The rate of growth of the population N(t) of a new city t years after its incorporation is estimated to be dN/dt=500+600(square root of t) where 0 is less than or equal to t which is less than or equal to 4. If the population was 3,000 at the time of incorporation, find the population 4 years later.
Answers
The population 4 years later is approximately 6,000. To find the population 4 years later, we need to integrate the rate of growth equation dN/dt = 500 + 600√t with respect to t.
The population of the new city 4 years after its incorporation can be found by integrating the rate of the growth equation dN/dt = 500 + 600√t with the initial condition N(0) = 3,000.
This will give us the function N(t) that represents the population at any given time t.
Integrating the equation, we have:
∫dN = ∫(500 + 600√t) dt
N = 500t + 400√t + C
To find the value of the constant C, we use the initial condition N(0) = 3,000. Substituting t = 0 and N = 3,000 into the equation, we can solve for C:
3,000 = 0 + 0 + C
C = 3,000
Now we can write the equation for N(t):
N(t) = 500t + 400√t + 3,000
To find the population 4 years later, we substitute t = 4 into the equation:
N(4) = 500(4) + 400√(4) + 3,000
N(4) = 2,000 + 800 + 3,000
N(4) ≈ 6,000
Therefore, the population of the new city 4 years after its incorporation is approximately 6,000.
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Related Questions
WILL GIVE BRAINLIEST! What is the measure of the angle formed by the lines 2x–7y+6=0 and 14x+4y–17=0?
Answers
Answer:
the measure of the angle formed by given lines is 90°
Step-by-step explanation:
Line 1:
2x - 7y + 6 = 0
- 7y = - 2x - 6
y = \(\frac{2}{7}\) x + \(\frac{6}{7}\)
Slope of line 1:
\(m_{1}\) = \(\frac{2}{7}\)
Line 2:
14x + 4y - 17 = 0 ⇔ y = - \(\frac{7}{2}\) x + \(\frac{17}{4}\)
Slope of line 2:
\(m_{2}\) = - \(\frac{7}{2}\)
\(m_{1}\) \(m_{2}\) = - \(\frac{7}{2}\) × \(\frac{2}{7}\) = - 1 ⇒ lines are perpendicular
The lengths of two sides of a triangle are shown below:
Side 1: 3x^2 − 4x − 1
Side 2: 4x − x^2 + 5
The perimeter of the triangle is 5x^3 − 2x^2 + 3x − 8.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points)
Part B: What is the length of the third side of the triangle? (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)
Answers
Answer:
Step-by-step explanation:
Part A: To find the total length of the two sides, you need to add the lengths of Side 1 and Side 2.
Side 1: 3x^2 − 4x − 1
Side 2: 4x − x^2 + 5
Adding these two expressions together, we get:
(3x^2 − 4x − 1) + (4x − x^2 + 5)
Rearranging the terms, we have:
(3x^2 - x^2) + (-4x + 4x) + (-1 + 5)
Combining like terms, we get:
2x^2 + 4
So, the total length of Side 1 and Side 2 is 2x^2 + 4.
Part B: The length of the third side of the triangle can be found by subtracting the sum of Side 1 and Side 2 from the perimeter of the triangle.
Perimeter of the triangle: 5x^3 − 2x^2 + 3x − 8
Total length of Side 1 and Side 2: 2x^2 + 4
Subtracting the sum of Side 1 and Side 2 from the perimeter, we get:
(5x^3 − 2x^2 + 3x − 8) - (2x^2 + 4)
Expanding and simplifying, we have:
5x^3 − 2x^2 + 3x − 8 - 2x^2 - 4
Combining like terms, we get:
5x^3 - 4x^2 + 3x - 12
So, the length of the third side of the triangle is 5x^3 - 4x^2 + 3x - 12.
Part C: The answers for Part A and Part B do show that the polynomials are closed under addition and subtraction. When we added the lengths of Side 1 and Side 2, we obtained the polynomial expression 2x^2 + 4, which is a polynomial. When we subtracted the sum of Side 1 and Side 2 from the perimeter of the triangle, we obtained the polynomial expression 5x^3 - 4x^2 + 3x - 12, which is also a polynomial. Therefore, both addition and subtraction of the polynomials resulted in valid polynomial expressions, indicating closure under these operations.
A swimming pool measures 25.8 meters by 11.9 meters. It is filled with water to a depth of 1.1 meters. The pool is emptied by a tube that emits 29.8 liters per second. Estimate the approximate time required to empty the pool
Answers
Answer:
11 Seconds
Step-by-step explanation:
Swimming pool volume:
25.8 × 11.9 × 1.1 = 337.722
Time to empty pool:
337.722 ÷ 29.8 = 11.3329530201 ≈ 11 seconds
PLS EXPLAINIIf y = 16x, which table shows the values of y for different values of x?
x 0 2 4
y 0 18 20
x 0 2 4
y 0 8 4
x 0 2 4
y 0 32 64
x 0 2 4
y 0 16 32
Answers
Answer:
Step-by-step explanation:
I think it's B but I'm not 100% sure
x 0 2 4
y 0 32 64
Explanation
When x = 0
y = 16 • 0 = 0
When x = 2
y = 16 • 2 = 32
When x = 4
y = 16 • 4 = 64
<~>\_/<~> Ho_odini <~>\_/<~>
Is the vertical component of velocity ever zero? If so, where?
Answers
The vertical component of velocity can be zero at specific points in the motion of an object.
What is Velocity?
Velocity is a vector quantity that describes the rate of change of an object's position in space over time. It is defined as the displacement of an object divided by the time interval during which the displacement occurred.
The vertical component of velocity can be zero at specific points in the motion of an object. This occurs when the object reaches the highest point in its vertical motion and begins to fall back down. At this point, the vertical component of velocity changes direction from upward to downward, and its magnitude becomes zero. This moment is known as the "instant of maximum height" or "instant of maximum altitude." Beyond this point, the vertical component of velocity becomes negative, indicating that the object is moving downward.
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Please help me! I’ll mark you as the brainiest but please don’t answer if you don’t know it
Answers
Answer:
x > 7
Step-by-step explanation:
If you look at the changes in degrees, you will see it get bigger on the bottom! That means the 7 will become smaller! Your Welcome!
Answer:
the answer is B bro
Step-by-step explanation:
Graph: y - 10 = -2(x – 10) Y χ y 30 20 10 X -10 10 20 -10 Draw Click or tap the graph to plot a point.
Answers
a new surgical procedure is said to be successful 90% of the time. suppose the procedure is performed five times. assume that the results of each procedure are independent of one another. in this binomial distribution application, which excel statement will find the probability of between 2 and 4, inclusively, successful surgical procedures?
Answers
The required probability is p(xS 2) =F(2).
Given that,
90% of the time, a novel surgical technique is deemed to be successful. Imagine that the technique is carried out five times. Count on the outcomes of each procedure being distinct from one another. in this application of the binomial distribution
BINOMDIST (2,5,90%, TRUE) is used to find the probability of 2 or fewer
to get 0.00856 because x =2 and n= 5 and TRUE indicates the cumulative
and the required probability is p(xS 2) =F(2)
Therefore, the required probability is p(xS 2) =F(2).
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Use the distributive property to simplity 3 (4x + 8).
7x+8
7x + 24
12x + 8
12x + 24
Answers
Answer:
d) 12x + 24
Step-by-step explanation:
Explanation:
A box has dimensions of 2.5 cm by 3.0 cm by 4.0 cm. The volume of the box in milliliters and liters is:
Answers
Answer:
30000 milliliters
0.03 liters
Step-by-step explanation:
The volume of the box is 2.5 x 3.0 x 4.0 = 30 cc
There are 1000 ml in 1 cc so 30cc = 30 x 1000 = 30000 ml
There are 1000 cc in 1 liter so 30 cc = 30/1000 = 0.03 liters
The volume of the box is 30 mL or 0.03 L.
What is volume?Volume is a metric magnitude that is defined as the extension in three dimensions of a region of space. Volume is defined as the amount of space occupied by the object or figure in three-dimensional space. Volume is measured in cubic units.
The volume of this prism depends on its three dimensions and is calculated as the multiplication of these dimensions,
Volume= Dimension 1× Dimension 2× Dimension 3
The volume of the box = 2.5 x 3.0 x 4.0 = 30 cc
There are 1000 ml in 1 cc so 30cc = 30 x 1000 = 30000 ml
There are 1000 cc in 1 liter so 30 cc = 30/1000 = 0.03 liters
Hence, the volume of the box is 30 mL or 0.03 L.
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Whitch of the following equations best describes the line containing all three points ?
Answers
Need Help ASAP
The cost of employing an electrician who charges $70 per hour if he worked from 12:30pm until 3:00 pm.
Answers
70*2,5=175$
Describe the long run behavior of f(x)=5(2)x+1:
As x→−[infinity], f(x) =
As x→[infinity], f(x) =
Answers
The long run behavior of the function f(x)=5(2)x+1 is that it approaches 1 as x approaches negative infinity and it approaches infinity as x approaches positive infinity.
The long-term behavior of the function f(x)=5(2)x+1 can be discovered by examining how the function behaves as x gets closer to negative and positive infinity.
As x→−[infinity], f(x) = 5(2)^ -∞+1 = 5(0)+1 = 1
As x approaches negative infinity, the value of the function approaches 1.
As x→[infinity], f(x) = 5(2)^ ∞+1 = 5(∞)+1 = ∞
As x approaches positive infinity, the value of the function approaches infinity.
As a result, the function f(x)=5(2)x+1 behaves in the long run in such a way that it approaches 1 as x approaches negative infinity and infinity as x approaches positive infinity.
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An arithmetic sequence is shown below.
−7,−3,1,5,9,...
Which represents an explicit formula for this sequence.
Answers
The following cone has a slant height of 17
cm and a radius of 8
cm.
What is the volume of the cone?
Responses
480π
320π
544π
Answers
The formula for the volume of a cone is:
V = (1/3)πr²h
where r is the radius of the base, h is the height of the cone, and π is pi.
In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:
h² = s² - r²
h² = 17² - 8²
h² = 225
h = 15
Now that we have the height, we can plug in the values for r and h into the formula for the volume:
V = (1/3)π(8²)(15)
V = (1/3)π(64)(15)
V = (1/3)(960π)
V = 320π
Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.
what are the five lessons or skills you learned in your t.l.e
9
Answers
Answer:
Step-by-step explanation:
Throughout life, we learn lessons and skills that drastically change the way we view the world and the decisions we make. For me, the lessons and skills that were the most important were the following ...
Don't be jealous of what others have.Invest as much as you can in your 20'sLearn to codeLearn to play GuitarHave goals.All of these lessons and skills have helped me visualize a future that would make me happy and has even opened some doors which would help make such a future a reality.
Which of the following are examples of rational numbers? Select all that apply.
√4+√16
√5 +√36
√9+√24
2* √4
√49 • √81
3√12
Answers
The rational numbers in the list of options are √4+√16, 2* √4 and √49 • √81
Selecting the rational numbers
The examples of rational numbers among the given options are:
2√4: √4 is equal to 2, so 2√4 = 2*2 = 4, which is a rational number.√49 • √81: √49 is equal to 7 and √81 is equal to 9, so √49 • √81 = 7 • 9 = 63, which is a rational number.√4+√16: √4 is equal to 2 and √16 is equal to 4, so √4+√16 = 2 + 4 = 6, which is a rational number.The other options are not rational numbers:
√5+√36: √5 is an irrational number, so √5+√36 is not a rational number.√9+√24: √24 is an irrational number, so √9+√24 is not a rational number.3√12: √12 is equal to 2√3, so 3√12 = 3 • 2√3 = 6√3, which is not a rational number.Read more about rational numbers at
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Q4. Which system of inequalities describes the graph?
Answers
Answer:
Step-by-step explanation:
Here is the set of numbers: 4, 5, 11, 12, 5, 38, 44
Based on your results of Mean and Median, is the Mean or Median larger in value?
Please answer with complete sentence(s), which explains why and how you made your choice.
Answers
Based on the results of Mean and Median, we can say that Mean is larger than median in value .
Mean of n observations can be calculated using the formula
Mean = (sum of all observations)/(number of observations) .
After arranging the data in ascending or descending order , the middle value can be called as Median .
In the question ,
the set of numbers is given as 4, 5, 11, 12, 5, 38, 44
rewriting them in ascending order ,we get 4, 5, 5, 11, 12 ,38 ,44 .
the sum of all the number = 4+5+5+11+12+38+44
= 119
number of observations = 7
hence the mean = 119/7 = 17
So, mean = 17
from the set of numbers 4, 5, 5, 11, 12 ,38 ,44 we can see that
the middle value of the set of numbers is 11 .
So , median = 11 .
On comparing the mean = 17 and the median = 11 ,
we can say that the mean is greater than median.
Therefore , based on the results of Mean and Median, we can say that
Mean is larger than median in value .
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1
If f(x) = 3x + 2 and g(x)=x+1, which expression is equivalent to (fog)(x)?
Answers
Answer:
(3x+2)^2+1
Step-by-step explanation:
(f°g)(x) =g(f(x)) =g(3x+2)=(3x+2)^2 +1
Answer:
3(x+1) + 2
Step-by-step explanation:
Determine the solution to the following set of linear equations by using the graph below
a) 2x + y = 5
2x - 2y = 2
Answers
Answer:
(2,1)
Step-by-step explanation:
Well first we single out y or x in one of the equations,
we’ll use 2x + y = 5 and single out y.
2x + y = 5
-2x to both sides
y = -2x + 5
So we can plug in -2x + 5 into y in 2x - 2y = 2.
2x - 2(-2x + 5) = 2
2x + 4x - 10 = 2
combine like terms,
6x - 10 = 2
Communicarice property
+10 to both sides
6x = 12
divide 6 to both sides
x = 2
If x is 2 we can plug 2 in for x in 2x + y = 5.
2(2) + y = 5
4 + y = 5
-4 to both sides
y = 1
(2,1)
Thus,
the solution is (2,1).
Hope this helps :)
in 20 seconds a rollercoaster goes up a 100-meter hill then down 72 meters and back up a 48-meter rise how much higher or lower from the start of the ride is the coaster after 20 seconds?
Answers
Darrell practiced the 50-meter freestyle and predicted how fast he would swim in a race. He was excited when he finished his first race in 25 seconds. His prediction was 8% longer than his actual time. What was Darrell's predicted time?
Answers
His prediction was 8% longer than his actual time. Then the predicted time will be 27 seconds.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
He was excited when he finished his first race in 25 seconds. His prediction was 8% longer than his actual time.
Let 'T' be the prediction time. Then the equation is given as,
T = 1.08 x 25
T = 27 seconds
His prediction was 8% longer than his actual time. Then the predicted time will be 27 seconds.
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What is the area of a triangle whose sides are 25, 5, and 2?
Answers
Answer:
i think its 125 but dont trust me
Step-by-step explanation:
so i added 25 , 5 , 2 and divided by two since the formula of a triangle is base x height / 2
If a family of 4 produces 3 bags of trash each week, how many of the same size bags of trash would you expect a family of 6 to produce each week?
Answers
Answer:
4 and a half
Step-by-step explanation:
4 people in a family produce 3 bags. 3/4 bags per person
3/4*6 = 18/4 or 4 and a half bags
Answer:
4.5 bags of trash
Step-by-step explanation:
We know
A family of 4 produces 3 bags of trash each week.
3 / 4 = 0.75 bags of trash
So, each produced 0.75 bags of trash.
How many of the same size bags of trash would you expect a family of 6 to produce each week?
6 x 0.75 = 4.5 bags of trash
So, the answer is 4.5 bags of trash
pls help me if ur able to thanks
Write the quadratic function f(x)=-3x^2-3x-46
in the form f(x)=a•(x-h)^2+k
Answers
Answer:
-3(x+0.5)^2-181/4 (if I calculated correctly)
Step-by-step explanation:
f(x)=-3x^2-3x-46
=-3(x^2+x+46/3)
=-3(x+0.5)^2-(0.5)^2+46/3
=-3(x+0.5)^2+181/12
=-3(x+0.5)^2-181/4
What is m∠PQR
need ASAP
Answers
Answer:
134
Step-by-step explanation:
Its 134, i did the math and my old answer had the explanation, but someone deleted it.
At the 6th grade school dance, there are 130 boys, 100 girls, and 20 adults. Write the ratio of the number of girls to the number of adults.
Answers
The ratio of the number of girls to the number of adults is 5 : 1.
What is the ratio?Ratio is used to compare two or more values together. Ratio shows the frequency of one number compared to the frequency of another number. The sign that is used to represent ratio is :.
The ratio of the number of girls to the number of adults = number of girls : number of adults
number of girls = 100
number of adults = 20
The ratio of the number of girls to the number of adults = 100 : 20
Express the ratio in its simplest form. To do this, divide both numbers by the greatest common factor of 100 and 20. The greatest common factor of 100 and 20 is 20.
The ratio of the number of girls to the number of adults = 5 : 1
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Is Paul's Online Math Notes a good enough source for self-teaching calculus 3 and ODE?
Answers
Yes, Paul's Online Math Notes is a good enough source for self-teaching calculus 3 and ODE.
The site is well-organized, with clear explanations and plenty of examples and practice problems. It also includes a section on differential equations, which is helpful for those studying ODE.
However, it is always a good idea to supplement your learning with additional resources, such as textbooks, online videos, and practice problems from other sources.
This will help you gain a deeper understanding of the material and ensure that you are well-prepared for exams.
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Simplify the following (minimum shown in parenthesis.): xyz + xyz' + x'yz' + x'y'z (3 terms, 7 literals)
Answers
The concept of simplifying a Boolean expression involves reducing the expression to its most concise form by applying logical rules and simplification techniques. This helps in reducing complexity, improving readability, and optimizing logic circuits by eliminating redundant terms and literals.
The simplified expression consists of two terms with a total of 5 literals.
To simplify the expression:
xyz + xyz' + x'yz' + x'y'z
We can apply Boolean algebra rules to simplify the terms:
Combine terms with common literals:
xyz + xyz' = xy(z + z') = xy
Combine terms with common literals:
x'yz' + x'y'z = x'z(y + y') = x'z
Now we have simplified the expression to:
xy + x'z
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