MATHEMATICS COLLEGE

1)What is the common ratio of the following geometric sequence?
100, 150, 225, 337.5, ...
A. 50
B. 0.5
C. 1.5
D. 1.25

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

hello :

the common ratio is : 3375/225=225/150=150/100 = 1.5

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Solve the equation
3(x + 1) = 9+ 2x

Answers

Answer:

$x=6$

Step-by-step explanation:

So we have the equation:

$3(x+1)=9+2x$

Distribute the left side:

$3x+3=9+2x$

Subtract 2x from both sides. The right side cancels:

$(3x+3)-2x=(9+2x)-2x\nx+3=9$

Subtract 3 from both sides:

$(x+3)-3=(9)-3\nx=6$

So, x is 6.

3x(x)=3x
3x1=3
3x+3=9+2x

A rumor spreads through a small town. Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor. a. Write the differential equation satisfied by y in terms of proportionality k.
b. Find k (in units of day−1, assuming that 10% of the population knows the rumor at time t=0 and 40% knows it at time t=2 days.
c. Using the assumptions in part (b), determine when 75% of the population will know the rumor.
d. Plot the direction field for the differential equation and draw the curve that fits the solution y(0)=0.1 and y(0)=0.5.

Answers

Answer:

The answer is shown below

Step-by-step explanation:

Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.

$(dy)/(dt)\ \alpha\ y(1-y)$

$(dy)/(dt)=ky(1-y)$

where k is the constant of proportionality, dy/dt = rate at which the rumor spreads

$(dy)/(dt)=ky(1-y)\n(dy)/(y(1-y))=kdt\n\int\limits {(dy)/(y(1-y))} \, =\int\limit {kdt}\n\int\limits {(dy)/(y)} +\int\limits {(dy)/(1-y)} =\int\limit {kdt}\n\nln(y)-ln(1-y)=kt+c\nln((y)/(1-y)) =kt+c\ntaking \ exponential \ of\ both \ sides\n(y)/(1-y) =e^(kt+c)\n(y)/(1-y) =e^(kt)e^c\nlet\ A=e^c\n(y)/(1-y) =Ae^(kt)\ny=(1-y)Ae^(kt)\ny=(Ae^(kt))/(1+Ae^(kt)) \nat \ t=0,y=10\%\n0.1=(Ae^(k*0))/(1+Ae^(k*0)) \n0.1=(A)/(1+A) \nA=(1)/(9) \n$

$y=((1)/(9) e^(kt))/(1+(1)/(9) e^(kt))\ny=(1)/(1+9e^(-kt))$

At t = 2, y = 40% = 0.4

c) At y = 75% = 0.75

$y=(1)/(1+9e^(-0.8959t))\n0.75=(1)/(1+9e^(-0.8959t))\nt=3.68\ days$

How many millimeters are equal to one kilometer. Show your work

Answers

Answer:

1,000,000

Step-by-step explanation:

1mm=1e-6km

10mm=1e-5km

100mm=1e-4km

1000mm=000.1km

10000mm=0.01km

100000mm=0.1km

500000mm=0.5km

1000000mm=1km

What are the roots of the polynomial equation x3 - 6x= 3x2 - 8? Use a graphing calculator and a system of equations

Answers

Answer:

Hence, the roots of the polynomial equation are:

-2, 1, 4

Step-by-step explanation:

We are asked to find the roots of the polynomial equation:

We can also equate this equation to y to obtain a system of equation as:

and

Hence, the roots of the polynomial; equation are the x-values of the point of intersections of the graph of the system of equations.

Hence, the point of intersection of the two graphs are:

(-2,4), (1,-5) and (4,40)

Hence, the roots of the polynomial equation are:

-2, 1, 4

Find the value of the expression below.

Answers

Answer:

what expression

Step-by-step explanation:

theres nothing attached bruv

In the diagram below, AB | CD, AD || BC, mZCDE = 45° andmZC = 73º. Find mZADE.
450
B
E
А

Answers

Answer:

The measure of angle ADE is equal to 62 degrees.

Step-by-step explanation:

Firstly, I want to remind you that the sum of the interior angles in a quadrilateral are 360 degrees. Now, we are given that CD || BA and CB || DA, which means that this quadrilateral is a parallelogram. This is important because we know that the opposite angles in a parallelogram are congruent, which means that angle C is congruent to angle A and angle B is congruent to angle D. Therefore, the measure of angle A is also 73 degrees. Next, we can represent angle D as x, which means that angle B is equal to x, so the sum of angle D and B is 2x. Finally, we can set up an equation where we solve for the value of x, and then subtract it with 45 degrees:

2x + 2(73) = 360

2x + 146 = 360

2x = 214

x = 107 = B = D

Now, we can subtract the measure of angle D with 45 degrees to get the measure of angle ADE:

ADE = 107 - 45

ADE = 62

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