A major corporation is building a 4,325-acre complex of homes, offices, stores, schools, and churches in the rural community of Glen Cove. As a result of this development, the planners have estimated that Glen Cove's population (in thousands) t years from now will be given by
(25t2 + 150t + 100)/(t2 + 6t + 24)
A) Find the rate at which Glen Cove's population is changing with respect to time.
B) What will be the population after 10 years?
C) At what rate will the population be increasing when t = 10?

Answers

Answer 1

Answer:

See explanation

Step-by-step explanation:

We have that;

P(t) = (25t2 + 150t + 100)/(t2 + 6t + 24)

a) rate at which Glen Cove's population is changing with respect to time.

dP/dt = (t^2 + 5t + 40) (50t + 125) - (25t^2 + 125t + 200) (2t + 5)/(t^2 + 5t + 40)^2

dP/dt = 1000t + 3000/(t^2 + 6t + 24)^2

b)  population after 10 years

P(t) = (25t2 + 150t + 100)/(t2 + 6t + 24)

P(t) =(25(10)^2 + 150(10) + 100)/((10^2 + 6(10) + 24)

P(t) = 4100/184

P(t) = 22283

c) when t = 10

dP/dt = 1000t + 3000/(t^2 + 6t + 24)^2

dP/dt = 1000(10) + 3000/(10^2 + 6(10) + 24)^2

dP/dt = 13000/33856

dP/dt = 0.384


Related Questions

determine the area of mrs wests backyard that is coverd grass and show ur work!!

Answers

Answer:

150 ft^2

Step-by-step explanation:

The formula is (30*10)/2 which is equal to 150.

Find the value of q which will make the quadratic expression 9x ^2-12x+q a perfect square ​

Answers

Answer:

The value of q that makes the expression a perfect square is q = 4.

Step-by-step explanation:

Perfect square:

A perfect square expression has the following format:

[tex](a - b)^2 = a^2 - 2ab + b^2[/tex]

In this question:

[tex]9x^2 - 12x + q[/tex] is a perfect square, we have to find the value of q.

First we have to find the value of a, looking at the equivalent formula above. So

[tex]a^2 = 9x^2[/tex]

[tex]a = \sqrt{9x^2}[/tex]

[tex]a = 3x[/tex]

Since the second term, which is -2ab, is -12x, we have that:

[tex]-2ab = -12x[/tex]

[tex]-2(3x)b = -12x[/tex]

[tex]-6xb = -12x[/tex]

[tex]6b = 12[/tex]

[tex]b = \frac{12}{6}[/tex]

[tex]b = 2[/tex]

q is b squared. So

[tex]q = b^2 = 2^2 = 4[/tex]

The value of q that makes the expression a perfect square is q = 4.

what are the next 3 terms in this:O,T,T,F,F

Answers

Answer:

Step-by-step explanation:

S, S, E.

Come on, do I have to spell it out for you?  :)

Leann wants to gift wrap a present she got for her little brother how many square inches of gift wrap will be needed to cover a box that is 4in by 6in by 2in ​

Answers

Answer:

48 square in.

Step-by-step explanation:

so first off you do 4x6 and you get 24 now you want t do 24x2 and get 48

Yuri thinks that 3/4 is a root of the following function.
q(x)=6x^3+19x^2-15x-28
Explain to Yuri why 3/4 cannot be a root.

Answers

Given:

The polynomial function is

[tex]q(x)=6x^3+19x^2-15x-28[/tex]

Yuri thinks that [tex]\dfrac{3}{4}[/tex] is a root of the given function.

To find:

Why [tex]\dfrac{3}{4}[/tex] cannot be a root?

Solution:

We have,

[tex]q(x)=6x^3+19x^2-15x-28[/tex]

If [tex]\dfrac{3}{4}[/tex] is a root, then the value of the function at [tex]\dfrac{3}{4}[/tex] is 0.

Putting [tex]x=\dfrac{3}{4}[/tex] in the given function, we get

[tex]q(\dfrac{3}{4})=6(\dfrac{3}{4})^3+19(\dfrac{3}{4})^2-15(\dfrac{3}{4})-28[/tex]

[tex]q(\dfrac{3}{4})=6(\dfrac{27}{64})+19(\dfrac{9}{16})-\dfrac{45}{4}-28[/tex]

[tex]q(\dfrac{3}{4})=3(\dfrac{27}{32})+\dfrac{171}{16}-\dfrac{45}{4}-28[/tex]

[tex]q(\dfrac{3}{4})=\dfrac{81}{32}+\dfrac{171}{16}-\dfrac{45}{4}-28[/tex]

Taking LCM, we get

[tex]q(\dfrac{3}{4})=\dfrac{81+342-360-896}{32}[/tex]

[tex]q(\dfrac{3}{4})=\dfrac{-833}{32}\neq 0[/tex]

Since the value of the function at [tex]\dfrac{3}{4}[/tex] is not equal to 0, therefore, [tex]\dfrac{3}{4}[/tex] is not a root of the given function.

Please Answer This question.

Answers

Answer:

K = 15

Step-by-step explanation:

From the question given above, the following data were obtained:

Sine x = 1/4

Cos² x = K / 16

K =?

Next, we shall determine the 3rd leg (i.e the adjacent) of the right angle triangle. This can be obtained as follow:

Sine x = 1/4

Sine x = Opposite / Hypothenus

Opposite = 1

Hypothenus = 4

Adjacent =?

Hypo² = Opp² + Adj²

4² = 1² + Adj²

16 = 1 + Adj²

Collect like terms

16 – 1 = Adj²

15 = Adj²

Take the square root of both side.

Adj = √15

Next, we shall determine Cos² x.

Adjacent = √15

Hypothenus = 4

Cos² x =?

Cos x = Adjacent / Hypothenus

Cos x = √15 /4

Square both side

Cos² x = (√15 /4)²

Cos² x = 15 / 16

Finally, we shall determine the value of K. This can be obtained as follow:

Cos² x = K / 16

Cos² x = 15 / 16

K / 16 = 15 / 16

K = 15

Becky made 63 carnival masks, which is 30% less than the number
her brother made. How many carnival masks did Becky and her
brother make in total?

Answers

Answer:

273

Step-by-step explanation:

63 ÷ 30% = 210

210 + 63 = 273

therefore your total is 273

hope this is right, and that it helps :)

Answer:

Becky and her brother made 90+63=153 masks in total

Step-by-step explanation:

Percentages

Let's call x=number of masks Becky's brother made.

We know Becky made 30% less than the number of masks her brother made.

30% of x is calculated by:

30*x/100 = 0.3x

Now subtracting from x:

x - 0.3x = 0.7x

Becky made 63 carnival masks, this means that:

0.7x = 63

Dividing by 0.7:

x = 63/0.7 = 90

Becky's brother made 90 masks.

Becky and her brother made 90+63=153 masks in total

Identify if the equation is growth
or decay and the rate.

Answers

Answer:B

Step-by-step explanation:m is the slope and m=-3

50 points I WILL ALSO MARK BRAINLIEST ITS TIMED PLZ HURRY

The coordinates of the vertices of a polygon are shown on the graph below.

On a coordinate plane, point A is at (negative 4, 3), point C is at (0, negative 3), and point B is at (negative 4, negative 3).
What is the name of the polygon?
octagon
pentagon
quadrilateral
triangle

Answers

Answer:

Triangle

Step-by-step explanation:

In My Knowledge

Option D. triangle

Please include the steps that took you to get your answer. I am very confused on what to do with the 1/2.

Answers

First let's review how to expand this!

(ax+b)^2=a^2*x^2+2abx+a^2

In this case

(2x^2+1/2)^2=2^2*x^2+2*1/2*2x+(1/2)^2

=4x^2+2x+1/4

Done!

Using the diagram below, what is the length of PR (Please answer within 10 min it's on a time limit.)

Answers

Answer:

oof

Step-by-step explanation:

Question- What method would you happen to be using to solve this problem?

Factorise fully 18j + 30jk

Answers

Answer:


6j (3+5k)



I hope you like my answer

Answer:

6j(5k+3)

Step-by-step explanation:

18j+30jk

Factor out 6.

6(3j+5jk)

Consider 3j+5jk. Factor out j.

j(3+5k)

Rewrite the complete factored expression.

6j(5k+3)

Someone please help me!!:(

Answers

Ether 3 4 Relize To always Look At the equation Of wat You’re Doing


solve each equation for given variable
- 12 = 6i- 6

Answers

Answer: i = -1

Explanation:
First get the variable by itself. To do that, add six to both sides of the equation. You will have -6 = 6i. Than divide both sides by 6. It will give you i = -1.
-12 = 6i - 6
-12 + 6 = 6i - 6 + 6
-12 + 6 = 6i
(-12 + 6)/6 = (6i)/6
(-12 + 6)/6 = i

i = (-12 + 6)/6

Please help me I’m giving brainliest!

Answers

Answer:  C) 4

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

Work Shown:

Applying the tangent-secant theorem will allow us to solve for x

x*(x+5) = (x+2)^2

x^2+5x = (x+2)*(x+2)

x^2+5x = x^2+4x+4

5x = 4x + 4 ..... subtracting x^2 from both sides; terms cancel

5x-4x = 4

x = 4

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

Check:

Plug in x = 4

x*(x+5) = (x+2)^2

4*(4+5) = (4+2)^2

4*(9) = (6)^2

36 = 36

The answer is confirmed.

What is the equation of the line that passes through the point (-3,2) and has a slope of -2/3

Answers

Answer: Y=2/3x+4

     ................................................

What is the velocity of a car that’s traveled 306 kilometers northeast in 3.4 hours

Answers

Answer : -302.6

Step-by-step explanation:

Solve the proportion: 9 is to 16 as M is to 32.

(please show working out!)​

Answers

Answer:

Step-by-step explanation:

9 : 16 :: M : 32

Means of extremes = means of means

= 9 x 32 = 16 x M

= 288 = 16M

288/16 = M

18 = M

PLEASE HELP THIS IS URGENT
Kayla is thinking of a 3-digit number. * It is divisible by 18. * It is a palindrome (It reads the same left-to-right as it does right-to-left, like 252 and 848). * It is one less than a multiple of 5. What is Kayla’s number?

Answers

Answer: 414

Step-by-step explanation: 414 is a palindrome that is divisible by 18 because it’s an even number and that it’s one less than 415 which is a multiple of 5.

Kayla's number is 414 and this can be determined by using the given data and also by using the arithmetic operations.

Given :

Kayla is thinking of a 3-digit number. It is divisible by 18.It is a palindrome.It is one less than a multiple of 5.

The following steps can be used in order to determine Kayla’s number:

Step 1 - Remember palindrome means 'reads the same left-to-right as it does right-to-left'.

Step 2 - The digit should be between 0 to 9 and according to the given data, the number is one than a multiple of 5 that is, the first and last digit must be 4 or 9.

Step 3 - So, the number which is divisible by 18 is 414.

For more information, refer to the link given below:

https://brainly.com/question/25277954

can someone help this is kinda confusing i’ll mark you as brainlilest.

Answers

Answer:

The answer is A, good luck on the test! :D

Step-by-step explanation:

Answer:

Step-by-step explanation:

A. In geometry, a cylinder is a three-dimensional shape with a circular base, ... So using the volume of cylinder formula we can find the volume of i

50 points
Yolanda received her telephone bill on July 27th and paid it three weeks later. What was the date that Yolanda paid her electric bill? A. July 6 B. July 17 C. August 17 D. August 18

Answers

Answer:

Aug 16th

Step-by-step explanation:

is it complementary, supplementary, vertical, or none of the above? i need this right now!!!!

Answers

Answer:

d. None of these

Step-by-step explanation:

Hope it helps you in your learning process.

[tex] m\angle 1 + m\angle 2 + 90\degree = 360\degree [/tex]

[tex] m\angle 1 + m\angle 2 = 360\degree- 90\degree [/tex]

[tex] m\angle 1 + m\angle 2 = 270\degree [/tex]

Answer:

D. None of the above.

Step-by-step explanation:

Complementary are 90 degrees and supplementary are 180 degrees.

A full circle is 360 degrees, and since there is a right angle, that means that angle 1 and 2 make up 270 degrees total.

This means it is neither.

The height of a standard coffee cup

would be about

7 meters

B

7 kilometers

7 centimeters

D

7 millimeters

Answers

Answer:

7 centimeters

Step-by-step explanation:

Standard size of a coffee cup is 7 centimeters

7 meters is too big

7 kilometers  is bigger than 7 meter

7 millimeters is too small

do's and donts in handling measuring tools

Answers

Here’s your answer mate :

Answer:

I need answer too

Pleaseee help us

Lindsay invest $250 in a bank account that pays 3% interest each year how much money will be in her account after one year?

Answers

257.5 I believe. Explanation) If she receives 3% of $250, then she will receive $7.50. Then you have to add that to $250 because that will still be in the account.

which word describes the slope of line ?

Answers

The slope of this line is zero.

What is the answer please

Answers

this is literally like impossible, i’ve been trying to figure it out for like 15 minutes lol

Look at this expression.
-3xfy
x3y2
Which of the following is the simplest form of this expression?
OA
-3x²y2
ОВ. -3x?у?
Ос. -3°у?
OD. -3x® yo

Answers

Answer:

‐3×2y2 is the most common correct answer

Pippin went to a game room that charged $4 admission, plus $0.25 per token. The equation which represents his total cost is y = 0.25x + 4.What are the ordered pairs for the equation when you use these x-values: 5, 10, 20?(5, 5), (10, 8), (20, 15)(5, 8), (10, 10), (20, 15)(5, 5.25), (10, 6.50), (20, 9)(5, 5.50), (10, 8.50), (20, 13)

Answers

Answer:

(5, 5.25) , (10, 6.50) , (20, 9)

Step-by-step explanation:

As given ,

y = 0.25x + 4

Now,

if x = 5

⇒ y = 0.25(5) + 4

      = 1.25 + 4

     = 5.25

⇒ y = 5.25

∴ the ordered pair be (x, y) = (5, 5.25)

if x = 10

⇒ y = 0.25(10) + 4

      = 2.5 + 4

     = 6.50

⇒ y = 6.50

∴ the ordered pair be (x, y) = (10, 6.50)

if x = 20

⇒ y = 0.25(20) + 4

      = 5 + 4

     = 9

⇒ y = 9

∴ the ordered pair be (x, y) = (20, 9)

Elena is designing a paint can with thickness ttt millimeters and height hhh centimeters. She calculates that the thickness of the can in milimeters must be at least 0.1, point, 1 times the height of the can in centimeters in order to withstand pressure. Due to cost constraints, the cost of material used, (0.2 + t+ 0.5h)cents, must be at most 12.2, point, 2 cents. Which system of inequalities best models the relationship between height and thickness?

Answers

Answer:

[tex]t \ge h[/tex] and [tex]t + 0.5h \le 12.0[/tex]

Step-by-step explanation:

Given

[tex]t= thickness[/tex]

[tex]h =height[/tex]

From the first statement, we have that:

[tex]t\ mm \ge 0.1 * h\ cm[/tex]

Convert mm to cm

[tex]t\ * 0.1*cm \ge 0.1 * h\ cm[/tex]

[tex]t\ *0.1 \ge 0.1 * h[/tex]

Divide both sides by 0.1

[tex]t \ge h[/tex]

From the second statement, we have that:

[tex]Cost \le 12.2[/tex]

Substitute 0.2 + t + 0.5h for Cost

[tex]0.2 + t + 0.5h \le 12.2[/tex]

Collect Like Terms:

[tex]t + 0.5h \le 12.2-0.2[/tex]

[tex]t + 0.5h \le 12.0[/tex]

So, the inequalities are:

[tex]t \ge h[/tex] and [tex]t + 0.5h \le 12.0[/tex]

Answer: it's a, the answer

Step-by-step explanation:

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