Solve the recurrence relation for the variables indicated below: bn = 8bn-1 - 15bn-2 b1 = 2 b2 = 16 If the explicit formula for the sequence is written in the form bn = u(s1)n + v(s2)n then find s1 and s2 .
The recurrence relation is given by bn = 8bn-1 - 15bn-2 with b1 = 2 and b2 = 16.
How to depict the solution?Since it is linear homogeneous recurrence relation ,so first find its characteristic equation.
r² - 8r + 15 = 0
( r - 3 )( r - 5 ) = 0
r = 3 , 5
So, the general solution of the given recurrence relation is
bn = u(3)n + v(5)n ------------ ( 1 )
Now use the initial conditions b1 = 2 and b2 = 16.
From ( 1 ) , b1 = u(3)1 + v(5)1
2 = 3u + 5v ---------- ( 2 )
and b2 = u(3)2 + v(5)2
16 = 9u+ 25v------- ( 3 )
Solving ( 2 ) and ( 3 ) , we get u= - 1 and v = 1
Therefore, the required solution is bn = - (3)n + (5)n
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A rectangle is drawn on a coordinate plane. Three vertices of the rectangle are points L(−7,14) , M(9,14) , and N(9,−12) . Point P is the fourth vertex of the rectangle. How long is the side of the rectangle connecting points L and P?
Answer:
the answer is 26 units
Step-by-step explanation:
evaluate x - 2y if x = -3 and y = -6
Thomas correctly spell 18 out of 20 words on his last spelling quiz. What decimal represent the portion of the rights that Thomas spelled correctly
Final answer:
Thomas spelled 18 out of 20 words correctly, which, when divided, gives us 0.9. This decimal represents the portion of the words he spelled correctly on his quiz.
Explanation:
To find the decimal that represents the portion of words Thomas spelled correctly on his quiz, we follow a simple process of division and conversion to a decimal.
Thomas spelled 18 out of 20 words correctly. So, we divide 18 by 20 which equals 0.9. This is the decimal that represents the portion of words Thomas spelled correctly.
Ted is installing lighting in a new block of 12 apartments. He will need 60 metres of cable for each apartment. Each new spool holds 100 metres of cable. What is the smallest number of new spools that Ted will need for this job ??
The smallest number of new spools that Ted will need for this job is 8 spools of cable.
Given that, Ted is installing lighting in a new block of 12 apartments. He will need 60 metres of cable for each apartment. Each new spool holds 100 metres of cable.
We need to find the smallest number of new spools that Ted will need for this job.
What are the spools?A cylindrical device on which film, magnetic tape, thread, or other flexible materials can be wound; a reel.
Now, 60 meters per apartment x 12 apartments =720 total meters for all 12 apartments.
720 meters / 100 meters per spool =7.2 spools
so, Ted will need at least 8 spools of cable.
Therefore, the smallest number of new spools that Ted will need for this job is 8 spools of cable.
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Bill is a car salesman he earns $200 for every car he sales plus a 3% commission if Bill sells three cars in one week for a total of $32,343 what are his total earnings for this week
What's the name of the line segment in the diagram below? A. B. C. D.
Which expression can be simplified by applying the additive inverse property
We have to identify the expression in which Additive inverse identity is applied.
Additive inverse property states that "The additive inverse of a number 'x' is a number that when it is added to 'x', yields zero".
Consider the first expression,
A. [tex] -329-164+513+206+(-164) [/tex]
There are no such numbers, which will yield zero on addition. Hence, additive inverse property is not applied here.
B. [tex] 1.6+0.2-1.8-0.5 [/tex]
There are no such numbers, which will yield zero on addition. Hence, additive inverse property is not applied here.
C. [tex] -\frac{7}{10}-\frac{3}{4}+1\frac{1}{2}+(-\frac{7}{10}) [/tex]
There are no such numbers, which will yield zero on addition. Hence, additive inverse property is not applied here.
D. [tex] 9\frac{3}{4}\+4\frac{5}{8}+(-9\frac{3}{4}+(2\frac{3}{5}) [/tex]
Here, [tex] 9\frac{3}{4} [/tex] when added to [tex] -9\frac{3}{4} [/tex] will yield zero. Therefore, [tex] -9\frac{3}{4} [/tex] is the additive inverse of [tex] 9\frac{3}{4} [/tex].
So, in option D, Additive inverse property is applied.
Compare the volumes of the rectangular prisms shown below. Which of the containers will hold more, X or Y? In your final answer, include all of your calculations.
The volumes of the rectangular prism 'X' (126 cu.cm.) is greater than the volumes of the rectangular prism 'Y' (110 cu.cm.).
What is the volume of the rectangular prism?[tex]V=l\times w\times h[/tex]
where, 'l' be the length of the rectangular prism,
'w' is the width of the rectangular prism,
'h' is the height of the rectangular prism
For given question,
We have been given two rectangular prisms 'X' and 'Y'.
The dimensions of the rectangular prism 'X',
[tex]l=7~cm,w=3~cm,h=6~cm[/tex]
Using the formula for the volume of the rectangular prism,
[tex]\Rightarrow V=l\times w\times h\\\\\Rightarrow V=7\times 3\times 6\\\\\Rightarrow V=126~cu.cm.[/tex] ...................(i)
The dimensions of the rectangular prism 'Y',
[tex]l=5~cm,w=2~cm,h=11~cm[/tex]
Using the formula for the volume of the rectangular prism,
[tex]\Rightarrow V=l\times w\times h\\\\\Rightarrow V=5\times 2\times 11\\\\\Rightarrow V=110~cu.cm.[/tex] ...............(ii)
From (i) and (ii),
the volume of the rectangular prism 'X' is greater than the volume of the rectangular prism 'Y'.
Therefore, the volume of the rectangular prism 'X' (126 cu.cm.) is greater than the volume of the rectangular prism 'Y' (110 cu.cm.)
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what is the answer
solve 4.8+n=6.2
Louis,Michelle, and Tonya were asked to find an equation for a function that passed through the points (1,6) and (8,12) Louis gave the function y 6(2)-112 Michelle gave the function y V2)22 Tonya gave the function y-6 3(x-1) Which students are correct?
when 80% of a number is added to the number, the result is 252. what is the number
What is the exact volume of the cylinder?, (a) 54in. (b) 108in. (c) 162in. (d) 324in.
PLEASE HELP
Law of sines:
Which represents the value of c?
Ethan is 3 years older than twice his brother Adrian’s age write an expersion to represent Ethan’s age ; if Adrian is 6 how old is Ethan;
On a winter’s day, 9 degrees Fahrenheit is the highest temperature recorded. Write an inequality that represents the temperature t in degrees Fahrenheit at any time on this day.
Answer: The inequality that represents the temperature t in degrees Fahrenheit at any time on this day is [tex]t\leq 9[/tex] degree Fahrenheit.
Explanation:
It is given that on a winter’s day, 9 degrees Fahrenheit is the highest temperature recorded. It means the temperature on this day must be less than or equal to 9 degree Fahrenheit.
Let t represents the temperature in degrees Fahrenheit at any time on this day. Then,
[tex]t\leq 9[/tex]
Therefore, the inequality that represents the temperature t in degrees Fahrenheit at any time on this day is [tex]t\leq 9[/tex] degree Fahrenheit.
Answer:
[tex]t\leq 9^{0}F[/tex]
Step-by-step explanation:
We have been given that highest temperature recorded on a winter’s day is 9 degrees Fahrenheit and we are asked to write an inequality that represents the temperature t in degrees Fahrenheit at any time on this day.
Since we know that highest temperature can't exceed 9 degrees Fahrenheit on the given day and it will be less than or equal to 9.
Therefore, our inequality will be,[tex]t\leq 9^{0}F[/tex]
The unit of measure of an area equal to 1 km by 1m
What is the slope of the line in the graph?
The slope of the line in the given graph with the coordinates (x₁ , y₁ ) = (4, 5) and (x₂ , y₂) = (2, 3) is equal to 1.
The slope of a line is calculated by rise over run.
Here is the formula for calculating the slope of a line:
Slope = (y₂ - y₁) / (x₂ - x₁)
Here, the points (x₁ , y₁ ) = (4, 5) and (x₂ , y₂) = (2, 3) are on the line. Plugging these points into the formula, we get:
Slope
= (3 - 5) / (2 - 4)
= (-2) / (-2)
= 1
Therefore, the slope of the line is 1.
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Kayleen left home at noon and drove to boston.she got there at 4:00.if boston is about 280 miles away,what was kayleens average speed
I am a closed shape made of 6 line segments. I have two angles less than right angle & no right angles. What shape am I?
3+7x<26 help me with this equaton
to function properly, rainwater outflow pipe must drop exactly 1 inch for every 25 inches of horizontal distance. A 40 foot long rain water pipe runs under the edge of a roof. What is the vertical distance, in inches, the pipe bust drop between its ends? Round your number to the nearest tenth.
Answer: Hence, There is vertical distance of 19 inches the pipe must drop between its ends.
Step-by-step explanation:
Since we have given that
Rainwater outflow pipe must drop exactly 1 inch for every 25 inches of horizontal distance.
For 1 inch = 25 inches of vertical distance the pipe must drop.
If there is a 40 foot long rain water pipe runs under the edge of a roof.
Then, we need to find the vertical distance in inches the pope must drop.
First, we change 40 feet into inches.
Since 1 foot = 12 inches
40 feet = 40×12 inches = 480 inches
So, Vertical distance the pipe must drop is given by
[tex]\dfrac{480}{25}\\\\=19.2\ inches[/tex]
Hence, There is vertical distance of 19.2 inches ≈ 19 inches the pipe must drop between its ends.
Sophie bikes at a speed of s miles per hour. Her friend Rana is slower, her biking speed is only r miles per hour.
Today the girls went for a 20 miles trip, each girl was biking at her usual speed. How long did Sophie wait for Rana after her own arrival to the finish?
Answer:
She waited for 20/r-20/s at the end of the line.
Step-by-step explanation:
The solution is, Time Sophie waits for Rana to arrive at finish point
=20/s - 20/r.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
Speed = Distance/ Time.
here, we have,
The speed of Sophie and Rana are given as s miles per hour and r miles per hour.
The distance traveled by Sophie and Rand are 20 miles each.
The time taken by Sophie and Rana to travel 20 miles can be calculated by the formula
Speed =distance/time
Or, Time =distance/speed
Time taken by Sophie to travel 20 miles =20/s
Time taken by Rana to travel 20 miles =20/r
Time Sophie waits for Rana to arrive at finish point =20/s - 20/r
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What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 5.5? A rectangle is shown. The length of the rectangle is labeled as 8 cm, and the width is labeled as 6 cm. Perimeter = 50 cm, area = 155.25 cm2 Perimeter = 50 cm, area = 1,452 cm2 Perimeter = 154 cm, area = 155.25 cm2 Perimeter = 154 cm, area = 1,452 cm2
Answer:
the answer is 154 cm, area = 1,452 cm2 I took the test
Step-by-step explanation:
An air freshener starts with 33 grams and evaporates. In each of the following situations define a function that gives the remaining mass of the air freshener (in grams) in terms of the number of days, t t, since the air freshener was first used.
help me please i dont know how to do all of this ill really appreciate it please
The price of a shirt was $38. It was reduced by 20% and then again by 10%.
a. What is the final price of the shirt?
b. What would the price of the shirt be if it were reduced by 30% from the original?
c. Explain why the two prices in a. and b. differ.
Answer:
A- The final price of the shirt was $27.36.
B- If it were reduced by 30% from the original price, the price of the shirt would be $26.6.
C- There is a difference between both prices because in the first case, the discount is split, making a first discount on a larger basis, and the second on a smaller basis, already made the first discount.
In contrast, at the second price, the entire percentage is made on the major basis. Therefore, the discount is larger.
Step-by-step explanation:
A- The final price of the shirt is determined by the following calculation:
(38 x 0.8) x 0.9 = FINAL PRICE
38 is multiplied by 0.8 because the price was reduced by 20% (0.2 is the 20% of 1, that is, of a unit. Therefore, the remaining price would be that 0.8 or 80%)
Then, using the same logic, we have to multiply that result by 0.9 in order to get the final price.
Therefore:
(38 x 0.8) x 0.9 = 30.4 x 0.9 = 27.36
B- Here, we would have to multiply 38 x 0.7, which gives a result of 26.6
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Jeremy and Caitlin collect baseball cards. the ratio of Jeremy’s cards and Caitlin’s cards was 9 to 3. After Jeremy gave 12 carss to Caitlin, they had an equal number of cards. How many cards did Caitlin and Jeremy have at first? Explain.
jane wants to fill her circular pool to a depth of 2m.determine the volume of water she needs,to the nearest cubic meter.
To find the volume of water needed to fill the pool to a depth of 2m, use the formula for the volume of a cylinder.
Explanation:To determine the volume of water needed to fill the circular pool to a depth of 2m, you can use the formula for the volume of a cylinder:
V = πr²h
Given that the pool is circular, h = 2m, and to the nearest cubic meter, you would need:
Volume of water = π( r )²( 2 )