - 5n + 2

2n² - 4n - n + 2

2n(n - 2) -1(n - 2)

(n - 2)(2n - 1)

Prime number is one which is divisible by itself and 1

n-2 = 1 n = 3

2n-1 = 1 n = 0

You might be interested in
A 2-column table with 5 rows. The first column is labeled hours spent exercising with entries 2, 4, 3, 4, 5. The second column i
slamgirl [31]

Answer:

second answer or B

Step-by-step explanation:

5 0
1 year ago
Read 2 more answers
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
Which equation can be used to solve for c? Triangle A B C is shown. Angle A C B is 90 degrees and angle A B C is 35 degrees. The
aliina [53]

Answer:

The correct option is B) c=\frac{5}{\cos35^0}.

Step-by-step explanation:

Consider the provided information.

Angle A C B is 90 degrees and angle A B C is 35 degrees.

The required figure is shown below:

We need to find the value of c.

Use the trigonometric function: \cos\theta=\frac{Adjacent}{Hypotenuse}

\cos35^0=\frac{5}{c}

c=\frac{5}{\cos35^0}

Hence, the correct option is B) c=\frac{5}{\cos35^0}.

4 0
1 year ago
Read 2 more answers
billy is creating a circular garden divided into 8 equal sections. The diameter of the garden is 12 feet. what is the area, in s
xxTIMURxx [149]
Area=πr^2

 find the area then divide by 8


we know that diameter=2radius or diameter/2=radius so 
12=diameter
12/2=radius=6
subsitute
area=π(6)^2
area=36π
divide 36π by 8
36π/8=18π/4=9π/2π=4.5π
area of one section is 4.5π square feet or if we aprox pito 3.14159 then we get
4.5(3.14159)=area=14.1372 square feet or 14.14 square feet
5 0
1 year ago
A turtle and a rabbit engage in a footrace over a distance of 4.00 km. The rabbit runs 0.500 km and then stops for a 90.0-min na
Oxana [17]

Answer:

(a) 2.29 km/h

(b) 9 km/h

Step-by-step explanation:

For part (a) you have to apply<em> the average speed formula</em>, which is defined by:

v=\frac{d}{t}

where d is the total distance traveled and t is the total time needed.

d=\frac{4.00}{1.75}=2.29 km/h

For part (b) you have to calculate the running time (T) , which is the total time of the race minus the nap time:

The nap time in hours is:

90/60 = 1.5 h (because there are 60 minutes in one hour)

The running time is:

T= 1.75 - 1.5 = 0.25 h

Let t1 represent the time before the nap and t2 the time after the nap:

t1+t2 = T

t1+t2 = 0.25

You have to apply the formula d=vt before and after the nap:

-Before the nap, the distance traveled was 0.50 km

0.50 = v1t1

-Afer the nap, the distance traveled was 3.50 km

3.50=v2t2

But v2=2v1 (because after the nap the rabbit runs twice as fast)

You have to solve the system of equations:

t1=0.25-t2 (I)

v1t1=0.50 (II)

2v1t2=3.50 (III)

Replacing (I) in (II)

v1(0.25-t2)=0.50

Applying distributive property and solving:

0.25v1-v1t2=.050

For (III) you have that v1t2=3.50/2=1.75. Hence:

0.25v1-1.75=0.50

Solving for v1:

v1 = 9 km/h

7 0
1 year ago
Other questions:
  • On a trip, you had to change your money from dollars to euros. You got 450 euros for 600 dollars. Which is a unit rate that desc
    15·1 answer
  • Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation?
    10·2 answers
  • Which of the following are in the correct order from least to greatest?
    7·2 answers
  • a science teacher has 0.4 L of seawater she gives each of her 22 students a container and a 5ml spoon she then asks her students
    12·2 answers
  • Bonnie is making a dipping sauce. She mixes 150 milliliters of soy sauce with 100 milliliters of vinegar. How much soy sauce doe
    5·3 answers
  • What is the value of minus 6 x cubed minus y squared minus 3 x y if if x = -2 and y = 4
    5·2 answers
  • A man is on a 1/4 on a bridge. A train is coming the same direction he is going. The man can run across the bridge in the same d
    13·1 answer
  • Given that lim x→a f(x) = 0 lim x→a g(x) = 0 lim x→a h(x) = 1 lim x→a p(x) = [infinity] lim x→a q(x) = [infinity], evaluate the
    11·1 answer
  • A dairy farmer accidentally allowed some of his cows to graze in a pasture containing weeds that would contaminate the flavor of
    9·1 answer
  • A bank representative studies compound interest, so she can better serve customers. She analyses what happens when $2,000 earns
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!