The solution to the question on the equilibrium of the cheese and bagels have been given below
How to get the equilibriuma) If the equilibrium price of cream cheese and the equilibrium quantity of bagels have both risen, this could be caused by a fall in the price of flour, one of the inputs used to produce bagels.
This decrease in the cost of production would cause the supply of bagels to increase, leading to a rightward shift in the supply curve. At the same time, the demand for bagels would increase as consumers substitute away from other breakfast foods and toward bagels, leading to a rightward shift in the demand curve.
These two shifts would result in a higher equilibrium price for cream cheese, since bagels and cream cheese are complements. The increased demand for bagels would lead to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward.
The diagram below illustrates this relationship. The initial equilibrium is at point A, with a price of P1 and a quantity of Q1. After the decrease in the price of flour, the supply curve for bagels shifts rightward to S', and the demand curve for bagels shifts rightward to D'. The new equilibrium is at point B, with a higher price of P2 and a higher quantity of Q2. The increase in the demand for bagels leads to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward to D'''. The new equilibrium for cream cheese is at point C, with a higher price of P3 and a higher quantity of Q3.
b) If the equilibrium price of cream cheese has risen but the equilibrium quantity of bagels has fallen, this could be caused by a rise in the price of milk, one of the inputs used to produce cream cheese.
This increase in the cost of production would cause the supply of cream cheese to decrease, leading to a leftward shift in the supply curve. At the same time, the demand for cream cheese would decrease as consumers substitute away from cream cheese and toward other breakfast foods, leading to a leftward shift in the demand curve.
These two shifts would result in a higher price for cream cheese, but a lower quantity of bagels consumed. The decreased demand for cream cheese would lead to a decrease in the demand for bagels, causing the demand curve for bagels to shift leftward.
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The opportunity cost of treating HIV/AIDS cases increases as more HIV/AIDS cases are treated.
Draw a curve that shows the production possibilities for the world economy that produces HIV/AIDS treatments and other goods and services. Label the curve PPF0.
Then draw the PPF that shows the effect of an advance in technology on HIV/AIDS treatments. Label the curve PPF1.
On solving the provided question, we can say that from the graphs The curve preceding technological advancement is called PPF0. PPF1 is the curve following technological advancement.
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
The curve preceding technological advancement is called PPF0. PPF1 is the curve following technological advancement.
Prior to technological advancement, the opportunity cost of treating HIV/AIDS rises as the world deviates from its PPF. The potential cost of treating more HIV/AIDS cases falls as a result of technological advancements since less other commodities and services must be sacrificed in order to treat more HIV/AIDS patients. Alternatively, the world might treat more HIV/AIDS patients right now by forgoing the same number of other commodities and services.
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The correct question is -
More than 50 years after it jumped the species barrier and became one of the most devastating viruses to affect mankind, HIV remains a stubborn adversary. Treatment has improved dramatically over the past 20 years and now, a cure could be in sight.
Source: The Guardian, November 30, 2018
Make a graph of the production possibilities frontier with HIV/AIDS cases treated on the x-axis and other goods and services on the y-axis before and after the advance in technology.
Question content area bottom left
Part 1
The opportunity cost of treating HIV/AIDS cases increases as more HIV/AIDS cases are treated.
Draw a curve that shows the production possibilities for the world economy that produces HIV/AIDS treatments and other goods and services. Label the curve PPF0.
Then draw the PPF that shows the effect of an advance in technology on HIV/AIDS treatments. Label the curve PPF1.
A certain antihistamine is often prescribed for allergies. A typical dose for a 100-pound person is 19 mg every six hours. Complete parts (a) and (b) below. a. Following this dosage, how many 13.2 mg chewable tablets would be taken in a week? b. This antihistamine also comes in a liquid form with a concentration of 13.2 mg/ 10mL. Following the prescribed dosage, how much liquid antihistamine should a 100-pound person take in a week?
A 100-pound person could take mL in a week? this is the question i need answered the most...thank you
Answer: First, let's find out how many times a 100-pound person would take the antihistamine in a week:
Every 6 hours * 24 hours/day = 4 times a day
4 times a day * 7 days/week = 28 times a week
Next, let's find the number of 13.2 mg chewable tablets taken in a week:
A typical dose of 19 mg * 28 doses/week = 532 mg
532 mg / 13.2 mg/tablet = 40 tablets
So, a 100-pound person would take 40 chewable tablets in a week following the prescribed dosage.
Now, let's find the amount of liquid antihistamine to be taken in a week:
A typical dose of 19 mg * 28 doses/week = 532 mg
532 mg / 13.2 mg/10 mL = 40.15 mL
So, a 100-pound person would take 40.15 mL of liquid antihistamine in a week following the prescribed dosage.
Step-by-step explanation:
Identify the percent of change as an increase or a decrease.
9 points to 4 points
o increase
decrease
Find the percent of change. Round to the nearest tenth of a percent if necessary.
The percent of change is
%.
The percent of change from 9 points to 4 points is approximate -55.6%, indicating a decrease of 55.6%.
What is the Percent of change?
The percent of change is a measure that compares the difference between two values to the original, or initial, value. It is usually expressed as a percentage and indicates how much a value has increased or decreased from its initial value.
To find the percent of change from 9 points to 4 points, we need to first calculate the amount of change, which is the difference between the final value (4 points) and the initial value (9 points):
Amount of change = Final value - Initial value = 4 - 9 = -5
The negative sign indicates a decrease in value.
Next, we can calculate the percent of change using the formula:
Percent change = (Amount of change / Initial value) x 100%
Substituting the values we get:
Percent change = (-5 / 9) x 100% ≈ -55.6%
Hence, the percent of change from 9 points to 4 points is approximate -55.6%, indicating a decrease of 55.6%.
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This question I can not figure out Someone please help.
Answer:
x y
0 -2
4 -1
graph: should look like the picture attached
explanation:
Find the x - and y -components of the vector d⃗ = (5.0 km , 29 ∘ left of +y -axis).
Express your answer in kilometers. Enter the x and y components of the vector separated by a comma.
The x- and y-components of the vector [tex]\mathbf{\hat d }[/tex] are approximately -2.25 km and 4.30 km, respectively.
What is vector?In physics and mathematics, a vector is a mathematical object that has both magnitude and direction. Vectors are often represented by arrows, with the length of the arrow indicating the magnitude of the vector, and the direction of the arrow indicating the direction of the vector.
For example, the velocity of a moving object is a vector quantity, because it has both a magnitude (the speed of the object) and a direction (the direction in which the object is moving).
To find the x-components and y-components of the vector [tex]\mathbf{\hat d }[/tex] = (5.0 km, 29° left of +y-axis), we can use trigonometry.
The magnitude (or length) of the vector is given by the first component, which is 5.0 km.
The angle between the vector and the positive y-axis is 29° left of +y-axis, which means it forms a 61∘ angle with the negative y-axis (since 29∘ + 61° = 90°).
The x-component of the vector can be found by multiplying the magnitude by the cosine of the angle:
x-component = magnitude x cos(angle) = 5.0 km x cos(61°) ≈ -2.25 km
The negative sign indicates that the x-component is in the opposite direction of the positive x-axis.
The y-component of the vector can be found by multiplying the magnitude by the sine of the angle:
y-component = magnitude x sin(angle) = 5.0 km x sin(61°) ≈ 4.30 km
Therefore, the x- and y-components of the vector [tex]\mathbf{\hat d }[/tex] are approximately -2.25 km and 4.30 km, respectively.
Expressed as an ordered pair, the components are (-2.25 km, 4.30 km).
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At the 2022 Winter Olympics, one country won a total of 150 medals. A circle graph of the medals is shown.
a circle graph titled 2022 Winter Olympic Medals, with three sections labeled gold 20 percent, silver 30 percent, and bronze 50 percent
How many gold and bronze medals were won?
50
70
105
120
Answer:
120
Step-by-step explanation:
The total number of medals won is 150, and the circle graph shows that the proportion of medals won as gold is 20 percent, as silver is 30 percent, and as bronze is 50 percent.
To find the number of gold and bronze medals won, we need to calculate the total number of medals won in each category by multiplying the total number of medals by the proportion of medals won in each category.
Gold medals: 150 * 20% = 30
Bronze medals: 150 * 50% = 75
So, a total of 30 + 75 = 105 medals were won as gold and bronze.
Each worker at a store gets paid $15.90 for that first 40 hours worked. After 40 hours, they earn time and a half wages. Every employee has a 28% of his/her gross pay deducted for taxes, insurance etc. how much of a net pay does each worker take home?
Each worker would take home a net pay of $586.71.
What is the net pay?
The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.
To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.
To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.
For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:
Gross Pay for 40 hours = $15.90/hour x 40 hours = $636
For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:
Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88
Therefore, their total gross pay would be:
Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88
Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:
Total Deductions = 28% x $814.88 = $228.17
Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:
Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71
Therefore, each worker would take home a net pay of $586.71.
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what must be added to each term of the ratio 49:64 , so that it becomes 3:4 ?
Answer:
Hence x= 8 should be added to the terms of 49:68 to get the ratio 3:4.
Step-by-step explanation:
have a nice day.
For a certain company, the cost function for producing x
items is C(x)=30x+200
and the revenue function for selling x
items is R(x)=−0.5(x−80)2+3,200
. The maximum capacity of the company is 130
items.
The profit function P(x)
is the revenue function R(x)
(how much it takes in) minus the cost function C(x)
(how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit!
Answers to some of the questions are given below so that you can check your work.
Assuming that the company sells all that it produces, what is the profit function?
P(x)=
Preview Change entry mode .
Hint: Profit = Revenue - Cost as we examined in Discussion 3.
What is the domain of P(x)
?
Hint: Does calculating P(x)
make sense when x=−10
or x=1,000
?
The company can choose to produce either 50
or 60
items. What is their profit for each case, and which level of production should they choose?
Profit when producing 50
items =
Number
Profit when producing 60
items =
Number
Can you explain, from our model, why the company makes less profit when producing 10 more units?
Answer: The profit function P(x) can be found by subtracting the cost function C(x) from the revenue function R(x), so:
P(x) = R(x) - C(x) = (-0.5(x-80)^2 + 3,200) - (30x + 200)
The domain of P(x) is the set of all possible values of x for which the profit calculation makes sense. In this case, the company has a maximum capacity of 130 items, so the domain of P(x) is 0 <= x <= 130.
To calculate the profit when producing 50 items and 60 items, we simply plug in these values for x in the profit function:
Profit when producing 50 items = P(50) = (-0.5(50-80)^2 + 3,200) - (30 * 50 + 200) = $2350
Profit when producing 60 items = P(60) = (-0.5(60-80)^2 + 3,200) - (30 * 60 + 200) = $2280
Since the profit is higher for producing 50 items, the company should choose to produce 50 items.
From our model, we can see that as the production increases, the cost also increases linearly with a slope of 30, while the revenue increases parabolically but with a negative slope, meaning that after reaching a certain point, the increase in revenue becomes slower compared to the increase in cost. This is why the profit decreases as the production increases, and therefore the company makes less profit when producing 10 more units.
Step-by-step explanation:
There are 12 consecutive parking slots available in a hotel parking lot in how many ways can four distinct cars be packed so that at least one parking slot remains vacant between into cars
Answer:
4 different spots
Step-by-step explanation:
12 - 4 spaces in between = 8 spaces
8 spaces / 4 cars = 4 spots
4 spots and 4 cars = 4 different spots for each car
16
Looking for answer key to Gina Wilson All Things Algebra Unit 3 Parallel and Perpendicular Lines Homework 5 Slopes of lines; Parallel and Perpendicular Lines
It's important to work through the problems yourself to improve your understanding and problem-solving skills.
For the unit 3 homework on parallel and perpendicular lines, you should have learned about the slope of lines, how to find the slope of a line given two points, and the relationship between parallel and perpendicular lines.
To find the slope of a line given two points, you can use the slope formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.
To determine if two lines are parallel, you can compare their slopes. Parallel lines have the same slope.
To determine if two lines are perpendicular, you can use the fact that the product of their slopes is -1. That is, if m1 and m2 are the slopes of two lines, and m1 * m2 = -1, then the lines are perpendicular.
It's important to practice working through problems using these concepts and formulas to develop your skills and understanding. Additionally, you can seek assistance from your teacher or tutor if you have specific questions or concerns.
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Mary plans to buy a kettle for R180-00, excluding vat.vat is charged at 15%.what is the total cost of the kettle vat is added
Answer:
R207
Step-by-step explanation:
R180 times 15% =27
27+180=207, therefore, R270 ir correct
Solve the quadratic equation by the square root method and write the solution in radical form. simplify the solution. 4y^2=80
Answer:
[tex]y=\pm2\sqrt{5}[/tex]
Step-by-step explanation:
[tex]4y^2=80\\y^2=20\\y=\pm\sqrt{20}\\y=\pm2\sqrt{5}[/tex]
The square root method for solving a quadratic equation involves isolating the squared term, and then taking the square root of both sides of the equation.
Starting with the equation 4y^2 = 80, we can isolate the squared term by dividing both sides of the equation by 4:
y^2 = 20
Next, we take the square root of both sides of the equation:
y = ±√20
The solution in radical form is y = ±√20. To simplify the radical, we can factor 20 into 2 * 10. Then, we can simplify the square root as follows:
y = ±√2 * √10 = ±2√10
So, the simplified solution is y = ±2√10.
Multiply. (Simplify your answer
(-5y4z)(-7y6z³)
Answer:
35y^(10)z^(4)
Step-by-step explanation:
Solution Given:
(-5y^(4)z)(-7y^(6)z³)
Here while opening bracket
If their is like terms they can be multiplied ,divided,subtracted as well as added.
So
Here
opening bracket and keeping in serially
-5*-7*y^(4)*y^(6)*z*z^(3)
here if their is like terms their power is added.
And solving remaining one.
35y^(4+6)z^(1+3)
Here -5*-7=35
Again
Solving it.
35y^(10)z^(4)
Answer:
[tex]35y^{10}z^4[/tex]
Step-by-step explanation:
Given expression:
[tex](-5y^4z)(-7y^6z^3)[/tex]
Apply the rule: (-a) · (-b) = ab
[tex]\implies 5y^4z \cdot 7y^6z^3[/tex]
Multiply the numbers: 5 · 7 = 35
[tex]\implies 35y^4zy^6z^3[/tex]
Collect like terms:
[tex]\implies 35y^4y^6z^3z[/tex]
[tex]\textsf{Apply exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\implies 35y^{(4+6)}z^{(3+1)}[/tex]
Simplify the exponents:
[tex]\implies 35y^{10}z^4[/tex]
Simplify this radical.
O 13√x
O 6x√x
O x√√x¹2
O x√x
If X and Y are independent and identically distributed uniform random variables on (0, 1), compute the joint density of
(a) U = X + Y, V = X/Y
(b) U = X, V = X/Y
(c) U = X + Y, V = X/(X+Y)
If X and Y are independent and identically distributed uniform random variables on (0, 1), then the joint density of
(a) U = X + Y, V = X/Y is u/v² for v > 1 and 0 ≤ u ≤ 1.
(b) U = X, V = X/Y is 1/v for v > 1 and 0 ≤ u ≤ 1.
(c) U = X + Y, V = X/(X+Y) is v/(1+v)² for v > 0 and v/(1+v) ≤ u ≤ 1.
In probability theory, joint density is a mathematical function that describes the probability distribution of two or more random variables. It represents the probability of occurrence of different values of those variables in a particular region of space. In this problem, we have to calculate the joint density of U and V, where U and V are functions of X and Y.
(a) For U = X + Y and V = X/Y, we can find the joint density as follows:
First, we need to find the distribution of U and V separately. Since X and Y are independent and identically distributed uniform random variables on (0, 1), their individual probability density functions are f(x) = 1 for 0 ≤ x ≤ 1.
To find the density of U, we can use the convolution formula, which states that the density of the sum of two independent random variables is the convolution of their individual densities. Thus,
fU(u) = ∫ fX(u - y)fY(y) dy
= ∫ 1 dy
= u for 0 ≤ u ≤ 1.
Next, to find the density of V, we need to transform X and Y using the change of variables formula. Let Z = X/Y, then
fV(v) = fZ(z)|dz/dv|
= fX(vz)/(z²) |z|
= 1/(v²) for v > 1.
Therefore, the joint density of U and V is given by the product of their individual densities:
fUV(u,v) = fU(u) fV(v)
= u/v² for v > 1 and 0 ≤ u ≤ 1.
(b) For U = X and V = X/Y, we can similarly find the joint density as:
fUV(u,v) = fX(u) fV(v)
= 1/v for v > 1 and 0 ≤ u ≤ 1.
(c) For U = X + Y and V = X/(X+Y), we can use the same method as in (a) to find the individual densities of U and V:
fU(u) = u for 0 ≤ u ≤ 1,
fV(v) = v/(1+v)² for v > 0.
Then, the joint density of U and V is given by:
fUV(u,v) = fU(u) fV(v) |du/dx|
= v/(1+v)² for v > 0 and v/(1+v) ≤ u ≤ 1.
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Write an equation of the circle graphed below
Answer:
Below
Step-by-step explanation:
Center (h,k) is - 2, -2 radius is 1
Equation for a circle with center (h,k) and radius r is :
(x-h)^2 + (y- k )^2 = r^2 <====you have to learn/remember this
Plug in the values above to get
(x+2)^2 + (y+2)^2 = 1
Answer:
(x+2)^2+(y+2)^2=0.5625
Step-by-step explanation:
trust
What is the measure of each angle in a regular polygon with 14 sides? If necessary, round your answer to the nearest tenth.
Answer:
154.3° (to the nearest tenth)
Step-by-step explanation:
1 exterior angle=360/number of sides
360/14=25.714285
To get the one angle within the 14 sided polygon, take 1 exterior angle away from 180, as they are on a straight line
180-25.714285=154.285714
To the nearest tenth:
154.3°
Which of the following is equivalent to the expression below?
√-98
A. -2i√7
B. 2i√7
c. 7i√2
D. -7i√2
Answer: Choice C) [tex]7i\sqrt{2}[/tex]
Work Shown:
[tex]\sqrt{-98} = \sqrt{-1*49*2}\\\\\sqrt{-98} = \sqrt{-1}*\sqrt{49}*\sqrt{2}\\\\\sqrt{-98} = i*7*\sqrt{2}\\\\\sqrt{-98} = 7i\sqrt{2}\\\\[/tex]
Alba Isabel bought a Bluray disc player on sale for $219.99. What is the sales tax if Alba lives in Kingston, New York, where the state tax is 4% and the county tax is 4%?
The sales tax on the Bluray disc player is $17.60.
What is percentage ?
Percentage can be defined as product of ratio of given value, total value and hundred.
To calculate the sales tax on the Bluray disc player, we need to add the state tax and county tax to the sale price of the player.
First, we can calculate the amount of the state tax. The state tax rate is 4%, which can be expressed as a decimal by dividing by 100:
State tax rate = 4% = 0.04
To find the amount of state tax, we can multiply the sale price by the state tax rate:
State tax = 0.04 x $219.99 = $8.80
Next, we can calculate the amount of the county tax. The county tax rate is also 4%, so we can use the same method as above to find the county tax:
County tax rate = 4% = 0.04
County tax = 0.04 x $219.99 = $8.80
Now, we can find the total sales tax by adding the state tax and county tax:
Total sales tax = State tax + County tax
= $8.80 + $8.80
= $17.60
Therefore, the sales tax on the Bluray disc player is $17.60.
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Use de Morgan’s laws to rewrite a statement that is equivalent to the following statement.
It is not true that April and August are both spring months
Using de Morgan’s laws to rewrite a statement : It is true that April is not a spring month OR August is not a spring month
What is de Morgan’s laws?This refers to a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan. He was a 19th-century British mathematician. De Morgan's laws can also be called De Morgan's theorem.
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The ratio 1500:1200 in its lowest terms is
Answer:
Step-by-step explanation:
To put a ratio in its lowest terms, we need to divide both terms of the ratio by their greatest common divisor (GCD). The GCD of 1500 and 1200 is 300, which is the largest number that divides both numbers evenly.
Dividing both terms of the ratio by 300, we get:
1500 / 300 : 1200 / 300 = 5 : 4
So, the ratio 1500:1200 in its lowest terms is 5:4.
In a class of 50 students, 20 play hockey and 35 play football . 10 students play both hockey and football.
The number of students who either play hockey or football is given by the equation n ( A ∪ B ) = 45 students
What is Set Theory Formula?The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
Given data ,
Let the total number of students in the class be n ( U ) = 50 students
Let the number of students who play hockey be n ( A ) = 20 students
Let the number of students who play football be n ( B ) = 35 students
Let the number of students who play hockey and football n ( A ∩ B ) = 10
So , from the set theory n(A∪B) = n(A) + n(B) - n(A⋂B)
Substituting the values in the equation , we get
The number of students who play hockey or football = 20 + 35 - 10
On simplifying the equation , we get
The number of students who play hockey or football = n( A ∪ B ) = 45 students
And , the number of students who do not play hockey or football is given by the equation = n ( U ) - n ( A ∪ B )
On simplifying the equation , we get
The number of students who do not play hockey or football = 50 - 45 = 5 students
Hence , the number of students who play hockey or football is 45 students
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10x² 18x -4
Factor number And find answer
Answer: 4(45x^(3)-1)
Step-by-step explanation:
Please help me with this question
<1 + <4 = 180 supplementary angles
180 - 95 = 85 degrees
A sprinter starts from rest, and accelerates at 1.87 m/s^2 over a distance of 14.0 m. What is a her final velocity?
Describe the long run behavior of f(p)=(p+1)^3(p+4)^3(p-1)
Answer:
Step-by-step explanation:
The long-run behavior of a function can be determined by examining its asymptotes and the behavior of the function near these asymptotes.
For the function f(p)=(p+1)^3(p+4)^3(p-1), there are three points to consider as possible asymptotes: p = -1, p = -4, and p = 1.
At p = -1, the factor (p-1) is equal to zero, so the function has a vertical asymptote there. This means that as p approaches -1 from either side, the function will approach infinity.
At p = -4, the factor (p+4)^3 is equal to zero, so the function also has a vertical asymptote there. Similarly, as p approaches -4 from either side, the function will approach infinity.
At p = 1, the factor (p+1)^3 is equal to zero, so the function has another vertical asymptote there. In this case, as p approaches 1 from either side, the function will approach negative infinity.
So, the long-run behavior of the function can be described as follows:
The function approaches infinity as p approaches -1 or -4 from either side.
The function approaches negative infinity as p approaches 1 from either side.
Therefore, the long-run behavior of f(p)=(p+1)^3(p+4)^3(p-1) is characterized by three vertical asymptotes at p = -1, p = -4, and p = 1.
Answer:
[tex]\text{As } p \to -\infty, f(p) \to -\infty\\\\\text{As } p \to \infty, f(p) \to \infty[/tex]
====================================================
Explanation:
Each factor is a cubic of degree 3.
The degree of the entire polynomial is 3+3+3 = 9.
Since the degree is odd and the leading coefficient is positive, this means the graph falls to the left and rises to the right.
"falls to the left" means [tex]\text{As } p \to -\infty, f(p) \to -\infty[/tex]
"rises to the right" means [tex]\text{As } p \to \infty, f(p) \to \infty[/tex]
This is verified using a graphing tool like Desmos as shown in the screenshot below. I'm using x in place of p.
Question 4 of 10
Which of the following is a root of the polynomial shown below?
f(x) = x³ + 2x²-x-2
OA. 0
OB. 2
O C. 1
OD. 3
SUBMIT
Answer:
1
Step-by-step explanation:
f(x)=x3+2x2-x-2
...................
The Roots of the given polynomials shown below f(x) = x^3+2x^2-x-2 are -1, 1, -2.
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and nonnegative exponentiation of variables involved.
Example: x² + 3x + 3 is a polynomial.
Since, The given polynomials is,
f(x) = x³ + 2x²-x-2
Now, Solve as;
f(x) = x³ + 2x²-x-2
f (x) = x² (x + 2) - 1 (x + 2)
f (x) = (x² - 1) (x + 2)
Hence, The Roots of the polynomials : -1, 1, -2
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DATE
10. If you laid the radius end to end around the circumference of a circle A, how many radii would
it take to fit exactly?
Answer:
Step-by-step explanation:
Step 1: Understand the formula for the circumference of a circle
The formula for the circumference of a circle is given by:
C = 2 * π * r
where C is the circumference of the circle, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. This formula expresses the relationship between the radius and the circumference of a circle.
Step 2: Substitute the radius of the circle for "r" in the formula
Let's say the radius of the circle is "r". Substitute "r" for "r" in the formula for the circumference:
C = 2 * π * r
Step 3: Divide the circumference by the radius
Now that you have the formula for the circumference, divide the circumference by the radius:
C/r = 2 * π
Step 4: Simplify the expression
The expression on the right side of the equation can be simplified to 2 times pi:
C/r = 2 * π
C/r = 2 * 3.14 = 6.28
Step 5: Conclusion
Therefore, it would take 6.28 radii laid end to end to fit exactly around the circumference of the circle.
Note: This answer is only an approximation, as the value of π is an irrational number that cannot be expressed exactly as a fraction or a decimal.
The terminal side of θ in standard position contains the point (–14, 0). Find the exact values of the six trigonometric functions of θ.
sin(θ) =
cos(θ) =
tan(θ) =
csc(θ) =
sec(θ) =
cot(θ) =
The exact values of the six trigonometric functions of θ are:
sin(θ) = 0
cos(θ) = -√2/2
tan(θ) = 0
csc(θ) = undefined
sec(θ) = -√2
cot(θ) = undefined
The given point (-14,0) lies on the x-axis in the negative x-axis direction. Drawing a line from the origin to this point creates a right triangle with the hypotenuse being the line from the origin to (-14,0), the opposite side being the y-coordinate of (-14,0), and the adjacent side being the x-coordinate of (-14,0). The length of the hypotenuse can be found using the Pythagorean theorem:
h^2 = (-14)^2 + 0^2
h^2 = 196
h = 14√2
Using the definitions of the six trigonometric functions in terms of the opposite, adjacent, and hypotenuse sides of a right triangle, we can find the exact values of these functions for θ:
sin(θ) = opposite/hypotenuse = 0/14√2 = 0
cos(θ) = adjacent/hypotenuse = -14/14√2 = -√2/2
tan(θ) = opposite/adjacent = 0/-14 = 0
csc(θ) = 1/sin(θ) = undefined (since sin(θ) = 0)
sec(θ) = 1/cos(θ) = -√2
cot(θ) = 1/tan(θ) = undefined (since tan(θ) = 0)
Therefore, the exact values of the six trigonometric functions of θ are:
sin(θ) = 0
cos(θ) = -√2/2
tan(θ) = 0
csc(θ) = undefined
sec(θ) = -√2
cot(θ) = undefined
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