Which of the following polynomial does not belong to the span{P_1, P_2} if
p_1(t)= -5t^2 – 1 and p_2(t) = 2t^2+t?
a. p(t)= - 25t^2 – 5t-3
b. None of them
c. p(t)=9t^2 +2t+1
d. p(t)= 14t^2 - 3t+2
e. p(t)= -3t^2+t-1
Answers
The answer is option (a) , the polynomial p(t) = \(-25t^2 - 5t - 3\) does not belong to the span{P_1, P_2}.
To determine which polynomial does not belong to the span{P_1, P_2}, we need to check if it is possible to write each polynomial as a linear combination of P_1 and P_2. If a polynomial cannot be written as a linear combination of P_1 and P_2, then it does not belong to their span.
Let's express each polynomial in the form of a linear combination of P_1 and P_2:
a. p(t) =\(-25t^2 - 5t - 3 = -5(-5t^2 - t) + (-3t^2 + 0t) = -5P_1(t) + (-3t^2)\)
b. None of them (all polynomials can be expressed as a linear combination of P_1 and P_2)
c. p(t) = \(9t^2 + 2t + 1 = (9/2)P_1(t) + (5/2)P_2(t)\)
d. p(t) = \(14t^2 - 3t + 2 = (14/11)P_1(t) + (25/11)P_2(t)\)
e. p(t) =\(-3t^2 + t - 1 = (-3/2)P_1(t) + (5/2)P_2(t)\)
Since we were able to express all polynomials except option (a) as a linear combination of P_1 and P_2, the answer is option (a). Therefore, the polynomial p(t) =\(-25t^2 - 5t - 3\) does not belong to the span{P_1, P_2}.
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Related Questions
rewrite in simplest terms u-6(-3u+3)
Answers
Answer:
19u - 18.
Step-by-step explanation:
u - 6(-3u + 3)
= u + (-6)(-3u) + (-6)(3)
= u + 18u - 18
= 19u - 18.
Hope this helps!
Answer:
19 u − 18
Step-by-step explanation:
Simplify
{-6(-3u+3)
Distribute
1. −6(−3+3)
2. +18−18
Combine like terms
1. u+18u-18
2. 19u-18
Austin is participating in a 30k race. He runs at an average speed of 10 kilometers per hour and walks at an average speed of 6 kilometers per hour. He wants to complete the race in 4 hours. Let x represent the number of hours he runs. Let y represent the number of hours he walks.
What equation in standard form relates x and y to the goal of covering 30 kilometers? (no spaces)
Answers
Using the relation between velocity, distance and time, the equation that relates x and y is given by:
x + y - 3 = 0.
What is relation between velocity, distance and time?Velocity is distance divided by time, hence:
\(v = \frac{d}{t}\)
In this problem, he wants to run 30 km at a rate of 10 km per hour, hence:
\(10 = \frac{30}{t}\)
10t = 30
t = 3.
The total time is 3 hours. Considering x as the number of hours he runs and y the number of hours he walks, along with the total time, the equation is given by:
x + y = 3.
In standard form:
x + y - 3 = 0.
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how to send kred to a krew member
Answers
To send Kred to a Krew member, you can follow the steps provided by the Kred platform. These steps typically involve accessing your Kred account, selecting the desired recipient, specifying the amount of Kred to send, and confirming the transaction.
Sending Kred to a Krew member usually requires using the features and functionalities provided by the specific Kred platform or service. The process may vary depending on the platform, so it is recommended to refer to the official documentation or guidelines provided by the platform. Typically, you would need to log in to your Kred account, navigate to the appropriate section for sending Kred, select the intended recipient from the list of Krew members, enter the desired amount of Kred to send, review the transaction details, and confirm the transfer. The platform may also offer additional options or settings for customizing the transfer process.
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a certain phone company charges $4.50 for the first five minutes of an international phone call. additional time is charged at $.50 per minute. how much would a customer be charged for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day?
Answers
A customer would be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day.
Charge for first 5 charged = $ 4.50
Charge for additional time = $ 0.50 per minute
Starting time = 9:35 p.m.
End time = 11:15 p.m.
Total minutes = 100 minutes
Total charge = 4.50 + (95 x 0.50)
= 4.50 + 47.50
= 52.00
Hence, a customer would be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day i.e. for 100 minutes.
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A pyramid-shaped hip roof is a good choice for a house in an area with many hurricanes.
A house is formed by a rectangular prism and a rectangular pyramid that share a base. The rectangular prism has a length of 40 feet, width 40 feet, and height 30 feet. The rectangular pyramid has a height of 20 feet.
a. What is the volume of the roof to the nearest tenth of a foot?
Question 2
b. What is the volume of the entire house, including the roof?
about
Answers
a. The vοlume οf the pyramid-shaped rοοf is 10,667 cubic feet.
b. The tοtal vοlume οf the hοuse, including the rοοf, is 58,667 cubic feet.
What is Vοlume οf square pyramid?Vοlume οf square pyramid = a³h/3 , where a = length οf base , h = height
a. It is necessary to calculate the volume of the rectangular pyramid in order to determine the volume of the rf. A pyramid's volume can be calculated using the formula V = (1/3) * base area * height.
The volume of the pyramid-shaped reservoir is
therefore: V = (1/3) * 1600 * 20 = 10,667 cubic feet (to the nearest tenth).
b. The rectangular prism, which forms the main structure of the house, has a volume equal to its own, so we must add its volume to the rf's volume to determine the volume of the entire house. The rectangular prism's volume is calculated as follows: V = 40 * 40 * 30 = 48,000 cubic feet.
In light of this, the total volume of the house, including the room, is:
\(V_total = V_prism + V_pyramid\)
= 48,000 + 10,667 = 58,667 cubic feet (to the nearest whole number)
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true or false? "Because in a randomized controlled trial (RCT), the assignment is random, therefore there is no coverage bias---by definition" g
Answers
The statement "Because in a randomized controlled trial (RCT), the assignment is random, therefore there is no coverage bias---by definition" g is false because, it is important to consider both randomization and other factors when assessing the potential for bias in an RCT.
Random assignment in an RCT can help to reduce selection bias, but it does not guarantee the absence of coverage bias.
Coverage bias can occur if the participants who are enrolled in the trial do not represent the population to which the results will be generalized.
For example, if the trial only includes participants who are healthier or more compliant than the typical patient, the results may not be applicable to the broader population.
Therefore, it is important to consider both randomization and other factors when assessing the potential for bias in an RCT.
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Thank you
Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: [x(t) = 5t² ly(t) = -2 + 5t The resulting equation can be written as x =
Answers
To eliminate the parameter t and find a Cartesian equation in the form x = f(y), the given parametric equations x(t) = 5t² and y(t) = -2 + 5t are used. By substituting the expression for t from the second equation into the first equation, a Cartesian equation x = (y + 2)² is obtained.
Given the parametric equations x(t) = 5t² and y(t) = -2 + 5t, the goal is to eliminate the parameter t and express the relationship between x and y in the Cartesian form x = f(y).
To eliminate the parameter t, we solve the second equation for t:
t = (y + 2) / 5
Substituting this expression for t into the first equation, we get:
x = 5((y + 2) / 5)²
x = (y + 2)²
The resulting equation, x = (y + 2)², is the Cartesian equation in the form x = f(y). It represents the relationship between x and y without the parameter t.
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Which expression has a positive quotient?
Negative three-fourths divided by Negative two-thirds
Negative StartFraction 1 over 8 EndFraction divided by 3 and one-fifth
2 and StartFraction 2 over 7 EndFraction divided by negative one-fifth
Negative 6 divided by Five-thirds
Answers
Answer:
Only 1st option Negative three-fourths divided by Negative two-thirds has positive quotient.
Option A is correct.
Step-by-step explanation:
We will solve to find out Which expression has a positive quotient.
We know the division rule: \(\frac{-a}{-b}=\frac{a}{b}\) and \(\frac{-a}{b}=\frac{-a}{b}\)
We will use these rules
1) Negative three-fourths divided by Negative two-thirds
\(=\frac{-\frac{3}{4} }{-\frac{2}{3} }\\=-\frac{3}{4}\times -\frac{3}{2}\\=\frac{9}{8}\)
The quotient is positive.
2) Negative StartFraction 1 over 8 EndFraction divided by 3 and one-fifth
\(\frac{-\frac{1}{8} }{3\frac{1}{5} }\\=\frac{-\frac{1}{8} }{\frac{16}{5} }\\=-\frac{1}{18} \times \frac{5}{16}\\=-\frac{5}{288}\)
The quotient is negative.
3) 2 and StartFraction 2 over 7 EndFraction divided by negative one-fifth
\(\frac{2\frac{2}{7} }{-\frac{1}{5} }\\= \frac{\frac{16}{7} }{-\frac{1}{5} }\\=\frac{16}{7} \times -5\\=-\frac{80}{7}\)
The quotient is negative.
4) Negative 6 divided by Five-thirds
\(\frac{-6}{\frac{5}{3} }\\=-6 \times \frac{3}{5}\\=-\frac{18}{5}\)
The quotient is negative.
So, only 1st option Negative three-fourths divided by Negative two-thirds has positive quotient.
Option A is correct.
Answer:
its A
Step-by-step explanation:
i did the test
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help meeeeeeeeeeeeee pleaseeeeeeeeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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Answers
The rocket shows up at its overall insane level at 1.5 seconds after farewell will be 39 feet.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
A toy rocket is shot upward up high from a take-off platform 3 feet over the ground with an underlying speed of 48 feet each second. The level h, in feet, of the rocket over the ground at t seconds after send-off is given by the capability h(t) = - 16t² + 48t + 3.
Differentiate the function and put it equal to zero.
h'(t) = 0
-32t + 48 = 0
32t = 48
t = 1.5 seconds
Then the maximum height is given as,
h(1.5) = - 16(1.5)² + 48(1.5) + 3
h(1.5) = 39 feet
The rocket reaches its maximum height at 1.5 seconds after launch will be 39 feet.
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In a city school, 60% of students have blue eyes, 55% have dark hair and 20% have neither blue eyes nor dark hair. determine the probability that a randomly selected student will have blue eyes and dark hair
Answers
The probability of of a random student having blue eyes and dark hair
is 35% .
let consider the total students in the school be (U) = 100%
out of them ,
students having blue eyes (A) = 60%
students having dark hair (B) = 55%
students with neither blue eyes nor dark hair (A∪B)' = 20%
let the students with blue eyes and dark hair be (A∩B) = x %
Then according to the set theorem
U = n(A∪B) + n(A∪B)'
U = n(A) + n(B) - n(A∩B) + n(A∪B)'
100 = 60 + 55 - x +20
∴ x = 60 + 55 +20 - 100
x = 35 %
So the probability of random student having blue eyes and dark hair is 35% .
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which of the following pair of lines are perpendicular?- Y=2/3x+4 and y=2/3x -8,if a line contains Q(5,1) and is parallel to line MN with M(-2,4) and N(2,1) which ordered pair would be on the perpendicular transversal if its equation is y=4/3x+1/3
Answers
The pair of lines that are perpendicular to one another are Y=2/3x+4 and y=2/3x
Any point on this line will be a point on the perpendicular transversal that intersects the line y=4/3x+1/3 at a right angle.
Let's take the example of the two lines given in the question: Y=2/3x+4 and y=2/3x-8. We can rewrite these equations in the slope-intercept form y=mx+b, where m is the slope and b is the y-intercept.
The slope of the first line is 2/3, and the slope of the second line is also 2/3. To determine if they are perpendicular, we need to find the product of their slopes:
(2/3) x (2/3) = 4/9
Since the product of their slopes is not equal to -1, these two lines are not perpendicular.
To find the slope of the perpendicular line, we need to use the fact that the product of the slopes of two perpendicular lines is -1. Therefore, the slope of the perpendicular line will be the negative reciprocal of the slope of the parallel line:
slope of parallel line = 4/3
slope of perpendicular line = -3/4
Now we can use the point-slope form of the equation of a line to find the equation of the perpendicular transversal. We are given a point Q(5,1) that is on the perpendicular transversal, and we know the slope of the line is -3/4. Therefore, the equation of the perpendicular transversal is:
y - 1 = (-3/4) (x - 5)
Simplifying this equation gives:
y = (-3/4)x + (19/4)
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analytics is often described as the study of historical data to
Answers
Therefore, analytics is a critical tool for businesses and organizations looking to gain a competitive advantage and improve their operations.
Analytics is often described as the study of historical data to extract insights and make informed decisions. It involves the collection, processing, and analysis of data to discover patterns, identify trends, and gain insights into business operations. By examining data sets, analytics can help businesses identify areas of improvement, optimize performance, and increase efficiency. Analytics tools and techniques can be used across many different fields, including finance, marketing, healthcare, and sports. In finance, analytics can be used to analyze market trends and predict future outcomes. In marketing, analytics can help businesses identify customer behavior patterns and optimize marketing campaigns. In healthcare, analytics can help identify patterns in patient data and improve healthcare outcomes. In sports, analytics can be used to analyze player performance and predict game outcomes.
Therefore, analytics is a critical tool for businesses and organizations looking to gain a competitive advantage and improve their operations.
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write the number 100 as a product of it's prime factor in the same way write the factors in order from smallest to largest
Answers
Answer:
Thx for my points back
Step-by-step explanation:
Answer:
Thx
Step-by-step explanation:
for free points.....
I need help with these
Answers
The 15 and 9 units side lengths of the parallelogram ABCD, and the 36° measure of the acute interior angle, A indicates the values of the ratios are;
1. AB:BC = 5:3
2. AB:CD = 1:1
3. m∠A : m∠C= 1 : 4
4. m∠B:m∠C = 4:1
5. AD: Perimeter ABCD = 3:16
What is a ratio?A ratio is a representation of the number of times one quantity is contained in another quantity.
The shape of the quadrilateral ABCD in the question = A parallelogram
Length of AB = 15
Length of BC = 9
Measure of angle m∠A = 36°
Therefore;
1. AB:BC = 15:9 = 5:3
2. AB ≅ CD (Opposite sides of a parallelogram are congruent)
AB = CD (Definition of congruency)
AB = 15, therefore, CD = 15 transitive property
AB:CD = 15:15 = 1:1
3. ∠A ≅ ∠C (Opposite interior angles of a parallelogram are congruent)
Therefore; m∠A = m∠C = 36°
∠A and ∠D are supplementary angles (Same side interior angles formed between parallel lines)
Therefore; ∠A + ∠D = 180°
36° + ∠D = 180°
∠D = 180° - 36° = 144°
∠D = 144°
m∠A : m∠C = 36°:144° =1:4
m∠A : m∠C = 1:4
4. ∠B = ∠D = 144° (properties of a parallelogram)
m∠B : m∠C = 144° : 36° = 4:1
5. AD ≅ BC (opposite sides of a parallelogram)
AD = BC = 9 (definition of congruency)
The perimeter of the parallelogram ABCD = AB + BC + CD + DA
Therefore;
Perimeter of parallelogram ABCD = 15 + 9 + 15 + 9 = 48
AD:Perimeter of the ABCD = 9 : 48 = 3 : 16
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What type of analytics is forecasting prescriptive predictive descriptive
causal
Answers
Forecasting, prescriptive, predictive, descriptive, and causal are all types of analytics.
Descriptive analytics involves examining past data to understand what has happened in the past and to identify patterns and trends.
It provides insight into what has happened and why.
Predictive analytics involves analyzing past data and using statistical algorithms and machine learning techniques to predict what is likely to happen in the future.
It is used to forecast trends, behaviors, and outcomes.
Prescriptive analytics involves analyzing data and using optimization algorithms to determine the best course of action to achieve a specific goal or objective.
It is used to make decisions that will maximize outcomes or minimize risks.
Causal analytics involves identifying cause-and-effect relationships between different variables.
It is used to understand how changes in one variable may affect another, and to identify the root causes of a particular outcome or phenomenon.
Forecasting analytics involves using statistical methods and data analysis techniques to make predictions about future trends and events. It is used to estimate future demand, sales, or other variables based on past data and trends.
In summary,
Each of these types of analytics serves a unique purpose in the data analysis process and can be used to gain insights and make informed decisions.
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Part A: If (72)x = 1, what is the value of x? Explain your answer. (5 points)
Part B: If (70)x = 1, what are the possible values of x? Explain your answer. (5 points)
Answers
Answer:
see step by step explanation
Step-by-step explanation:
part a: x=1/72 because there are 72 x's in the one so 1/72
part b: x=1/70 because there are 70 x in 1 so x = 1/70
Answer:
(7^2)^0
Step-by-step explanation:
The Zero rule property states that anytime you multiple an exponent by 0 it always equals 1. So, if you multiply the equation by 0 it will equal one.
PLLLZZZZ I NEED HELP WITH THIS!
Answers
Answer:
8
Step-by-step explanation:
now, just draw a pic and it will make sense
solve the following system of equations
x-2y=6 and y=11-3x
Answers
Answer:
m=1/2 this is the 1st question.
m= -3 is the second question.
Step-by-step explanation:
Use the slope-intercept form.
Answer:
(x,y)
1. (10,4)
2. (3,22)
Step-by-step explanation:
If you substitute 10 for the x and 4 for the y in the first problem, it becomes true.
x-2y=6 ---> 10- 2(2)=6
2 times 2 is 4 and 10 minus 4 equals 6.
Same rules apply to the second problem.
a sample of 158 college students asked them if they liked statistics. 93% said yes. calculate a 89% confidence interval for the true population proportion of those who like statistics
Answers
We must find p′, q′ in order to calculate the confidence interval; the sample proportion is p′ = 0.842; This is the population proportion's point estimate. Since CL = 0.95 is the requested confidence level, = 1 – CL = 1 – 0.95 = 0.05 (2) (2) = 0.025.
For P, what is the confidence interval at 95 percent?
Since 95% of the area under the curve falls within this interval, the interval (-1.96, 1.96) serves as a 95% confidence interval for the standard normal distribution.
What is the 95 percent confidence interval for the population's proportion of smokers?
Standard Error for Proportion Calculating a 95% Confidence Interval for each group separately is another way to consider whether smokers and nonsmokers have significantly different proportions with wrinkles. For the smokers, we have a certainty time period ± 2(0.0394) or 0.63 ± 0.0788.
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Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year. If this continues, what will Tacoma's population be in 2012?
Answers
Answer:
503634
Step-by-step explanation:
The formula for calculating future value:
FV = P (1 + r) n
FV = Future value
P = Present value
R = interest rate
N = number of years
200,000(1.08)^12
find the indicated length
Answers
Answer:
ion know
Step-by-step explanation:
Please help I will give a brainliest
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Completing table 1)
Given the function
y = -3x+2
put x = 3
y = -3(3)+2 = -9+2 = -7
so (x, y) = (3, -7)
Given the function
y = -3x+2
put x = 1
y = -3(1)+2 = -3+2 = -1
so (x, y) = (1, -1)
Given the function
y = -3x+2
put x = 0
y = -3(0)+2 = 0+2 = 2
so (x, y) = (0, 2)
Given the function
y = -3x+2
put x = -1
y = -3(-1)+2 = 3+2 = 5
so (x, y) = (-1, 5)
So the table becomes
x y = -3x+2 y (x, y)
3 y = -3(3)+2 -7 (3, -7)
1 y = -3(1)+2 -1 (1, -1)
0 y = -3(0)+2 2 (0, 2)
-1 y = -3(-1)+2 5 (-1, 5)
The graph of the equation y = -3x+2 is also attached below.
On the diagram, the red line represents the y = -3x+2 line.
Similarly,
Completing table 2)
Given the function
y = 2x+4
put x = 0
y = 2(0)+4=0+4 = 4
so (x, y) = (0, 4)
Given the function
y = 2x+4
put x = 1
y = 2(1)+4=2+4 = 6
so (x, y) = (1, 6)
Given the function
y = 2x+4
put x = 2
y = 2(2)+4=4+4 = 8
so (x, y) = (2, 8)
Given the function
y = 2x+4
put x = -1
y = 2(-1)+4=-2+4 = 2
so (x, y) = (-1, 2)
So the table becomes
x y = 2x+4 y (x, y)
0 y = 2(0)+4 4 (0, 4)
1 y = 2(1)+4 6 (1, 6)
2 y = 2(2)+4 8 (2, 8)
-1 y = 2(-1)+4 2 (-1, 2)
The graph of the equation y = 2x+4 is also attached below.
On the diagram, the blue line represents the y=2x+4 line.
Write the correct postulate, theorem, property, or definition that justifies the statement below the diagram.
Answers
The correct theorem or definition that justifies the given statement for the diagram is; Definition of a Right angle Triangle
What is the angle postulate?We are given that;
∠MRS ≅ ∠MRO
Now, what that means is that ∠MRS is congruent to ∠MRO. Thus, to understand this concept of equality or congruence, we can prove it since from the given image, we see that;
m∠MRS = m∠MRO = 90°
Since they are both right angles then we can say that the correct theorem is the definition of a right angle triangle.
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A country has two political parties, the Demonstrators and the Repudiators. Suppose that the national senate consists of 100 members, 44 of which are Demonstrators and 56 of which are Repudiators. (a) How many ways are there to select a committee of 10 senate members with the same number of Demonstrators and Repudiators
Answers
Can I drink some nice internet juice
Answers
Answer: Um sure you can
of stion Instructions: Use the ratio of a 45-45-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. m 512 n 45° N т n =
Answers
From the diagram, we can see that
\(\begin{gathered} \sin \text{ 45 = }\frac{m}{5\sqrt[]{2}} \\ \frac{1}{\sqrt[]{2}}\text{ = }\frac{m}{5\sqrt[]{2}} \\ 1\text{ = }\frac{m}{5} \\ m\text{ = 1 x 5 = 5} \end{gathered}\)\(\begin{gathered} \cos \text{ 45 = }\frac{n}{5\sqrt[]{2}} \\ \frac{1}{\sqrt[]{2}}\text{ = }\frac{n}{5\sqrt[]{2}} \\ 1\text{ = }\frac{n}{5} \\ n\text{ = 1 x 5 = 5} \end{gathered}\)how do you calculate ratios
Answers
Answer:
A link for a calculator that I use for ratios
Step-by-step explanation:
https://www.calculatorsoup.com/calculators/math/ratios.php
Find WSK in figure 2
a. 50
b. 80
c. 85
d. 90
Please help me!!
Answers
Answer:
85
Step-by-step explanation:
Angle Formed by Two Chords = 1/2 (sum of Intercepted Arcs)
< WSK = 1/2 ( 35+ 135)
= 1/2 ( 170)
=85
Use the drawing tool(s) to form the correct answers on the provided number line.
Yeast, a key ingredient in bread, thrives within the temperature range of 90°F to 95°FWrite and graph an inequality that represents the temperatures where yeast will NOT thrive.
Answers
The inequality of the temperatures where yeast will NOT thrive is T < 90°F or T > 95°F
Writing an inequality of the temperatures where yeast will NOT thrive.from the question, we have the following parameters that can be used in our computation:
Yeast thrives between 90°F to 95°F
For the temperatures where yeast will not thrive, we have the temperatures to be out of the given range
Using the above as a guide, we have the following:
T < 90°F or T > 95°F.
Where
T = Temperature
Hence, the inequality is T < 90°F or T > 95°F.
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Carry all interim calculations to 5 decimal places and then round your final answer to a whole number. If entering a negative number, use negative (−) sign preceding the number. The tolerance is ±2. Attempts: 1 of 1 used Partb If the future worth at the end of year 7 is $130,000, what is the value of the gradient G ? Click here to access the TVM Factor Table Calculator. Carry all interim calculations to 5 decimal places and then round your final answer to a whole number. If entering a negative number, use negative (−) sign preceding the number. The tolerance is ±4. An inventor's royalty stream begins at the end of the first year with a payment of $12,000. Over the following 6 years, that royalty stream changes each year by a constant amount, or gradient. Interest is 9% per year. Part a Your answer has been saved. See score details after the due date. If the present worth of the 7 years of royalties is $45,000, what is the value of the gradient G ? Click here to access the TVM Factor Table Calculator. $ Carry all interim calculations to 5 decimal places and then round your final answer to a whole number. If entering a negative number, use negative (−) sign preceding the number. The tolerance is ±2. Attempts: 1 of 1 used Partb If the future worth at the end of year 7 is $130,000, what is the value of the gradient G ? Click here to access the TVM Factor Table Calculator.
Answers
Part a:
The value of the gradient G for the royalty stream is $5,143.
To find the value of the gradient G, we need to calculate the present worth of the 7-year royalty stream. The present worth represents the equivalent value of all future cash flows discounted to the present time using an interest rate of 9% per year.
Let's denote the value of the gradient G as G. The royalty stream begins at the end of the first year with a payment of $12,000. From year 2 to year 7, the royalty stream changes by G each year. Therefore, the cash flows for each year are as follows:
Year 1: $12,000
Year 2: $12,000 + G
Year 3: $12,000 + 2G
Year 4: $12,000 + 3G
Year 5: $12,000 + 4G
Year 6: $12,000 + 5G
Year 7: $12,000 + 6G
To calculate the present worth, we need to discount each cash flow to the present time. Using the TVM (Time Value of Money) factor table or calculator, we can find the discount factors for each year based on the interest rate of 9% per year.
Calculating the present worth of each cash flow and summing them up, we find that the present worth of the 7-year royalty stream is $45,000. Therefore, we can set up the following equation:
$45,000 = $12,000/(1+0.09)^1 + ($12,000+G)/(1+0.09)^2 + ($12,000+2G)/(1+0.09)^3 + ($12,000+3G)/(1+0.09)^4 + ($12,000+4G)/(1+0.09)^5 + ($12,000+5G)/(1+0.09)^6 + ($12,000+6G)/(1+0.09)^7
Solving this equation will give us the value of the gradient G, which is approximately $5,143.
Part b:
The value of the gradient G for the royalty stream, given a future worth at the end of year 7 of $130,000, cannot be determined based on the information provided.
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