We can say that after answering the offered question Therefore, the equation constant of proportionality in this scenario is 11.25.
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
In this case, we may use the following formula to calculate the proportionality constant:
proportionality constant = output/input
where the output is John's pay and the input is the number of hours he worked.
As a result, the proportionality constant is:
Paycheck/hours worked = proportionality constant
proportionality constant = 450/40
proportionality constant = 11.25
As a result, the proportionality constant in this scenario is 11.25.
In this case, we may use the following formula to calculate the proportionality constant:
proportionality constant = output/input
where the output is John's pay and the input is the number of hours he worked.
As a result, the proportionality constant is:
Paycheck/hours worked = proportionality constant
proportionality constant = 450/40
proportionality constant = 11.25
Therefore, the constant of proportionality in this scenario is 11.25.
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There are N people, numbered from 0 to N-1, playing a game. The K-th person is assigned the letter S[K]. At the beginning the 0th person sends a message, consisting of a single letter S[0], to the A[0]-th person. When the K-th person receives the message, they append their letter S[K] to the message and forward it to A[K]. The game ends when the 0th person receives the message. Find the final message
The final message would be "ABCE"
It prompts the user to enter the number of people (N), the letters assigned to each person (S), and the forwarding indices (A).
It initializes a message array with the first letter (S[0]).
It follows the forwarding chain until it reaches the 0th person. For each person K in the chain, it appends the corresponding letter (S[A[K]]) to the message.
It terminates the message with a null character (\0) and prints the final message.
The C program will be:
#include <stdio.h>
#include <stdlib.h>
#define MAX_N 100
int main() {
char S[MAX_N];
int A[MAX_N];
int N, K;
printf("Enter the number of people (N): ");
scanf("%d", &N);
printf("Enter the letter assigned to each person:\n");
for (K = 0; K < N; K++) {
printf("S[%d]: ", K);
scanf(" %c", &S[K]);
}
printf("Enter the forwarding indices:\n");
for (K = 0; K < N; K++) {
printf("A[%d]: ", K);
scanf("%d", &A[K]);
}
char message[MAX_N];
message[0] = S[0];
K = 0;
while (A[K] != 0) {
message[K+1] = S[A[K]];
K = A[K];
}
message[K+1] = '\0';
printf("Final message: %s\n", message);
return 0;
}
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(a) Assume that the carrying capacity for the US population is 800 million. Use it and the fact that the population was 282 million in 2000 to formulate a logistic model for the US population. (Let t = 0 correspond to the year 2000. Use k for your constant.
P(t) = _____ millions
(b) Determine the value of k in your model by using the fact that the population in 2010 was 309 million.
k= _____
(c) Use your model to predict the US population in the years 2100 and 2300.
year 2100:
million
year 2300:
million
(d) Use your model to predict the year in which the US population will exceed 600 million.
By looking at the logistic model of US population, it can be said that the population will exceed 600 million by the year 2148.
(a) The logistic model for the US population is given by P(t) = (C/1 + Ae^(-kt)), where C is the carrying capacity, A is a constant, k is a constant, and t is time. Given that the carrying capacity for the US population is 800 million and the population was 282 million in 2000, we can formulate the logistic model as follows:
P(t) = (800/1 + Ae^(-kt))
To find the value of A, we can plug in the initial conditions. Let t = 0 correspond to the year 2000 and P(0) = 282:
282 = (800/1 + Ae^(0))
282 = (800/A + 1)
A = (800/282) - 1
A = 1.84
Therefore, the logistic model for the US population is:
P(t) = (800/1 + 1.84e^(-kt))
(b) To determine the value of k in the model, we can use the fact that the population in 2010 was 309 million. Let t = 10 correspond to the year 2010 and P(10) = 309:
309 = (800/1 + 1.84e^(-10k))
1.84e^(-10k) = (800/309) - 1
e^(-10k) = 0.593/1.84
-10k = ln(0.593/1.84)
k = -0.076
Therefore, the value of k in the model is k = -0.076.
(c) To predict the US population in the years 2100 and 2300, we can plug in the values of t = 100 and t = 300 into the model:
P(100) = (800/1 + 1.84e^(-100(-0.076))) = 535.7 million
P(300) = (800/1 + 1.84e^(-300(-0.076))) = 762.2 million
Therefore, the predicted US population in the year 2100 is 535.7 million and in the year 2300 is 762.2 million.
(d) To predict the year in which the US population will exceed 600 million, we can set P(t) > 600 and solve for t:
(800/1 + 1.84e^(-kt)) > 600
1.84e^(-kt) < (800/600) - 1
e^(-kt) < 0.333/1.84
-kt < ln(0.333/1.84)
t > -ln(0.333/1.84)/k
Using the value of k from part (b), we get:
t > -ln(0.333/1.84)/(-0.076) = 147.7
Therefore, the population of US will exceed 600 million by the year 2148.
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The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = 3 sine (StartFraction pi Over 2 EndFraction (t + 2)) + 5. Which of the following is the graph of this equation?
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (2, 8), and then decreases to (6, 2).
On a coordinate plane, a curve crosses the y-axis at (0, 8). It decreases to (4, 2), and then increases to (8, 8).
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (1, 8), and then decreases to (3, 2).
On a coordinate plane, a curve crosses the y-axis at (0, 5). It decreases to (2, 1), and then increases to (3, 8).
The coordinate plane of curve crosses the y-axis at (0, 5), it increases to (2, 8), and then decreases to (6, 2). The graph of the equation, shown below.
What is the term graph means?The term "graph" can refer to a visual representation of data or information, typically in the form of a diagram or chart. Graphs can be used to show relationships or patterns between different sets of data.
For the given equation,
[tex]h=3Sin [\frac{\pi }{2} (t+2)] +5[/tex]
Follow the steps for drawing the graph,
Choose a range of values for t that we want to graph. Since the period of the oscillation is 2 seconds, we can choose a range of t values that spans one or more full periods of the oscillation.Substitute each t value into the equation to find the corresponding h value. For example, when t = 0,[tex]h = 3 Sin [\frac{\pi }{2} (0 + 2)] + 5 = 3 Sin [\pi] + 5 = 5[/tex]
This means that when the ball is at the midpoint of its oscillation (i.e., at time t = 0), its height is 5 feet above the equilibrium position.
Plot the (t, h) pairs as points on a graph, with t values on the x-axis and h values on the y-axis.Connect the plotted points with a smooth curve to create the graph of the equation.The coordinate plane of curve crosses the y-axis at (0, 5), it increases to (2, 8), and then decreases to (6, 2).Using these steps, we can create the graph of the equation, which looks like the below diagram.
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work out b-a when a-b=5
(that's the question)
Answer:
b - a = -5
Step-by-step explanation:
I am not sure if I am right, but I am thinking -5
a = 0 and b - -5
a -b = 5
0 - (-5) = 5
5 = 5 If this is true, then
b - a would be
-5 - 0 = -5
-5 = -5
Helping in the name of Jesus.
Answer:
-5
Step-by-step explanation:
We know that a - b = 5,
so to find b - a, we can rearrange this equation as follows:
a - b = 5
a = b + 5
b = a - 5
Therefore, b - a = (a - 5) - a
= -5
So, b - a = -5.
Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary. 27 , 45 , 75 , . . . 27,45,75,...
The sum of the first 8 terms of the sequence is 720.
What is sequence ?A sequence is a set of numbers that are arranged in a specific order, according to some rule or pattern. Each number in the sequence is called a term, and the position of the term in the sequence is called its index or subscript. Sequences can be either finite or infinite.
According to the given information :We can see that this is an arithmetic sequence with a first term a = 27 and a common difference d = 18. To find the sum of the first 8 terms of the sequence, we can use the formula for the sum of an arithmetic sequence:
Sn = n/2[2a + (n-1)d]
where Sn is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.
Plugging in the values we know, we get:
S8 = 8/2[2(27) + (8-1)(18)]
= 4[54 + 126]
= 4(180)
= 720
Therefore, the sum of the first 8 terms of the sequence is 720.
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PLEASE SHOW WORK!!!!!!!!!
The angle between the cable and the ground is given by the trigonometric function tan⁻¹(7/4). Option E is the correct answer.
What is angle?When two rays are united at a common point, an angle is created. The two rays are referred to as the arms of the angle, while the common point is referred to as the node or vertex. The symbol "" stands for the angle. The Latin word "Angulus" is where the term "angle" originated. The construction of an angle is a type of geometric shape made by connecting two rays at their termini.
The angle between the cable and the ground is given by the trigonometric function tangent.
Tan gives the relationship between opposite side and adjacent side.
Thus,
Tan A = 7/4
A = tan⁻¹(7/4)
Hence, the angle between the cable and the ground is given by the trigonometric function tan⁻¹(7/4). Option E is the correct answer.
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Please help me. Offering brainlest!
Answer:
64cm³
Step-by-step explanation:
Surface area of a cube is 6a²
6a² = 96
Divide both sides by 6
a² = 16
Square root of both sides
a = 4cm
Volume of a cube is a³
Volume =4³
Volume 64cm³
please help me on this please
Answer:
[tex]\boxed{\mbox{\large{\quad 54\quad }}} \quad\text{ 25\% of last year's attendance}\\\\\boxed{\mbox{\large{\quad 216\quad }}}\quad\text{100\% of last year's attendance}\\\\[/tex]
Step-by-step explanation:
If we let x be the number of attendees last year then since this year's attendees 270 is 125% of x we get
125% of x = 270
125% as a decimal = 125/100 = 1.25
So we get the equation
1.25x = 270
Divide by 1.25 to get
1.25x/1.25 = 270/1.25
x = 216
So there were a total of 216 attendees last year
25% of last year attendees = 0.25 x 216 = 54
give answers to these questions, and thereby flesh out a coordinate descent method. for (i), your solution should do something at least a bit more adaptive than merely picking a coordinate at random.
To flesh out a coordinate descent method : (i) One common approach is to choose coordinate with the largest gradient. (ii) One common approach is to use a line search, where we try out step sizes along the chosen coordinate and select the one that leads to the largest decrease in the function value. (iii) One common stopping criterion is to stop when the change in function value.
This can be done by computing the partial derivatives of the function with respect to each coordinate, and selecting the one with the largest absolute value. This approach is known as "greedy" coordinate descent, and it can help speed up convergence by focusing on the most important directions.
This approach can be more computationally efficient, since it doesn't require computing the gradient at each step. Another approach is to use a fixed step size, which can be simpler to implement but may not always lead to the best results.
By choosing the coordinate to optimize along, determining the step size, and setting a stopping criterion, we can develop a coordinate descent method that is well-suited to our particular optimization problem.
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Simplify. Express your answer using positive exponents. m9m4
Answer:
[tex] {m}^{9} {m}^{4} = {m}^{9 + 4} = {m}^{13} [/tex]
A sports memorabilia store makes $6 profit on each football it sells and $5.50 profit on each baseball it sells. In a typical month, it sells between 35 and 45 footballs and between 40 and 55 baseballs. The store can stock no more than 80 balls total during a single month. What is the maximum profit the store can make from selling footballs and baseballs in a typical month?
$457.50
$460.00
$462.50
$572.50
Answer: C $462.50
Step-by-step explanation:
It's $462.50 because since $6 has a higher profit you would want to try and sell more of that product (The football). So $6 times 45 is 270. And the max number of balls the store can have is 80, 80 minus 45 is 35 so there can only 35 baseballs left. 35 times $5.50 is 192.50. Lastly, you add the two products, and you get 462.50.
The maximum profit the store can make from selling footballs and baseballs in a typical month is $462.50.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example: so
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Let's say the store sells x footballs and y baseballs.
The total number of balls sold can be expressed as x + y ≤ 80.
Also, we know that 35 ≤ x ≤ 45 and 40 ≤ y ≤ 55.
To maximize the profit, the store should sell the maximum number of footballs and baseballs that it can stock.
From the constraints, we see that the maximum number of footballs the store can sell is 45 and the maximum number of baseballs it can sell is 55, which together make a total of 100 balls.
However, this exceeds the 80-ball limit, so we need to adjust the numbers.
Let's say the store sells 45 footballs and y baseballs.
Then, y ≤ 35 since 45 + 35 = 80, which is the maximum number of balls the store can stock.
Similarly, let's say the store sells x footballs and 55 baseballs.
Then, x ≤ 25 since 25 + 55 = 80.
To find the maximum profit, we need to calculate the profit from selling 45 footballs and 35 baseballs, which will give the highest profit among the feasible combinations.
The profit from selling 45 footballs is 45 × $6 = $270.
The profit from selling 35 baseballs is 35 × $5.50 = $192.50.
The total profit is $270 + $192.50 = $462.50.
Therefore,
The maximum profit the store can make from selling footballs and baseballs in a typical month is $462.50.
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2.22 consider flipping coins until either two heads hh or heads then tails ht/th first occurs. by conditioning on the first coin toss, find the probability that ht/th occurs before hh.
The probability that ht/th occurs before hh, given that the first coin toss is H or T, is 1/4.
To find the probability that ht/th occurs before hh, by conditioning on the first coin toss is as follows: The sample space can be represented as T or H. 1) If the first toss is a T, then the following toss should be an H to obtain the sequence ht, which is what we want. The probability of this event is 1/2. If the second toss is T, we get the sequence tt, and the process repeats.
2) If the first toss is an H, then we need to obtain the sequence th. The probability of this event is 1/2. If we obtain the sequence hh, the process repeats. We now have two cases that must be considered: case 1: If the first toss is a tail, then the probability that ht occurs before hh can be calculated as follows:
P(ht occurs before hh|first toss is a T) = P(ht occurs before hh|TT)P(TT)+ P(ht occurs before hh|HT)P(HT)= 0 * 1/4 + (1/2) * 1/2= 1/4Therefore, the probability of ht occurring before hh, given that the first toss is a T, is 1/4. case 2: If the first toss is an H, then the probability that ht occurs before hh can be calculated as follows:
P(ht occurs before hh|first toss is an H) = P(ht occurs before hh|TH)P(TH)+ P(ht occurs before hh|HH)P(HH)= (1/2) * 1/2 + 0 * 1/2= 1/4Therefore, the probability of ht occurring before hh, given that the first toss is an H, is 1/4. Therefore, the probability that ht occurs before hh, given that the first coin toss is H or T, is 1/4.
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Solve the equation:
27 - h = 14
H = [?]
Answer:
h=13
Step-by-step explanation:
have a good day
Answer:
13
Step-by-step explanation:
27-h=14
-h=14-27
-h=-13
To get rid of the negative sign, divide both sides by -1
Therefore h=13
Calculate the correlation coefficient of the following data:
X
1
4
8
6
2
y
9
16
22
24
12
Answer:
0.177
Step-by-step explanation:
A perfect correlation is 1. So .998 or even .863 is a good correlation.
since our decimal isn't close to that at all, we have a weak positive correlation.
gcf of 17,22, and 46
Answer:
1
Step-by-step explanation:
17 is a prime number, so only 1 and 17 are its factors. 17 is not a factor of either 22 or 46, but 1 is.
What are the solutions to the following quadratic?
5x² + 18x=25x+15+3x²
(x+5)(2x-3)
O (5,-3/2)
(x - 5)(2x+3)
(-5,3/2)
Answer:
We can start by simplifying both sides of the equation:
5x² + 18x = 25x + 15 + 3x²
2x² - 7x - 15 = 0
Now we need to factor this quadratic equation:
2x² - 7x - 15 = (2x + 3)(x - 5)
Setting each factor equal to zero gives us the solutions:
2x + 3 = 0 or x - 5 = 0
Solving for x, we get:
x = -3/2 or x = 5
Therefore, the solutions to the quadratic equation are x = -3/2 and x = 5.
So, the correct answer is (x - 5)(2x+3).
in the science fiction section of the bookstore there are 19 bookcases each bookcase has 72 books in it how many science fiction books are there in the bookstore
Answer: 1,368 books
Explanation: To find the total number of science fiction books in the bookstore, you need to multiply the number of bookcases by the number of books in each bookcase. In this case, there are 19 bookcases, each containing 72 books:
19 bookcases × 72 books per bookcase = 1,368 books
So, there are 1,368 science fiction books in the bookstore.
Question 18
5 pts
An airplane flying into a headwind travels 1176.00 miles in 4 hours and 54 minutes. On the return flight, the
distance is traveled in 4 hours. Find the airspeed of the plane and the speed of the wind, assuming that both
remain constant.
plane speed = 282 mph; wind speed = 274 mph
plane speed = 267.00 mph; wind speed = 27.00 mph
plane speed = 282 mph; wind speed = 27.00 mph
plane speed = 244 mph; wind speed = 256 mph
plane speed = 244 mph; wind speed = 27.00 mph
Using the system of equations, we found that :
plane speed = 267.00 mph; wind speed = 27.00 mph
What is meant by an equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
The distance travelled = 1176.00 miles
Time taken = 4 hours and 54 minutes = 4*60 + 54 = 294 minutes
The times taken for return flight = 4 hours = 240 minutes
Let,
x = speed of the plane
y = speed of the wind
In a headwind the speed reduces.
So the relative speed of the plane is (x-y)
distance = speed * time
1176 = (x-y) * 294
x-y = 4
Now for the return flight, the wind is tailwind and the speed increases.
So the relative speed of the plane is (x+y).
1176 = (x+y) * 240
x + y = 4.9
Now we have a system of equations.
x - y = 4
x + y = 4.9
Adding,
2x = 8.9
x = 4.45 miles/min = 4.45 * 60 miles/hour = 267 miles/hour
and
y = 4.9 - x = 4.9 - 4.45 = 0.45 miles/min = 0.45*60 = 27 miles/hour
Therefore using the system of equations, we found that :
plane speed = 267.00 mph; wind speed = 27.00 mph
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Please ASAP Help
Will mark brainlest due at 12:00
Answer: -2
Step-by-step explanation:
Answer:
plot the point at -2
Step-by-step explanation:
WHAT IS THE ANSWER?
HELP ME PLeese
Answer:
Step-by-step explanation:
An African elephant weighs 5,500 pounds. How many ounces is that?
An African elephant weighs 88,000 ounces. To convert pounds to ounces, we need to know the conversion factor between the two units.
There are 16 ounces in one pound, which means we can convert pounds to ounces by multiplying the weight in pounds by 16. A pound is equal to 28 grams. A one-quarter ounce contains seven grams. A half-ounce has 14 grams in it. One-eighth of an ounce has 3.5 grams.
In this case, the African elephant weighs 5,500 pounds. To find out how many ounces that is, we can multiply 5,500 by 16:
5,500 pounds x 16 ounces/pound = 88,000 ouncesTherefore, the African elephant weighs 88,000 ounces.
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You pick a card at random, put it back, and then pick another card at random.
2
3
4
5
6
What is the probability of picking a 4 and then picking a number greater than 4?
Write your answer as a percentage.
Answer:8%
Step-by-step explanation:Since the cards are put back after each pick, the two picks are independent events.
The probability of picking a 4 on the first pick is 1/5, as there is one card with a value of 4 out of five cards in total.
The probability of picking a number greater than 4 on the second pick is 2/5, as there are two cards with values greater than 4 (5 and 6) out of five cards in total.
The probability of both events occurring (picking a 4 and then a number greater than 4) is the product of the probabilities of each event:
1/5 x 2/5 = 2/25
So the probability of picking a 4 and then picking a number greater than 4 is 2/25.
To express this as a percentage, we can multiply by 100:
2/25 x 100 = 8%
Therefore, the probability of picking a 4 and then picking a number greater than 4 is 8%.
What is the correct way to name the following image?
The correct way to name the image is Southwest Vector BA, indicating the direction of the vector from B to A.
How do we name the vector diagram?
Vector BA : This notation indicates that the vector starts at point B and ends at point A, and it is read as "vector B-A" or "B-A vector". The order of the letters reflects the direction of the arrow, from B to A.
Arrow SW or SW arrow: This notation indicates the direction of the vector, which is towards the southwest, and it is read as "arrow southwest" or "southwest arrow". The order of the letters reflects the direction of the vector, from the northwest to the southeast.
Southwest Vector BA : This notation combines both the direction and the points of the arrow, and it is read as "southwest vector B-A" or "B-A southwest vector". The order of the words reflects the direction of the vector, from the northwest to the southeast, and the order of the letters reflects the starting and ending points of the arrow.
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g(x) = 4x - 1
f(x) = x + 3
Find (gof)(x/2)
For the function (g o f)(x/2) the value is obtained as 2x + 11.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The function g(x) is given as g(x) = 4x - 1.
The function f(x) is given as f(x) = x + 3.
To find (g o f)(x/2), we need to first find f(x/2) and then substitute this value into g(x) in place of x.
f(x) = x + 3
So, f(x/2) = (x/2) + 3
Now, substitute this into the equation of g(x) in place of x -
g(x) = 4x - 1
g(f(x/2)) = 4(f(x/2)) - 1
= 4((x/2) + 3) - 1 (substituting f(x/2))
= (4x/2 + 12) - 1
= 2x + 11
Therefore, the value is (g o f)(x/2) = 2x + 11.
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Please help...I have absolutely no idea what Im doing.
By handing the survey to every third person, Kyle used a: 1. nonrandom sampling.
Each student in his class had an unequal chance of being selected to receive the survey.
A statement that best explain why Kyle's survey may be biased is: 3. Two out of every three students entering Kyle's class didn't receive the survey.
What are the types of sampling?In Mathematics and Statistics, there are different types of sampling used by researchers and these include the following;
Stratified sampling.Cluster sampling.Random sampling.Convenience sampling.Systematic sampling.Based on the information provided about the survey conducted by Kyle, we can reasonably infer and logically deduce that a systematic sampling method (nonrandom sampling) was adopted.
Consequently, the survey may be considered as being biased because each student in Kyle's class had an unequal chance of being selected to receive the survey.
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A carton of juice has spilled on a tile floor. The juice flow can be expressed with the function , where t represents time in minutes and j represents how far the juice is spreading. The flowing juice is creating a circular pattern on the tile. The area of the pattern can be expressed as .
Part A: Find the area of the circle of spilled juice as a function of time, or . Show your work. (6 points)
Part B: How large is the area of spilled juice after 2 minutes? You may use 3.14 to approximate in this problem. (4 points)
Use the equation editor in your responses. (10 points)
Finding the area of the circle of spilled juice as a function of time is: j(t) = πr(t)²
What is Equation?An equation is mathematical statement that asserts equality of two expressions. It contains one or more variables, and typically consists of terms on either side of equals sign.
Part A:
Let the radius of the circular pattern be r at time t. Then, we have:
j = πr²
Taking the derivative of both sides with respect to time, we get:
dj/dt = 2πr(dr/dt)
Since the rate of change of the radius is unknown, we can express it in terms of the rate of change of j:
dr/dt = (1/2πr)(dj/dt)
Substituting this expression for dr/dt back into our original equation, we get:
j = πr²
dj/dt = π(2r)(dr/dt)
dj/dt = 2πr(dr/dt)
dj/dt = 2πr(1/2πr)(dj/dt)
dj/dt = dj/dt
Therefore, the area of the spilled juice as a function of time is:
j(t) = πr(t)²
Part B:
If we assume that the rate of change of the radius is constant over the first 2 minutes, we can use the formula for the area of a circle to find the area of the spilled juice after 2 minutes:
j(2) = πr(2)²
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There are 70 students traveling to a soccer tournament. All of the vans can take 9 students each. How many vans are needed to take all of the students to the tournament?
Answer:
They need 8 vans.
Step-by-step explanation:
8 × 9 is 72. If you have 8 vans that carry 9 students each, you will have room for 72 students. Then you have enough room for 70 students.
If you only have 7 vans you can only transport 7 × 9, or 63 students. That is not enough. They need 8 vans.
Shirley's water bottle is half full. She pours
it into another bottle that is one-third full,
and it fills that bottle. If the second bottle
holds 2 quarts, how much did the first
bottle hold?
Answer:
Shirley's water bottle holds 4 quarts when it is half full.
Step-by-Step-Explanation
If the second bottle is one-third full and holds 2 quarts, then it means that it can hold a total of 2 / (1/3) = 6 quarts when completely full.
Let's call the amount of water in Shirley's bottle "x" quarts. We know that when she pours it into the second bottle, it becomes completely full with 6 quarts. So we can set up the equation:
x + 2 = 6
Solving for x, we get:
x = 6 - 2
x = 4
I need help with this.
According to the information, the scale that you would use for the pictogram would be 10 for each symbol.
Which scale is the best for the pictogram on the table?To choose the most appropriate pictogram for the information in the table, we must take the data into account. In this case, we must find a divisor number of all the numbers to take it as the value of the scale. In this case we can take 10, because it divides all the numbers as shown below:
80 / 10 = 840 / 10 = 470 / 10 = 760 / 10 = 6According to the above, 8 sports symbols, 4 reading symbols, 7 game symbols and 6 music symbols should be used to represent the values, taking into account that each symbol is equal to 10 units.
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Find value of x in simplest form
The value of x in its simplest form is x = 67√2 = 94.75.
What is sine function?The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilise the sine function. The ratio between the side perpendicular to the angle and the hypotenuse is known as the sine of an angle in a right-angled triangle.
The relation between the opposite side and the hypotenuse is given by the sine function.
Thus,
sin (45) = opposite side / hypotenuse = 67 / x
1 / √2 = 67/x
x = 67√2 = 94.75
Hence, the value of x in its simplest form is x = 67√2 = 94.75.
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