Im learning about Recursive and Explicit in Pre-Calc, and it says to use the rule to write the first three terms of each sequence. I have no idea how to figure these out. Only know the first one or two because they give it to you but I have no idea how to figure out for a third one. Someone PLZ HELP!!!!!!!
Answers
Hello,
4. you have sequences defined by the first term and a recursive relation.
[tex]a_1=3\\\\a_n=2a_{n-1} \ \ \text{ for n}> 1[/tex]
Take n = 2, it gives
[tex]a_2=2a_1[/tex] , right?
But you know [tex]a_1=3[/tex]
so [tex]a_2=2a_1=2*3=6[/tex]
This is the second term. You are asked to find the first three terms.
Now, let's take n = 3
[tex]a_3=2a_2=2*6=12[/tex]
So the first three terms are 3, 6, 12.
6.
[tex]a_1=12\\\\a_2=\dfrac{1}{2}a_1+1=\dfrac{12}{2}+1=6+1=7 \\ \\a_3=\dfrac{1}{2}a_2+1=\dfrac{7}{2}+1=\dfrac{9}{2}[/tex]
8.
[tex]a_1=10\\ \\a_2=-3a_1=-3*10=-30\\\\a_3=-3a_2=-3*(-30)=90[/tex]
10.
[tex]a_1=2\\\\a_2=-1\\\\a_3=a_2+a_1=-1+2=1\\\\a_4=a_3+a_2=1-1=0[/tex]
Do not hesitate if you have any question.
Thank you
Related Questions
If z=(x+y)ey and x=u2+v2 and y=u2−v2, find the following partial derivatives using the chain rule. Enter your answers as functions of u and v.
∂z/∂u= ______
∂z/∂v= ______
Answers
Answer:
Step-by-step explanation:
Given the functions z=(x+y)[tex]e^y\\[/tex] and x=u²+v² and y=u²−v²
Using the composite derivative formula;
∂z/∂u= ∂z/∂x*∂x/∂u+∂z/∂y*∂y/∂u
∂z/∂u = y[tex]e^y[/tex]*2u + [(x+y)[tex]e^y[/tex]+x[tex]e^y[/tex]]*2u
∂z/∂u =y[tex]e^y[/tex]*2u + 2u[x[tex]e^y[/tex]+y[tex]e^y[/tex]+x[tex]e^y[/tex]]
∂z/∂u = y[tex]e^y[/tex]*2u + 2u[2x[tex]e^y[/tex]+y[tex]e^y[/tex]]
∂z/∂u = 2u[u²−v²][tex]e^{u^2-v^2}[/tex]+ 2u[2(u²+v²)[tex]e^{u^2-v^2}[/tex]+y[tex]e^{u^2-v^2}[/tex]]]
∂z/∂v= ∂z/∂x*∂x/∂v+∂z/∂y*∂y/∂v
∂z/∂v = y[tex]e^y[/tex]*2v + [(x+y)[tex]e^y[/tex]+x[tex]e^y[/tex]]*-2v
∂z/∂v =y[tex]e^y[/tex]*2v -2v[x[tex]e^y[/tex]+y[tex]e^y[/tex]+x[tex]e^y[/tex]]
∂z/∂v = y[tex]e^y[/tex]*2v -2v[2x[tex]e^y[/tex]+y[tex]e^y[/tex]]
∂z/∂v = 2v[u²−v²][tex]e^{u^2-v^2}[/tex]-2v[2(u²+v²)[tex]e^{u^2-v^2}[/tex]+y[tex]e^{u^2-v^2}[/tex]]
Find the value of the expression 63 - 21 + (3 x 11)
Answers
Answer: First solve the parentheses using order of operations. Then add and subtract from left to right.
Demo:
(3 * 11) = 33
Equation now looks like:
63 - 21 + 33
63 - 21 = 42
Equation now looks like:
42 + 33
42 + 33 = 75
The value of this expression is 75.
Answer:
Step-by-step explanation:
What would be the coordinate of point Lif the figure was shifted 2 units
left and 4 unit up?"
Answers
Answer: D. (-2, 1)
Step-by-step explanation:
original coordinate of L: (0, -3)
2 units left: x-2
4 units up: y+4
(x-2, y+4)
=(0-2, -3+4)
=(-2, 1)
Hope this helps!! :)
You believe the population is normally distributed. Find the 80% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to twp decimal places.
Answers
You intend to estimate a population mean μ from the following sample. 26.2 27.7 8.6 3.8 11.6 You believe the population is normally distributed. Find the 80% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to twp decimal places.
Answer:
The Confidence interval = (8.98 , 22.18)
Step-by-step explanation:
From the given information:
mean = [tex]\dfrac{ 26.2+ 27.7+ 8.6+ 3.8 +11.6 }{5}[/tex]
mean = 15.58
the standard deviation [tex]\sigma[/tex] = [tex]\sqrt{\dfrac{\sum(x_i - \mu)^2 }{n}}[/tex]
the standard deviation = [tex]\sqrt{\dfrac{(26.2 - 15.58)^2 +(27.7 - 15.58)^2 +(8.6 - 15.58)^2 + (3.8 - 15.58)^2 + (11.6 - 15.58)^2 }{5 } }[/tex]
standard deviation = 9.62297
Degrees of freedom df = n-1
Degrees of freedom df = 5 - 1
Degrees of freedom df = 4
For df at 4 and 80% confidence level, the critical value t from t table = 1.533
The Margin of Error M.O.E = [tex]t \times \dfrac{\sigma}{\sqrt{n}}[/tex]
The Margin of Error M.O.E = [tex]1.533 \times \dfrac{9.62297}{\sqrt{5}}[/tex]
The Margin of Error M.O.E = [tex]1.533 \times 4.3035[/tex]
The Margin of Error M.O.E = 6.60
The Confidence interval = ( [tex]\mu \pm M.O.E[/tex] )
The Confidence interval = ( [tex]\mu + M.O.E[/tex] , [tex]\mu - M.O.E[/tex] )
The Confidence interval = ( 15.58 - 6.60 , 15.58 + 6.60)
The Confidence interval = (8.98 , 22.18)
Alice works for a paint manufacturer. She is paid 3% commission on her first $20,000 of monthly sales and 8% commission on all sales over $20,000. In March her sales were $54,500; in April, her sales totaled $47,300. What were the total commissions she earned for the 2 months?
Answers
Answer: $6,144
Step-by-step explanation:
In March her commission was;
= 3% * 20,000 + 8% ( 54,500 - 20,000)
= $3,360
In April;
= 3% * 20,000 + 8% ( 47,300 - 20,000)
= $2,784
Total commission
= 3,360 + 2,784
= $6,144
If you use a 0.10 level of significance in a two-tail hypothesis test, what is your decision rule for rejecting a null hypothesis that the population mean equals 500 if you use the Z test
Answers
Answer:
Our decision rule will be to reject The null hypothesis H0 if the test statistic is less than -1.645, or if it is greater than +1.645.
Step-by-step explanation:
The hypotheses would be;
Null hypothesis;H0: μ = 500
Alternative hypothesis;Ha: μ ≠ 500
Since it's two - tailed at 0.1 level of significance, then each tail will contain 5% or 0.05. From the z-table attached, the corresponding critical value of 0.05 is approximately 1.645 standard deviations from the mean.
Thus, our decision rule will be to reject The null hypothesis H0 if the test statistic is less than -1.645, or if it is greater than +1.645.
Is -4 a irrational number?
Answers
Answer:
No.
Step-by-step explanation:
Irrational numbers are numbers that you can't solve like 3 squared. See you can't find the end of 3 squared, the numbers will go on forever just like pi.
Answer:
No
Step-by-step explanation:
A rational number can be written as the ratio of integers
-4/-1 = -4
This is a rational number
all areas of the country use a BAC of .10 as the legal intozication level . is it possible that the mean BAC of all drivers involved in a fata accident
Answers
Answer:
The answer is "It is not highly probable".
Step-by-step explanation:
In the given question some data is missing, that's why first we define value than its solution:
Missing value:
[tex]\bar x= 0.15\\\\s=0.06[/tex]
Solution:
[tex]\to \ H_0 : \mu \leq 0.10\\\to H_1: \mu > 0.10[/tex]
Formula:
[tex]Z= \frac{x-\mu}{s}\\\\[/tex]
[tex]=\frac{0.15- 0.10}{0.06}\\\\=\frac{0.05}{0.06}\\\\=\frac{0.05}{0.06}\\\\=.833\\[/tex]
calculating the value of x:
formula:
[tex]x=X(Z>z)[/tex]
[tex]=0.833-0.841\\\\=-0.008[/tex]
What is 0.658 rounded to 1 significant figure?
Answers
Answer: 0.07 calculatorsoup for significant rounding
separate the number 18 into two parts where the product of the part is 77
Answers
Answer:
7 and 11.
Step-by-step explanation:
so if we say the 2 "parts" are "a" and "b" then we are left with 2 equations
a + b = 18
ab = 77
a = 18 - b
so if ab = 77
b (18 - b) also equals 77
so
-b^2 + 18b = 77
b^2 - 18b + 77 = 0
So b = 7 and 11
You could also solve this via trial and error, but this is a more analytical approach.
Jon is 3 years younger than Laura. The product of their ages is 1,330. If j represents Jon's age and j + 3 represents Laura's age, what value of j
could be Jon's age?
Answers
Answer:
35
Step-by-step explanation:
j(j + 3) = 1330
Trial and error method:
j and j + 3 are pretty close to each other. Start by taking the square root of 1330.
sqrt(1330) = 36.5. One number is less than 36.5 and the other number if 3 more than that.
Since the product of j and j + 3 is 1330 which ends in 0, it is a multiply of 10 and 5.
Try 35 and 38. 35 * 38 = 1330
Answer: 35
Equation method:
j(j + 3) = 1330
j^2 + 3j - 1330 = 0
(j + 38)(j - 35) = 0
j = -38 or j = 35
Answer: 35
If Jon is 3 years younger than Laura, then Jon's age is 35years.
Let the age of John be j
If Jon is 3 years younger than Laura, then;
Laura's age = j + 3
Based on the question, we are told that the product of their ages is 1,330, this can be expressed as:
j(j+3) = 1330
Expand
j²+3j = 1330
j²+3j - 1330 = 0
j²+38j-35j-1330 =0
j(j+38)-35(j+38) = 0
(j−35)(j+38) = 0
j = 35 and j = -38
j = 35
Hence Jon's age is 35years.
Learn more here: https://brainly.com/question/14294864
The vector parametric equation for the line through the points (−1,−4,2) and (−1,0,−3) is:_______
Answers
Answer: [tex]x(t)=-1[/tex]
[tex]y(t)=-4+4(t)[/tex]
[tex]z(t)=2-5(t)[/tex]
Step-by-step explanation:
To find: The vector parametric equations for the line through the points (−1,−4,2) and (−1,0,−3).
Let A (−1,−4,2) and B(−1,0,−3)
First we find direction vectors : [tex]\overrightarrow{AB}=<-1-(-1),0-(-4),-3-2>[/tex]
[tex]<0,4,-5>[/tex]
Now, the parametric equations of the line:
[tex]x(t)=-1+0(t)[/tex]
[tex]y(t)=-4+4(t)[/tex]
[tex]z(t)=2-5(t)[/tex]
Hence, the vector parametric equations for the line through the points (−1,−4,2) and (−1,0,−3):
[tex]x(t)=-1[/tex]
[tex]y(t)=-4+4(t)[/tex]
[tex]z(t)=2-5(t)[/tex]
Recall that a reinforcement beam will extend from one strut to the other when the two struts are 2 feet apart. Algebraically determine the x-value of where the beam should be placed. Explain where to place the beam.
Answers
Answer:
Graph the two struts on the model of the roller coaster. Take a screenshot of your graph and paste the image below, or sketch a graph by hand. (5 points)
Recall that a reinforcement beam will extend from one strut to the other when the two struts are 2 feet apart.
•
• Algebraically determine the x -value of where the beam should be placed. (15 points)
root(x + 8) = 2 + rootx − 4)
x + 8 = 4 + 4root(x − 4) + x − 4
8 = 4root(x − 4)
2 = root(x − 4)
x − 4 = 4
x = 8
• Explain where to place the beam. (10 points)
The beam should be places 8 feet apart.
Step-by-step explanation:
I don't have a graph. Correct on E2020
Hope that this helps. If someone finds a graph i have a question on my page that needs it
Peace and love
Answer:
Here is the missing graph.
(10c^6d^-5)(2c^-5d^4)
Answers
10c^6d^-5×2c^-5d^4
20cd^-1
20c×1/d
20c/d
A bank withdraw of $50
Answers
Answer:
-$50 lol
Step-by-step explanation:
Hi :)
To find your balance after you withdraw $50, simply take your balance, and subtract $50
balance-withdraw=balance
Hope this helps,
Jeron
Find the sum of (root2+root3)+(root3-root7)+(root7-root2
Answers
Answer:
Step-by-step explanation:
√2 + √3 + √3 - √7 + √7 - √ 2
by changing the position
√2 - √2 + √3 + √3 - √7 + √7
√2 and -√2 gets canceled
-√7 and √7 gets cancelled
we are left out with √3 + √3
√3 + √3 gives 2√3
so the answer is 2√3
hope this helps
plz mark as brainliest!!!!!!!!
Use an integer to represent 35 degrees Celsius. Answer fast, I will give brainliest.
Answers
Answer: Hi! The answer you're looking for is 35
An integer is a positive or negative whole number. Since we're looking at +35 degrees (I put the plus for perspective; it's positive), the integer for the question would be 35.
If this was 35 degrees below 0, it would be -35.
Hope this helps!
SOMEONE PLEASE HELP ME(picture is added!)
Given: circle A extremely tangent to circle B
Answers
Answer:
line r
Step-by-step explanation:
Given that circle A is externally tangent to Circle B
line AM is perpendicular to line r
If a family eats out 4 nights a week, what is the ratio of eating out nights to not eating out nights per week?
Answers
Answer: 4:3
eats out : not eating out
Step-by-step explanation:
so theres 7 days in a week so you do simple subtraction and do 7-4=3
then you get the remaining days of the week that you dont eat out.
Daniel is starting his own sewing business. Daniel has calculated that he needs to earn $360 per week to support his family. If he knows he will only be able to work 30 hours per week, what is the minimum amount of dollars per hour will he need to charge his customers?
Answers
Answer:
$12 the hour
Step-by-step explanation:$360 divided by 30 is 12, meaning he will need to make a minimum of 12 an hour to support his family.
Answer: 12 dollars
Step-by-step explanation:
360 divided by 30 is 12
PLEASE HELP ME, I DON'T UNDERSTAND! :(
Answers
Answer:
(x + 1) (x + 2) / 2
Step-by-step explanation:
(x² − 4x − 5) / (x − 2) ÷ (2x − 10) / (x² − 4)
To divide by a fraction, multiply by its reciprocal.
(x² − 4x − 5) / (x − 2) × (x² − 4) / (2x − 10)
Factor.
(x − 5) (x + 1) / (x − 2) × (x − 2) (x + 2) / (2 (x − 5))
Reduce.
(x + 1) × (x + 2) / 2
(x + 1) (x + 2) / 2
The blue and orange lines represent a system. Use the sliders to manipulate the orange line to determine which equations would create a system that has no solution.
Answers
2x + y = -5
-2x = y
2x = 4 - y
Answer: A/D/E
Step-by-step explanation:
2x + y = -5
-2x = y
2x = 4 - y
In ΔKLM, the measure of ∠M=90°, the measure of ∠L=18°, and KL = 8.3 feet. Find the length of MK to the nearest tenth of a foot.
Answers
Answer:
2.6 ft
Step-by-step explanation:
8.3/sin 90 = MK/sin 18
MK = 8.3 sin 18 / sin 90
MK = 2.6 ft
Answer:
2.6
Step-by-step explanation:
What is 39,800,000 in scientific notation? A. 3.98 x 10 B. 398 x 10 C. 3.98 x 10 D. 39.8 x 10
Answers
the answer is c hope this help's
Will mark brainliest
Answers
Answer:
Interquartile range => 7
Third quartile => 22
Range => 13
First quartile => 15
Step-by-step explanation:
Order your data set, from the least amount to the highest amount:
$12, $14, $15, $15, $15, $15, $16, $22, $24, $25
Interquartile range (IQR) = third quartile (Q3) - first quartile (Q1)
Q1 = the middle value of the lower part of the data set, from the median to your left.
Q3 = the middle value of the upper part of the data set, from the median to your right.
The median lies between the 5th and 6th value that is enclosed in the parenthesis below:
$12, $14, ($15), $15, $15,[Median], $15, $16, ($22), $24, $25
The median divides the data set into upper and lower part.
Median = [tex] \frac{15 + 15}{2} = 15 [/tex]
First quartile: Q1 = $15
Third quartile: Q3 = $22
IQR = $22 - $15 = $7
Range = highest amount - least amount = 25 - 12 = $13
sameer usually drinks 3 cups of coffee in the morning. How many liters of coffee does he drink? Round your answer to the nearest tenth
Answers
Answer: 0.7 liters
Step-by-step explanation:
First convert 3 cups to Liters
3 cups = 0.709765
Now round 0.709765 to the nearest 10 which give you 0.7
Answer:
0.7 liters Hope this helps!
Step-by-step explanation:
On her first week of summer Kelly teacher gave her 694 used markers 78 of those markers were out of ink and she gave 136 markers to a friend. How many useable markers does kelly have after her first week of summer
Answers
Answer:
480 markers
Step-by-step explanation:
694 - (78+136) =
694 - 214
= 480 markers
Answer:
694 - 78 = 616, then you take 616 - 136 = 480 total markers left.
(out of ^ ink) (the ones she ^ gives to her friend)
Step-by-step explanation:
480 markers are left for her first week of summer! hope this helps, good luck!
Uma folha de papel foi dobrada como mostra o esquema abaixo. Determine o valor do ângulo alfa.
Answers
Answer:
[tex]\alpha = 35º[/tex]
Step-by-step explanation:
Primeiro, vamos dizer que essa folha tem extremidades nos pontos [tex]A, B, C, D[/tex].
E vamos chamar os vértices do triângulo que contém o ângulo [tex]\alpha[/tex] de [tex]E, F, G[/tex].
Na semireta de baixo, formada por [tex]DC[/tex], a gente tem um ângulo de [tex]70º[/tex] e um outro ângulo de [tex]90º[/tex] (porque ele indica um ângulo reto).
Vamos dizer que estes dois ângulos se encontram no ponto [tex]E[/tex], que combinamos antes, como vértice (extremidade) do triângulo de cima.
Como os dois ângulos, estão num mesmo ponto, [tex]E[/tex], podemos dizer que existe um terceiro ângulo para o qual sua soma seja [tex]180º[/tex]. E tem, seria o ângulo à esquerda de
Vamos chamar este ângulo de [tex]\beta _{I}[/tex]. Portanto:
[tex]\beta _{I} + 90º + 70º = 180º\\\beta _{I} = 180º - 160º\\\beta _{I} = 20º[/tex]
Agora, temos um outro triângulo no canto inferior esquerdo da folha, cujos ângulos são [tex]\beta x_{I}[/tex], [tex]90º[/tex] e um outro ângulo, que vamos chamar de [tex]\beta x_{II}[/tex]
Esse último vai ser o ângulo superior deste triângulo, tá legal?
Então, vamos ter que:
[tex]\beta _{I} + 90º + \beta _{II} = 180º\\\beta _{I} + \beta _{II} = 90º\\[/tex]
Como [tex]\beta _{I} = 20º[/tex],
[tex]\beta _{I} + \beta _{II} =20º + \beta _{II}[/tex]
[tex]20º + \beta _{II} = 90º\\\beta _{II} = 90º - 20º\\\beta _{II} = 70º[/tex]
Ou seja, o ângulo superior do triângulo no canto inferior esquerdo, é 70º.
Vamos concordar, que este mesmo triângulo tem vértices nos pontos [tex]F, D, E[/tex]. Onde [tex]F[/tex] é o ponto superior, [tex]D[/tex] é a extremidade inferior esquerda do retângulo e [tex]E[/tex] é aquele mesmo ponto em que se encontram os ângulos de [tex]90º[/tex]e [tex]70º[/tex].
Mais à frente, você vai entender o porquê é importante nomear estes pontos, eu fiquei 40 minutos tentando fazer essa questão sem fazer isso e não conseguia porque empacava numa parte da resolução.
Então, agora, sabemos que o ângulo [tex]\beta _{II}[/tex], que é o encontro dos seguimentos [tex]FD[/tex] e [tex]EF[/tex] vale [tex]70º[/tex].
Até aqui, foi só aplicar propriedades. Mas, a partir desse ponto, você vai precisar usar a criatividade.
Então, você entende que o ângulo [tex]\beta _{II}[/tex] está inserido numa reta com outros dois ângulos concentrados no ponto [tex]F[/tex].
Então, pode dizer que esse ângulo externo é o suplemento de [tex]\beta _{II}[/tex].
Vamos chamar todo ele de [tex]\beta _{III}[/tex]
[tex]\beta _{II} + \beta _{III} = 180º\\70º + \beta _{III} = 180º\\\beta _{III} = 180º - 70º\\\beta _{III} = 110º[/tex]
Agora, vamos elevar o nível de criatividade no raciocínio e ver também que temos um quadrilátero formado pelos pontos [tex]A, G, F, E[/tex]
A soma dos ângulos de qualquer quadrilátero é 360º.
E temos que esse mesmo quadrilátero é formado por dois ângulos retos, além do ângulo de 110º que calculamos.
A última extremidade que falta é um ângulo formado pela soma de [tex]\alpha[/tex] a um outro ângulo, que vamos chamar de [tex]\beta _{IV}[/tex].
Então, temos que:
[tex]90º + 110º + 90º + \alpha + \beta _{IV} = 360º\\\alpha + \beta _{IV} +290º = 360º\\\alpha + \beta _{IV} = 360º + 290º\\\alpha + \beta _{IV} = 70º\\[/tex]
De todas, as etapas dessa resolução essa é a mais importante de entendermos os pontos que definimos. Eu refiz ela várias vezes porque não fiz isso antes.
Mas, veja, quando a gente dobra a folha, pegamos um formato qualquer e destacamos do resto dela.
Isso quer dizer que o formato que ficou dobrado é o mesmo que falta na folha. Do contrário, estaríamos criando folha ou excluindo matéria, o que não é possível no caso de uma simples dobra.
Em outras palavras, os triângulos [tex]AGF[/tex] e [tex]EFG[/tex] são os mesmos. (Eu recomendo que você construa esse desenho e coloque as letras em cada ponto, pra visualizar melhor.)
Isso é o mesmo que dizer que os ângulos de um vão ser os ângulos do outro.
Portanto, os ângulos são equivalentes. (Mesmos ângulos para ambos os triângulos, mudando só de posição.)
Assim, você pode afirmar que [tex]\alpha[/tex] = [tex]\beta _{IV}[/tex]
Se subirmos um pouco a resolução, vamos lembrar que encontramos que [tex]\alpha + \beta _{IV} = 70º\\[/tex]
Se [tex]\alpha = \beta _{IV}[/tex]
Temos:
[tex]\alpha + \alpha = 70º\\2\alpha = 70º\\\alpha = \frac{70º}{2} \\[/tex]
e TCHARAAN!
[tex]\alpha = 35º[/tex]
-------------------------
Força, guerreiro(a). Sucesso e que Deus te abençoe nos estudos.
In which set(s) of numbers would you find the number
67
Orational number
irrational number
O whole number
integer
O natural number
O real number
Answers
Answer:
Rational
Explanation: because it can be expressed in the quotient of two integers:67÷1
Mike earned $3500 last month. His employer deducted one-eighth of that amount for taxes. Mike also had $90 out of
what was left taken out for an automatic savings plan. How much money, to the nearest cent, did Mike have left after
these deductions?
Answers
Answer:
2972.5
Step-by-step explanation:
3500*7/8 - 90 = 2972.5