A 12 inch board is cut into three pieces so that the second piece is as long as the first piece and the third piece is 3 times as long as the first piece of x represents the first piece find the lengths

Answer:

a) P(t) = 6.57e ^{0.0287t}P(t)=6.57e

0.0287t

b) P(6) = 7,805\ millionP(6)=7,805 million

c) t = 14.64\ yearst=14.64 years

d) t = 24.15\ yearst=24.15 years

Step-by-step explanation:

a) The function of exponential growth for a population has the following formula:

P(t) = p_0e ^{rt}P(t)=p

0

e

rt

In this equation:

p_0p

0

is the initial population

r is the growth rate

t is the time in years

In this problem we know that

r = 2.87\% = 0.0287r=2.87%=0.0287

p_0= 6.57p

0

=6.57 million in the year 2012.

So the equation is:

P(t) = 6.57e ^{0.0287t}P(t)=6.57e

0.0287t

Where t = 0t=0 represents the year 2012

b) If t = 0t=0 in 2012, then in 2018 t = 6t=6

The population in 2018 is:

\begin{gathered}P(t = 6) = 6.57e ^{0.0287(6)}\\\\P(6) = 7,805\ million\end{gathered}

P(t=6)=6.57e

0.0287(6)

P(6)=7,805 million

c) To know when the population is equal to 10 million we must equal P(t) to 10 and solve for t.

\begin{gathered}P(t) = 10 = 6.57e ^{0.0287t}\\\\\frac{10}{6.57} = e ^{0.0287t}\\\\ln(\frac{10}{6.57}) = 0.0287t\\\\t = \frac{ln(\frac{10}{6.57})}{0.0287}\end{gathered}

P(t)=10=6.57e

0.0287t

6.57

10

=e

0.0287t

ln(

6.57

10

)=0.0287t

t=

0.0287

ln(

6.57

10

)

t = 14.64\ yearst=14.64 years

d) The function is doubled when P(t) = 2p_0P(t)=2p

0

P(t) = 2(6.57) = 13.14 = 6.57e ^{0.0287t}P(t)=2(6.57)=13.14=6.57e

0.0287t

We solve for t.

\begin{gathered}\frac{13.14}{6.57} = e ^{0.0287t}\\\\ln(\frac{13.14}{6.57}) = 0.0287t\\\\t = ln{13.14}{6.57})}{0.0287})\

end

{gathered}

6.57

13.14

=e

0.0287t

ln(

6.57

13.14

)=0.0287t

t=

0.0287

ln(

6.57

13.14

)

)

t = 24.15\ yearst=24.15 years

Answer:

[tex]x^{3}-8x^{2} +5x+14[/tex]

Step-by-step explanation:

n=3

f(x) = (x-(-1))(x-2)(x-7)

=(x+1)(x-2)= [tex](x^{2} -x-2)[/tex](x-7)=[tex]x^{3}-8x^{2}+5x+14[/tex]

Answer:

x > 0.5

Step-by-step explanation:

Let the number be x.

6 + 5x > x + 8

4x > 2

x > 0.5

This is a question on inequalities. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

Answer:

y = 3x - 1

Step-by-step explanation:

Well I really don't understand what you're asking, but I'll give it a go.

y = 3x -1

That's what the equation would look like.

Hope this is what you wanted!!!

Answer:

The ratio is eight to twelve

Answer:

1/5x

Step-by-step explanation:

A gradient is another word for slope.

every 4 minutes the volume increases by 20

so = rise/run = 4/20

now reduce

4/20

2/10

1/5

Answer:

k = 0.2

A = (M / P₀) − 1

Step-by-step explanation:

dP/dt = kP

When t = 0, P = 1000 and dP/dt = 200.

200 = 1000k

k = 0.2

P = M / (1 + Ae⁻ᵏᵗ)

When t = 0, P = P₀.

P₀ = M / (1 + A)

1 + A = M / P₀

A = (M / P₀) − 1

Answer:

6 1/3

Step-by-step explanation:

Answer:

[tex]1.6456 * 10^{3}[/tex]

Step-by-step explanation:

Step 1:  Convert to Scientific Notation

[tex]1645.6[/tex] is in standard notation

[tex]1.6456 * 10^{3}[/tex] is in scientific notation

Answer:  [tex]1.6456 * 10^{3}[/tex]

Answer:14 4/9

Step-by-step explanation:

Answer:

3g−5h

Step-by-step explanation:

i just used a calculator lol but i wanted to help still

Answer:

3g-5h

Step-by-step explanation:

Answer: X googled it

This converts to the number 99

=========================================================

Explanation:

The upper case letter i means the number 1 in roman numerals. The X represents 10. The C represents 100.

I = 1

X = 10

C = 100

When we form something like IX, we have the smaller digit first and then a larger digit next. Whenever this happens, we subtract

IX = 10-1 = 9

Similarly

XC = 100-10 = 90

So we can see that

IX + XC = 9 + 90 = 99

---------------------------

Since XC is larger than IX, we list XC first when it comes to adding

In other words, we need to write IX+XC as XC+IX which collapses to XCIX

Placing XC next to IX without a plus sign implies the plus sign is there. This is effectively how roman numerals work (they are additive)

So,

XCIX = XC+IX = 90+9 = 99

Note how the XC takes care of the tens digit while IX takes care of the units digit.

Answer:

dependent care FSA

Health FSA

IRA

Step-by-step explanation:

Answer:

x = -3

Step-by-step explanation:

Subtract 2 from both sides of the equation.

3x + 2 = 4x + 5

3x + 2 - 2 = 4x + 5 - 2

Step 2.

Simplify. Subtract the numbers 3x =4x + 3

Now subtract 4 from both sides.

Combine like terms -x = 3

Divide both sides of the equation.

Cancel terms that are in both the numerator and denominator

Divide the numbers

And that's how X = -3

Hope this helped you! If it did, please mark as brainliest this helps me and others a lot. Have a wonderful day.

Answer: Where is the graph? You can solve for the slope by doing y2-y1 over x2-x1

Step-by-step explanation:

Answer:

772.22

Step-by-step explanation:

A=$700(1+0.0332)2(3). Simplify using the order of operations: A=$700(1.0165)6=$700(1.103174712)≈$772.22.

Answer:

I am thinking that it is A and C

Step-by-step explanation:

If I am right may I get a brailiest

If I am wrong I am so very sorry

Answer:

23.59 - 14.89 = x

x = 8.7

Step-by-step explanation:

To find x, you need to add all of the other sides and subtract it from the perimeter. 5.62 + 5.62 + 3.65 = 14.89.

23.59 - 14.89 = x, so x = 8.7

Answer:

8.7

Step-by-step explanation:

Add all the numbers together (5.62, 5.62, and 3.65) then take away from the result (23.59) to get answer.

Answer:40

Step-by-step explanation:

Answer: A

Step-by-step explanation:You are painting a 1/3 of a 1/4 so it's A

Answer:

C, 1 1/14

Step-by-step explanation:

You would convert 1/2 to 7/14 and convert 4/7 to 8/14. You can now add them together, and once you do you get 15/14. You can now simplify, giving you your answer of 1 1/14.

Answer:

67

Step-by-step explanation:

You have to use fractions to show your work and I'm not going to do that but just know that it is the answer.

Answer:

x = 100

Step-by-step explanation:

Alex's house (point F) lies on the same street as her school (point H). Alex's bus stop (point G) lies between her house and her school. Given FG=2x meters, GH=1,000 meters and FH=1,200 meters. What is the value of x in meters?

FG=2x meters, GH=1,000 meters and FH=1,200 meters.

FH = FG + GH

1200 = 2x + 1000

1200 - 1000 = 2x

200.= 2x

x.= 200/2

x = 100

Answer:

Step-by-step explanation:

2x² + 6x - 5 = 0

D = 36 + 40 = 76 = (2√19)²

[tex]x_{1}[/tex] = ( - 6 - 2√19) / 4 = ( - 3 - √19) / 2

[tex]x_{2}[/tex] = ( - 3 + √19) / 2