What are the first three terms of the sequence modeled by the recursive function An=1/2a n-1 , when a1=1?
Answers
Answer:
A on edge trust
Step-by-step explanation:
The first three term of the sequence are,
⇒ 1/2 , 1/4, 1/8
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The recursive function is,
⇒ \(A_{n} = \frac{1}{2} a_{n - 1}\)
And, We have;
⇒ a₁ = 1
Now, The recursive function is,
⇒ \(A_{n} = \frac{1}{2} a_{n - 1}\)
Put n = 2;
⇒ \(A_{2} = \frac{1}{2} a_{2 - 1}\)
⇒ \(A_{2} = \frac{1}{2} a_{1}\)
⇒ \(A_{2} = \frac{1}{2}\ * 1\)
⇒ \(A_{2} = \frac{1}{2}\)
Put n = 3;
⇒ \(A_{3} = \frac{1}{2} a_{3 - 1}\)
⇒ \(A_{3} = \frac{1}{2} a_{2}\)
⇒ \(A_{3} = \frac{1}{2}\ * \frac{1}{2}\)
⇒ \(A_{3} = \frac{1}{4}\)
Put n = 4;
⇒ \(A_{4} = \frac{1}{2} a_{4 - 1}\\\)
⇒ \(A_{4} = \frac{1}{2} a_{3}\)
⇒ \(A_{4} = \frac{1}{2}\ * \frac{1}{4}\)
⇒ \(A_{4} = \frac{1}{8}\)
Thus, The first three term of the sequence are,
⇒ 1/2 , 1/4, 1/8
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Related Questions
Solve the initial-value problem y' = (8 sin(x))/sin(y), y(0) = pi/2
Answers
Answer:
8cosx-cosy=8.
Step-by-step explanation:
dy/dx=8sinx/siny;
sinydy=8sinxdx;
-cosy= -8cosx+C;
according to the condition y(0)=pi/2:
-cos(pi/2)= -8cos0+C;
-8+C=0; ⇔ C=8, then
8cosx-cosy=8.
The solution to the given initial-value problem y' = (8 sin(x))/sin(y) with the given condition y(0) = π/2 is equal to y = -cos⁻¹(x).
To solve the initial-value problem y' = (8 sin(x))/sin(y) with the initial condition y(0) = π/2, separate variables and then integrate.
Separate variables.
y' = (8 sin(x))/sin(y). To separate variables, multiply both sides by sin(y) and divide by (8 sin(x)):
sin(y) dy = dx
Integrate both sides.
Now, integrate both sides of the equation with respect to their respective variables:
∫sin(y) dy = ∫dx
Integrating the left side:
∫sin(y) dy = -cos(y) + C₁ (where C₁ is the constant of integration)
Integrating the right side:
∫dx = x + C₂ (where C₂ is the constant of integration)
Apply initial condition.
Now, apply the initial condition y(0) = π/2 to find the values of C₁ and C₂:
When x = 0, y = π/2
cos(π/2) + C₁ = 0 (substitute y = π/2 into -cos(y) + C₁)
C₁ = 0 (since cos(π/2) = 0)
So, the equation becomes:
-cos(y) = x + C₂
Solve for y.
Now, isolate y on one side of the equation:
y =-cos⁻¹(x + C₂)
Find C₂ using the initial condition.
Now, use the initial condition y(0) = π/2 to find C₂:
When x = 0, y = π/2
π/2 = -cos⁻¹(0 + C₂)
cos⁻¹(C₂) = -π/2
C₂ = cos(-π/2) = 0
Final solution.
Finally, substitute C₂ = 0 into the equation y = -cos⁻¹(x + C₂) to get the final solution:
y = -cos⁻¹(x)
Therefore, the solution to the initial-value problem y' = (8 sin(x))/sin(y) with y(0) = π/2 is y = -cos⁻¹(x).
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2. How many radians are in 27"?
Answers
The answer is 0.471 radians.
FORMULA:
Just do 27° × π/180 = 0.4712rad but then cut off the two.
Select interior, exterior, or on the circle (x - 5) 2 + (y + 3) 2 = 25 for the following point. (3, 2) on the circle interior exterior
Answers
The point (3, 2) is exterior to the circle with this equation (x - 5)² + (y + 3)² = 25 as shown in the image attached below.
What is the equation of a circle?Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r² ....equation 1.
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.From the information provided, we have the following equation of a circle:
(x - 5)² + (y + 3)² = 25 ......equation 2.
Comparing equation 1 and equation 3, we have the following:
Center (h, k) = (5, -3)
Radius, r = 5
By critically observing the graph (see attachment), we can logically deduce that point (3, 2) is exterior to the circle.
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I need help with this one
Answers
Answer:
-12
Step-by-step explanation:
DONT ANSWER WAIT 5 MINUTES LM AO
Answers
oooooooooooooooopppppppppppppppppppppppppssssssssssss
Answer:
thankssssssssss cuhhhhhhh
Step-by-step explanation:
lm ao like if they are gonna wait lol
Solve the system of equations by graphing. y=1/3x+33x-y=5
Answers
Answer:
The solution to the system of equations is the point at which the two lines meet:
\(\begin{gathered} (3,4) \\ x=3 \\ y=4 \end{gathered}\)Explanation:
Given the system of equation;
\(\begin{gathered} y=\frac{1}{3}x+3\text{ ---1} \\ 3x-y=5\text{ ---2} \end{gathered}\)rewrite equation 2 in slope intercept form;
\(\begin{gathered} 3x-y=5 \\ y=3x-5\text{ ----2a} \end{gathered}\)Let us derive two cordinate points for each equation;
\(\begin{gathered} y=\frac{1}{3}x+3\text{ ---1} \\ at\text{ x=0;} \\ y=\frac{1}{3}(0)+3 \\ y=3 \\ (0,3) \\ at\text{ x=3;} \\ y=\frac{1}{3}(3)+3 \\ y=1+3 \\ y=4 \\ (3,4) \end{gathered}\)\(\begin{gathered} y=3x-5\text{ ----2a} \\ at\text{ x=0;} \\ y=3(0)-5 \\ y=-5 \\ (0,-5) \\ \text{at x=3;} \\ y=3(3)-5 \\ y=9-5 \\ y=4 \\ (3,4) \end{gathered}\)Plotting the coordinate points on the graph we have;
Graphing the two equations, the solution to the system of equations is the point at which the two lines meet.
\(\begin{gathered} (3,4) \\ x=3 \\ y=4 \end{gathered}\)
The question is asked in the attached file,. Kindly someone answer it in the best way.
Answers
According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.More can be learned about the Empirical Rule at https://brainly.com/question/10093236
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HELP ME!!!!
ZEARN!!!!!!!!!
Answers
A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.
Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.
Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.
Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of
To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).
First, let's convert the fractions 1/5 and 2/3 to fifteenths:
\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)
\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)
Now we can rewrite the expression using the common denominator:
\(3 + \frac{3}{15}+\frac{10}{15}\)
Which statements are true about the area of the figure? Check all that apply.
Answers
The statements that are true about the area of the figure is that the area can be found by multiplying 3 by 2 1/2 and adding the product of 1/2 and 1/2 .
How to find the statement?Recall that In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle
Also, the area of a rectangle can be found by multiplying the length of the rectangle by its width and using the formula, where is the base and is the height of the triangle.
Area of the rectangle - LB
Area = (1/2 * 1/2) + (7/2*7/2)
Area = 1/4 + 35/4
Simplifying the fraction to get
36/4
Area of the figure is 9 square units
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A function, f left parenthesis x right parenthesis comma models the depth of water in a wading pool that is filling at a rate of 11 gallons per minute. Which of these describes why f left parenthesis x right parenthesis can be considered a linear function? I. For every 1 minute interval, the depth of water in the wading pool increases by the same amount. II. The function grows by equal factors every minute. III. The slope of the function is constant.
Answers
Answer:
quiz let or brainy helps me just look up the chapter question and you will get the answer
Step-by-step explanation:
hope this helps
f(x) can be considered as a linear function because of the following conclusions -
1 → For every 1 minute interval, the depth of water in the wading pool increases by the same amount of 11 gallons/minute.
2 → The slope of the function is constant.
What is the general equation of a straight line?
The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is the following statement representing a function - f(x), that models the depth of water in a wading pool that is filling at a rate of 11 gallons per minute.
Assume that we represent the depth of the water rate by [y] and the time in minutes by [m]. We can write the function f(x) as -
y = f(x) = 11m
This is a linear relation and its graph will be a straight line passing through origin.
From this equation, we can make the following conclusions -
1 → For every 1 minute interval, the depth of water in the wading pool increases by the same amount of 11 gallons/minute.
2 → The slope of the function is constant.
Therefore, f(x) can be considered as a linear function because of the following conclusions -
1 → For every 1 minute interval, the depth of water in the wading pool increases by the same amount of 11 gallons/minute.
2 → The slope of the function is constant.
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Isosceles and equilateral triangle
Answers
Answer:
Step-by-step explanation:
so the side is 44 because the isosceles triangle tells you that the other one is also 44
since the other triangle is equilateral, it tells you that all three sides are 3x+20 or 44. so now we know 3x+20=44
since 24+20=44, we know 3x=24, to find x now, simply divide 24 by 3 nd you get 8, so X=8
Find the quotient. 2 1/3 ÷ 1
help
Answers
Answer:
\(2 \frac{1}{3} \div 1 \frac{1}{3} \\ = \frac{7}{3} \div \frac{4}{3} \\ = \frac{7}{3} \times \frac{3}{4} \\ = \frac{7}{4} \)
PLEASE MARK ME BRAINLIESTPlease answer this correctly
Answers
4 cards. The probability of picking the 6 would be 1/4 ( 1 out of 4 cards)
After the first card is picked you have 3 cards left, 2 are less than 6, so you would have a 2/3 Probability.
The probability of both happening is:
1/4 x 2/3 = 2/12 = 1/6
The answer is 1/6
If C = x2 + 7 and D = 3x2 - 4x + 3, find an expression that equals 3C + 3D in standard form.
Answers
Answer:
The new expression is: 12 x^2 - 12 x+ 30
Step-by-step explanation:
if C = x^2 + 7
and
D = 3 x^2 - 4 x + 3
Then, 3 C + 3 D can be obtained via:
3 ( x^2 + 7 ) + 3 ( 3 x^2 - 4 x + 3 ) = 3 x^2 + 21 + 9 x^2 - 12 x + 9 =
= 12 x^2 - 12 x+ 30
the number of pumps in use at both a six-pump station and a four-pump station will be determined. give the possible values for each of the following random variables. (enter your answers in set notation.) (a) t
Answers
For each variable, the possible values are:
a) T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
b) X = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}
c) U = {0, 1, 2, 3, 4, 5, 6}
d) Z = {0, 1, 2}
Item a:
In total, there are 10 pumps, hence the possible values are all integers from 0 to 10, that is:
T = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Item b:
In the first, there are 6 pumps, and in the second 4, hence, the difference ranges from -4 to 6, that is:
X = {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6}
Item c:
The maximum number in a station is 6 pumps, hence this variable ranges from 0 to 6.
U = {0, 1, 2, 3, 4, 5, 6}
Item d:
Either none of the stations has exactly two pumps in use, or one has or both, hence the variable ranges from 0 to 2.
Z = {0, 1, 2}
The question is incomplete. The complete question is:
"The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables. (Enter your answers in set notation.)
a. T = the total number of pumps in use
b. X = the difference between the numbers in use at stations 1 and 2.
c. U = the maximum number of pumps in use at either station
d. Z = the number of stations having exactly two pumps in use"
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Write an equation describing the relationship of the given variables.
y varies inversely as the cube root of x and when x=64 , y=2.
Answers
Answer:
\(y = 8x^{-1/3}\)
Step-by-step explanation:
If y varies inversely as the cube root of x, we can write this relationship mathematically as:
y = k / (x^(1/3))
where k is a constant of proportionality. To solve for k, we can use the given information that when x=64, y=2:
2 = k / (64^(1/3))
Simplifying, we have:
2 = k / 4
Multiplying both sides by 4, we get:
k = 8
Therefore, the equation describing the relationship between x and y is:
y = 8 / (x^(1/3))
or equivalently:
y = 8x^(-1/3)
x^2-7x=0 solve the equation
Answers
Answer:
x = 0, 7
Step-by-step explanation:
Step 1: Write out equation
x² - 7x = 0
Step 2: Factor out x
x(x - 7) = 0
Step 3: Find roots
x = 0
x - 7 = 0
x = 7
Answer:
x = 0, 7
Step-by-step explanation:
x²-7x = 0x(x-7) = 0x = 0 & x =7During a fundraiser, Ms. Dawson’s class raised
$
560
$560, which is
25
%
25% more than Mr. Casey’s class raised.
Mr. Casey’s class raised
$
$
.
Answers
Mr. Casey's class raised $448 during the fundraiser.
What much did mr. Casey’s class raised?Percentage is simply number or ratio expressed as a fraction of 100.
Given that, Ms. Dawson’s class raised $560, which is 25% more than Mr. Casey’s class raised.
To determine how much Mr. Casey’s class raised,
We represent the amount raised by Mr. Casey's class as "x".
Since Ms. Dawson's class raised 25% more than Mr. Casey's class.
To calculate 25% more than x, we can multiply x by 1.25
(since 25% is equivalent to 0.25 in decimal form and 100% is 1) and set it equal to $560.
Hence:
1.25x = 560
To solve for x, we divide both sides of the equation by 1.25:
x = 560 / 1.25
x = 448
Therefore, Mr. Casey's class raised $448.
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O LINEAR EQUATIONS AND INEQUALITIES
Graphing a compound inequality o...
Graph the compound inequality on the number line.
x>-8 and x≤-3
Answers
The compound inequality on the number line is shown below.
We have been given a compound inequality. We are asked to graph the given inequality on number line.
x>8 and x≤3
The solution for the inequality is all values of x less than or equal to 3 and greater than or equal to 8.
We will have solid dots at x>-8 and x≤-3 .
One arrow of the number line would be from 3 to left of the number line (towards negative infinity). The other arrow will be from 8 to right side of number line towards positive infinity.
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1. describe the end behavior. 2. determine whether it represents an odd degree or an even degree function.3. state the number of real zeroes
Answers
1. Quadratic curve
2. Odd degree function
3. TWO REAL ZEROS
there+are+4+tablespoons+in+1/4+cup+there+are+2+cups+in+1+pint+How+many+tablespoons+are+in+1+pint
Answers
Answer:
32 tablespoons are in 1 pint
Step-by-step explanation:
1/4 cup = 4 tablespoons
2/4 = 8 tablespoons
3/4 = 12 tablespoons
4/4 (1 cup) = 16 tablespoons
16*2 = 32
1 pint = 2 cups = 32 tablespoons
Erica earned a total of $67,250 last year from her two jobs. The amount she earned from her job at the store was $1,250 more than three times the amount she earned from her job at the college. How much did she earn (in dollars) from her job at the college?
Answers
Step-by-step explanation:
x = earnings from the store
y = earnings from the college
x + y = 67,250
x = 3y + 1,250
now we use the identity of the second equation in the first equation :
(3y + 1,250) + y = 67,250
4y = 66,000
y = $16,500
x = 3y + 1,250 = 3×16,500 + 1,250 = 49,500 + 1,250 =
= $50,750
Convert 10 pounds and 12 ounces to ounces.
Answers
Answer: 172 ounces
Step-by-step explanation:
We are given 10 pounds and 12 ounces to convert to ounces.
There are 16 ounces in 1 pound.
We can create a proportion to find out how much ounces 10 pounds is.
10 pounds / x ounces = 1 pound / 16 ounces
We need to solve for x by isolating the variable x.
10/x = 1/16
10 = x/16
10 * 16 = x
160 ounces = x
so 10 pounds is equivalent to 160 ounces. But we are not done yet.
We were asked to convert 10 pounds and 12 ounces.
So add together the ounces to find the total ounces:
160 ounces + 12 ounces = 172 ounces.
A water desalination plant can produce 2.46x10^6 gallons of water in one day. How many gallons can it produce in 4 days?
Write your answer in scientific notation.
Answers
The desalination plant can produce \(9.84*10^6\) gallons of water in four days in scientific notation.
We must divide the daily production rate by the number of days in order to get the total volume of water that a desalination plant can generate in four days:
4. days at a rate of \(2.46*10^6\) gallons equals \(9.84*10^6\) gallons.
Hence, in four days, the desalination plant can produce \(9.84 * 10^6\)gallons of water.
Large or small numbers can be conveniently represented using scientific notation, especially when working with measurements in science and engineering. A number is written in scientific notation as a coefficient multiplied by 10 and raised to a power of some exponent. For example, \(2.46*10^6\) denotes 2,460,000, which is 2.46 multiplied by 10 to the power of 6.
The solution in this case is \(9.84*10^6\), or 9,840,000, which is 9.84 multiplied by 10 to the power of 6. Large numbers can be written and compared more easily using this format, and scientific notation rules can be used to conduct computations with them.
In conclusion, the desalination plant has a four-day capacity of \(9.84 * 10^6\) gallons of water production.
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What is the quotient of
15y^3+ 28y^2+ 7y-6 / 5y+6?
Answers
Answer: The quotient is 3y² + 2y - 1.
Step-by-step explanation:
You can use long division to solve this expression by setting the dividend under the roof and the divisor outside as you would normally do when dividing numbers.
1) Look at the first term of the dividend, 15y³, and the first term of the divisor, 5y. Determine what value multiplied by 5y would give you 15y³. The answer is 3y², and given the number, you multiply it by the WHOLE divisor.
3y²(5y + 6) = 15y³ + 18y² <-- subtract this from the dividend.
2) Continue this process and make sure to drag down the next term for each new value you form after subtracting. Keep in mind of any negative values! When you reach up to -5y, determine what value multiplied by 5y would give you the value of -5y, which would be -1.
3) You should be left with a remainder of 0, leaving you with a quotient of 3y² + 2y - 1.
The surface area of this cylinder is 20,761.68 square yards. What is the height?
Use ≈ 3.14 and round your answer to the nearest hundredth.
29 yd
h=
Submit
h
yards
Answers
The height of the cylinder whose surface area is given would be = 85 yards.
How to calculate the height of a cylinder?The cylinder is a type of shape that has three sides which consists of two opposite circles that are joined by a curved surface.
To calculate the height of a cylinder, the formula that should be used is given as follows:
Surface area of cylinder = 2πrh + 2πr²
radius = 29 yards
surface area = 20,761.68 square yards
height = ?
That is ;
20,761.68 = 2×3.14× 29×h + 2×3.14× 29×29
20,761.68 =182.12h + 5281.48
182.12h = 20,761.68-5281.48
182.12h = 15480.2
h = 15480.2/182.12
= 85 yards
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Stephen is inviting 3 friends to a party. He has 12 cookies. How many cookies will each friend get?
Answers
Answer:
4 cookies
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
Help with both? PLEASE lol this is a review and we’ve been in class for 40 mins I’ve got nothing
Answers
Answer:
Step-by-step explanation:
\(2) y^{\frac{3}{2}}=y^{3*\frac{1}{2}}\\\\=(y^{3}}^{\frac{1}{2}}\\\\=\sqrt{y^{3}}\)
b
\(3)a^{\frac{2}{3}}=a^{2*\frac{1}{3}}\\\\=(a^{2})^{\frac{1}{3}}\\\\=\sqrt[3]{a^{2}}\)
c
Pls help I’ll brainlest
Is it rational or irrational show your work
Answers
Answer:
Step-by-step explanation:
#4
√25= 5 and 5 is rational.
#7
√(1/2) is equivalent to √1 / √2. √1 is rational but √2 is irrational.
Thus the expression √(1/2) is irrational.
4. 5
7. 1/2
Order -6, -9, -14, 0 from greatest to least (absolute value)
Answers
Answer:
Step-by-step explanation:
the absolute value of a number is the positive number, meaning the absolute value of these would be |-6| = 6, |-9|=9 |-14|=14 |0|=0
so the answer would be: |-14|, |-9|, |-6|, |0|
the only time it wouldn't be positive is when the negative sign is on the outside. (-|9|=-9 etc.)