Use the recursive formula to find the first five terms in the arithmetic sequence.
Answers
The first five terms of the given arithmetic sequence are:
1/5, 2/5, 3/5, 4/5, 1 (Fourth option)
The arithmetic sequence is given as follows,
f(n) = f(n-1) + 1/5 ............ (1)
Now, for finding the first five term of this arithmetic sequence, we will substitute n as 1, 2, 3, 4, and 5 one by one. Using the above formula for the arithmetic sequence, we can deduce the first five terms.
It is already given that f(1) = 1/5 ......... (2)
f(1) is the first term of the sequence.
Now, putting n=2 in equation (1), we get,
f(2) = f(2-1) + 1/5
f(2) = f(1) + 1/5
Substitute f(1) = 1/5 from equation (2)
⇒ f(2) = 1/5 + 1/5
f(2) = 2/5
To find the third term of the arithmetic sequence, put n = 3 in equation (1)
f(3) = f(3-1) + 1/5
f(3) = f(2) + 1/5
⇒ f(3) = 2/5 + 1/5
f(3) = 3/5
Similarly, we can find the fourth and fifth terms of the arithmetic sequence by substituting n = 4 and n = 5 respectively.
∴ f(4) = f(3) + 1/5
⇒ f(4) = 3/5 + 1/5
f(4) = 4/5
Likewise, f(5) = f(4) + 1/5
⇒f(5) = 4/5 + 1/5
f(5) = 1
Thus, using the recursive formula, the first five terms of the arithmetic sequence come out to be:
1/5, 2/5, 3/5, 4/5, 1
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Related Questions
Garland has 9/10
of a pizza, the pizza needs to be equally divided between garland and her five friends. What fraction
of the pizza will each friend get?
Answers
Answer:
9/50
Step-by-step explanation:
We simply divide the pizza we have (9/10) by the number of friends (5):
9/10 : 5 = 9/50
Step by step
We will divide 9/10 of a pizza by 6 (Garland + 5 friends)
9/10 divided by 6
Flip the 6 and multiply across
9/10 x 1/6 = 9/60
Simplify by dividing top and bottom by 3 = 3/20 of a pizza
Check your work
9/10 is .9 as a decimal, you can divide .9 by 6 = .15 or 15/100 of the pizza, the same as 3/20.
write the following numbers in p by q form 2.015151515...
Answers
Answer:
[tex]\frac{133}{66}[/tex]
Step-by-step explanation:
we require 2 equations with the repeating digits placed after the decimal point.
let x = 2.01515... ( multiply both sides by 10 and 1000 )
10x = 20.1515.... (1)
1000x = 2015.1515... (2)
subtract (1) from (2) thus eliminating the repeating digits
990x = 1995 ( divide both sides by 990 )
x = [tex]\frac{1995}{990}[/tex] = [tex]\frac{133}{66}[/tex] ← in simplest form
If the first two angles of a triangle measure 37° and 104°, what is the measurement of the third?
Answers
Answer:
67
Step-by-step explanation:
All triangles have three angles. The sum of the three angles should equal up to 180 degrees.
108-104-37= 67
PQRS is a cyclic quadrilateral.Chord RS is produced to T.K is a point on RS and W is a point on the circle such that QRKW is a parallelogram. PS and QW intersect at U. PST = 136° and Q₁ =100° Determine, with reasons, the size of: 8.1.1.R 8.1.2.P 8.1.3.PQW 8.1.4.U2
Answers
Answer:
Step-by-step explanation:
PS and QW intersect at U. PST = 136° and Q₁ =100°
f(x)
Which type of function describes f(x)?
•
Rational
Polynomial
O Logarithmic
• Exponential
Answers
Answer:
Exponential function
[tex]y=1.25(2)^x[/tex]
Step-by-step explanation:
Definitions
Asymptote: a line that the curve gets infinitely close to, but never touches.
Hole: a point on the graph where the function is not defined.
Polynomial Function[tex]f(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_2x^2+a_1x+a_0[/tex]
An equation containing variables with non-negative integer powers and coefficients, that involves only the operations of addition, subtraction and multiplication.
A continuous function with no holes or asymptotes.
Rational Function[tex]f(x)=\dfrac{h(x)}{g(x)}[/tex]
An equation containing at least one fraction whose numerator and denominator are polynomials.
A rational function has holes and/or asymptotes.
A rational function has holes where any input value causes both the numerator and denominator of the function to be equal to zero.A rational function has vertical asymptotes where the denominator approaches zero.If the degree of the numerator is smaller than the degree of the denominator, there will be a horizontal asymptote at y = 0.If the degree of the numerator is the same as the degree of the denominator, there will be a horizontal asymptote at y = ratio of leading coefficients.If the degree of the numerator is exactly one more than the degree of the denominator, slant asymptotes will occur. Logarithmic Function[tex]f(x) =\log_ax[/tex]
A continuous function with a vertical asymptote.
A logarithmic function has a gradual growth or decay.
Exponential Function[tex]f(x)=ab^x[/tex]
The variable is the exponent.
A continuous function with a horizontal asymptote.
An exponential function has a fast growth or decay.
Answer: exponential
Step-by-step explanation:
(50 POINTS!!!) find the total surface area and volume, then multiply by $0.004. please show your work!!
Answers
The Total surface area of the square pyramid = 115.2 in.²
The Volume of the square pyramid = 1,024 in.³.
What is the Total Surface Area of a Square Pyramid?The total surface are of a square pyramid is given as: TSA = SA = 1/2(P × l), where:
P = perimeter of the square base
l = slant height of the pyramid
What is the Volume of a Square Pyramid?The volume of a square pyramid = 1/3(a³ × h), where:
a = edge of the square base
h = height of the pyramid
Find the Total surface area of the Pyramid:
P = 4(a) = 4(8) = 32 in.
l = 7.2 in.
Total surface area of the square pyramid = 1/2(32 × 7.2)
Total surface area of the square pyramid = 115.2 in.²
Volume of the square pyramid:
a = 8 in.
h = 6 in.
Volume of the square pyramid = 1/3(8³ × 6)
Volume of the square pyramid = 1,024 in.³
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3 cm ▼ 2 cm The diagram shows a prism. Work out the volume of the prism. 4 cm 1 cm 12 cm
Answers
=96
The volume occupied by 34 grams of brass is 4.0 cubic centimeters. the density of the brass is...
Answers
Answer:
8.5 g/cm^3
Step-by-step explanation:
Density = mass/volume
= 34 g / 4 cm^3 = 8.5 g/cm^3
Answer:
8.5 grams per cubic centimeter.
Step-by-step explanation:
Density = mass / volume
= 34 / 4
= 8.5 grams / cubic centimeter.
What is the end behavior of the function f of x equals 3 times the cube root of x? as x → –[infinity], f(x) → –[infinity], and as x → [infinity], f(x) → [infinity]. as x → –[infinity], f(x) → [infinity], and as x → [infinity], f(x) → –[infinity]. as x → –[infinity], f(x) → 0, and as x → [infinity], f(x) → 0. as x → 0, f(x) → –[infinity], and as x → [infinity], f(x) → 0.
Answers
The function [tex]f(x)=4\sqrt[3]{x}[/tex] is a cube root function and the function end behavior is: [tex]x[/tex] → [tex]+[/tex] ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞, and as [tex]x[/tex] → - ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞
What is end behavior?The end behavior of a function f defines the behavior of the function's graph at the "ends" of the x-axis. In other words, the end behavior of a function explains the graph's trend when we look at the right end of the x-axis (as x approaches +) and the left end of the x-axis (as x approaches ).To determine the end behavior:
The equation of the function is given as: [tex]f(x)=4\sqrt[3]{x}[/tex]To determine the end behavior, we plot the graph of the function f(x).We can see from the accompanying graph of the function:As x approaches infinity, so does the function f(x), and vice versa.As a result, the function end behavior is:[tex]x[/tex] → [tex]+[/tex] ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞, and as [tex]x[/tex] → - ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞
Therefore, the function [tex]f(x)=4\sqrt[3]{x}[/tex] is a cube root function and the function end behavior is: [tex]x[/tex] → [tex]+[/tex] ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞, and as [tex]x[/tex] → - ∞, [tex]f(x)[/tex] → [tex]+[/tex] ∞
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The complete question is given below:
What is the end behavior of the function f of x equals negative 4 times the cube root of x?
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞.
As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0.
As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0.
Answer:
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
Step-by-step explanation:
I got it right on the test.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the inverse of the given function.
Answers
The inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3 is f⁻¹(x) = 4x² - 3, for x ≤ - 1/2.
In the question, we are asked to find the inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3.
The domain for the given function is x ≥ -3.
Thus, its range is x ≤ - 1/2.
To find the inverse, we equate f(x) = y, to get:
(-1/2)√(x + 3) = y,
or, √(x + 3) = -2y.
Squaring both sides, we get:
x + 3 = (-2y)²,
or, x + 3 = 4y²,
or, x = 4y² - 3.
Thus, the inverse of the function f(x) = (-1/2)√(x + 3), is, f⁻¹(x) = 4x² - 3.
The inverse will have the domain equal to the range of the original function, that is, x ≤ - 1/2.
Thus, the inverse of the function, f(x) = (-1/2)√(x + 3), x ≥ -3 is f⁻¹(x) = 4x² - 3, for x ≤ - 1/2.
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The provided question is incomplete. The complete question is:
"Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the inverse of the given function.
f(x) = (-1/2)√(x + 3), x ≥ -3
f⁻¹(x) = x² - , for x ≤ ."
Solve the system u=3x-4y, v=x+4y for x and y in terms of u and v. then find the value of the jacobian
Answers
Eliminate [tex]y[/tex].
[tex]u + v = (3x - 4y) + (x + 4y) = 4x \implies x = \dfrac{u+v}4[/tex]
Eliminate [tex]x[/tex].
[tex]u - 3v = (3x - 4y) - 3 (x + 4y) = -16y \implies y = \dfrac{3v-u}{16}[/tex]
The Jacobian for this change of coordinates is
[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} \dfrac14 & \dfrac14 \\\\ -\dfrac1{16} & \dfrac3{16} \end{bmatrix}[/tex]
with determinant
[tex]\det(J) = \dfrac14\cdot\dfrac3{16} - \dfrac14\cdot\left(-\dfrac1{16}\right) = \dfrac1{16}[/tex]
Two marbles are to be pulled from a bag that contains 2 yellow marbles, 4 green marbles, and 6 orange marbles. After the first marble is drawn, it is not replaced. What is the probability that two red marbles are chosen from the vase?
Answers
Using it's concept, the probability that two red marbles are chosen from the vase is of 0%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that there are no red marbles, hence the number of desired outcomes is of 0, and there is a 0% probability that two red marbles are chosen from the vase.
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5. Enter the answer as a decimal
Calculate the rate of interest, when simple interest = $5,616;
loan amount = $7,200 and time = 12 years.
Answers
Answer:
6.5%
Step-by-step explanation:
I = prt
5616 = 7200 × r × 12
r = 5616/(7200 × 12)
r = 0.065
r = 6.5%
evaluate 4 + 6 x 6 / 8
Answers
Answer:
8.5
Step-by-step explanation:
4 + (6)(6)/8=
17/2 = 8.5
Answer:
8.5
Step-by-step explanation:
6 x 6 = 36/8 = 4.5 + 4 = 8.5
If a hypothesis test is found to have power = 0. 80, which is the probability that the test will result in a type ii error?
Answers
The probability that the hypothesis test will result in a type ii error, β is 0.20.
In this question,
A type II error is one of two types of statistical errors that can result from a hypothesis test (the other being a type I error). A type II error will occur if the statistical test is not powerful enough. And it occurs when one rejects the alternative hypothesis (fails to reject the null hypothesis) when the alternative hypothesis is true.
The probability of a type II error is denoted by *beta*, β.
Power of a test = 0.80
The relation between power of a test and type II error is given as,
Power = 1 - type II error
⇒ Type II error, β = 1 - 0.80
⇒ Type II error, β = 0.20
Hence we can conclude that the probability that the hypothesis test will result in a type ii error, β is 0.20.
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Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.
What are the missing segment lengths shown in the image?
Answers
By applying Pythagoras theorem, the missing segment lengths of this triangles include:
CD = 10√2AC = 10√2BC = 10AB = 10How to find the missing segment lengths?Since triangle ACD is a right-angle triangle, we would use Pythagoras theorem to find the missing segment lengths of this triangles as follows:
c² = a² + b² ≡ AD² = CD² + AC²
Next, we would use cos trigonometric ratio to find side CD,
cos45 = adjacent/hypotenuse
cos 45 = CD/20
1/√2 = CD/20
CD = 1/√2 × 20
CD = (20√2)/2
CD = 10√2
For side AC, we have:
AD² = CD² + AC²
AC² = AD² - CD²
AC² = 20² - (10√2)²
AC² = 400 - 100(2)
AC = √200
AC = 10√2
From triangle ABC, we have:
cos45 = BC/10√2
BC = 10√2 × cos45
BC = 10√2 × 1/√2
BC = (10√2)/√2
BC = 10
For side AB, we have:
AB² = (10√2)² - 10²
AB² = 200 - 100
AB² = 100
AB = 10.
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The following are the ages of 13 history teachers in a school district. 24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56 Notice that the ages are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum: Interquartile range:
Answers
The five-number summary and the interquartile range for the data set are given as follows:
Minimum: 24.Lower quartile: 29.Median: 43.Upper quartile: 50.Maximum: 56.Interquartile range: 50 - 29 = 21.What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference between the third quartile and the first quartile.In this problem, we have that:
The minimum value is the smallest value, of 24.The maximum value is the smallest value, of 56.Since the data-set has odd cardinality, the median is the middle element, that is, the 7th element, as (13 + 1)/2 = 7, hence the median is of 43.The first quartile is the median of the six elements of the first half, that is, the mean of the third and fourth elements, mean of 29 and 29, hence 29.The third quartile is the median of the six elements of the second half, that is, the mean of the third and fourth elements of the second half, mean of 49 and 51, hence 50.The interquartile range is of 50 - 29 = 21.More can be learned about five number summaries at https://brainly.com/question/17110151
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Area of triangle in coordinate geometry
Answers
Select the correct answer.
Consider function g.
9(z) = 3 sin (TZ)
Function g is horizontally stretched by a factor of 2 and then translated 2 units down to obtain function f. Which graph matches the described
transformation?
Answers
The y-intercept exists reduced by 2 units. Hence there exists a translation of 2 units down.
How to find the graph of the given function?
Let the function be g(z) = 3 sin (TZ).
A vertical stretch by a factor of k indicates that the point (x, y) on the graph of f (x) exists transformed to the point (x, ky) on the graph of g(x), where k < 1.
If k = 1, then the same graph we get, and if k > 1 we get a vertically shrink graph.
In our question, there exists a vertical stretch of 2. This means the new graph would have points as (x, y/2)
i.e. instead of f(x) = y, we have now f(x) = y/2
So transformation is g(x) = 3f(x)
The y-intercept exists reduced by 2 units. Hence there exists a translation of 2 units down.
Therefore, the correct answer is option C.
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The graph of a quadratic function is represented by the table.
x f(x)
6 -2
7 4
8 6
9 4
10 -2
What is the equation of the function in vertex form?
Substitute numerical values for a, h, and k.
Big fraction
Parentheses
Vertical bars
Square root
Root
Superscript (Ctrl+Up)
Subscript (Ctrl+Down)
Plus sign
Minus sign
Middle dot
Multiplication sign
Equals sign
Less-than sign
Greater-than sign
Less-than or equal to
Greater-than or equal to
Pi
Alpha
Beta
Epsilon
Theta
Lambda
Mu
Rho
Phi
Sine
Cosine
Tangent
Arcsine
Arccosine
Arctangent
Cosecant
Secant
Cotangent
Logarithm
Logarithm to base n
Natural logarithm
Bar accent
Right left arrow with under script
Right arrow with under script
Angle
Triangle
Parallel to
Perpendicular
Approximately equal to
Tilde operator
Degree sign
Intersection
Union
Summation with under and over scripts
Matrix with square brackets
Answers
The equation of the function in vertex form exists f(x) = -2·(x - 8)² + 6.
What is the equation of the function in vertex form?The given values exist
x, f(x)
6, -2
7, 4
8, 6
9, 4
10, -2
The equation of the function in vertex form exists
f(x) = a(x - h)² + k
To estimate the values of a, h, and k,
When x = 6, f(x) = -2 then
-2 = a(6 - h)² + k
= (h²-12·h+36)·a + k.............(1)
When x = 7, f(x) = 4 then
4 = a( 7- h)² + k
= (h²-14·h+49)·a + k...........(2)
When x = 8, f(x) = 6
6 = a( 8- h)² + k ...........(3)
When x = 9, f(x) = 4.
4 = a( 9- h)² + k ..........(4)
When x = 10, f(x) = -2
-2 = a(10- h)² + k ...........(5)
Subtract equation (1) from (2)
4 - 2 = a( 7- h)² + k - (a(6 - h)² + k )
= 13·a - 2·a·h........(6)
Subtract equation (4) from (2)
a (9 - h)² + k - a( 7- h)² + k
32a -4ah = 0
Simplifying the equation, we get
4h = 32
h = 32/4 = 8
From equation (6) we have;
13·a - 2·a·8 = 6
-3a = 6
a = -2
From equation (1), we have;
-2 = -2 × ( 10- 8)² + k
-2 = -8 + k
k = 6
The value of k = 6.
The equation of the function in vertex form exists f(x) = -2·(x - 8)² + 6.
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an object moves at a speed of 3/16 feet per second. what is the speed, in yards per second? (3 feet= 1 yard)
Answers
3/16 * 1/3
3*1 / 16*3
3/48
1/16 yd/sec
Which graph shows the solution to this system of in
y>-1/3x+1
y> 2x-3
Answers
Answer:
Step-by-step explanation:
the graph is down below
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answers
[tex]y = mx + n[/tex]
[tex]m = \frac{y - y}{x - x} = \frac{5 - ( - 1)}{ - 5 - ( - 3)} = \frac{6}{ - 2} = - 3[/tex]
[tex]y = - 3x + n \\ [/tex]
Since both ( -3 , -1 ) and ( -5 , 5 ) pass through the line, they both satisfy its equation. Substitute any point in the new equation, I will choose ( -5 , 5 )[tex]5 = - 3( - 5) + n \\ n = 5 - 15 = - 10[/tex]
[tex]y = - 3x - 10[/tex]
Satia drives for 4 hours from a to b. angelique drives at half the speed of safia. find how many hours angelique takes to drive from a to b
Answers
Angelique takes 8 hours to drive from a to b.
What is the concept of speed, distance and time?How quickly something or someone is moving is indicated by their speed. If you know how far something travels and how long it takes, you can calculate their average speed. Speed equals distance x times time, according to the speed formula. Knowing the units for distance and time will help you determine what the units are for speed.
According to given Information:let us assume distance from a to b be x units.
let us assume speed of vehicle be y units/hour.
For case -1For Satia, speed=y units time=4 hours we know the formula of distance is:
distance=speed × time distance=(y× 4) units -------------------(1)
For case - 2Angelique :speed=y / 2 units time=?
We know the formula of distance is:
Distance=speed × time distance=(y/2)× time -------------------(2)
We can see that distance in both cases is equal,
So compare case (1) ad (2) ,
We get (y× 4)=(y/2)× time
On rearranging ,
Time= (4×2) hours=8 hours
hence,
Angelique takes 8 hours to cover the distance from a to b.
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The numbers of questions answered correctly by various students on a 1010-question quiz are an example of which type of data?
Answers
The numbers of questions answered correctly by various students on a 10 question quiz are an example of discrete data.
What is discrete data?Discrete data is the type of data that has clear spaces between values.
As a result, the test-scores are discrete data. Although most discrete data, refers to things we can count easily, it does not have to be numeric. Non-numeric categories could be described as discrete data.
Discrete data is a count that involves integers — only a limited number of values is possible. This type of data cannot be subdivided into different parts. Discrete data includes discrete variables that are finite, numeric, countable, and non-negative integers.
Discrete data is a type of quantitative data that includes figures and statistics of non divisible, single points of data that you can count. You typically write discrete data points as numbers that represent exact values, and discrete data usually represents single events that have already occurred. When reviewing discrete data, companies analyze exact figures like units that were sold on a given day or the hours that an employee worked during a certain week.
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There are different types of correlation one can use based on the types of variables being examined. When conducting an analysis, when do you need to use spearman’s rho instead of pearson’s r ?.
Answers
The correct option is A.
When the data are nominal or ordinal.
What are the Types of correlation?There are three types of correlation:
1. Positive and negative correlation
2. Linear and non-linear correlation
3. Simple, multiple, and partial correlation
According to the information:There are different types of correlation one can use based on the types of variables being examined.
Spearman’s rho is a superb choice when you have nominal or ordinal data because Pearson’s isn't appropriate. Ordinal data have a minimum of three categories and the categories have a natural order. for instance , first, second, and third during a race are ordinal data.
Briefing:Two variables can have some quite relationship, i.e., change in one may cause a change within the other.
If a change within the value of one variable causes a simultaneous change in the other variable in the same or opposite direction, then it’s termed as correlation, or these variables are said to be correlated. Keeping these in mind the answer to this question is When the data are nominal or ordinal
When the data are nominal or ordinal.
So the option no A is correct.
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I understand that the question you are looking for is:
There are different types of correlation one can use based on the types of variables being examined. When conducting an analysis, when do you need to use spearman’s rho instead of Pearson's r ?
A. When the data are nominal or ordinal.
B. When the data are ratio or interval.
C. When the data are random.
D. Spearman's rho should never be used for correlations.
NEED HELP PLEASE ASAP!!!
Find the quotient of 213.21 and 15.8. Round your answer to the nearest tenth.
13.4
1.4
1.3
13.5
Answers
Answer:
13.5
Step-by-step explanation:
213.21/15.8 ---> ((213.21)100)/((15.8)100)
21321/1580 = 13 R 781.
781/1580 = 0.49~~~
We only need to be concerned about the tenth and hundredth place digits.
The decimal tells us that it rounds up from 4, so it's 5.
Thus, the answers 13+0.5, which is 13.5
The bisectors BO and CO of the angles at B and C of ABC meet at O. Prove that BOC = 90° + A/2.
Answers
The prove that BOC = 90° + A/2. is given below:
What is the bisector about?Note that, bisectors of angles B and C and that of a triangle ABC is one that pass across each other at the point O.
Hence: one need to to prove that ∠BOC = 90° + A/2
Since:
BO is said to be the bisector of angle B e.g. ∠OBC = (∠1)
CO is said to be the bisector of angle C e.g. ∠OCB = (∠2)
Looking at the triangle BOC, to interpret by the use of angle sum property, then:
∠OBC + ∠BOC + ∠OCB = 180°
∠1 + ∠BOC + ∠2 = 180° ---- ( equation 1)
Looking at triangle ABC and by the use of angle sum property, So;
∠A + ∠B + ∠C = 180°
∠A + 2(∠1) + 2(∠2) = 180°
Then we divide by 2 on the two sides, and it will be:
∠A/2 + ∠1 + ∠2 = 180°/2
∠A/2 + ∠1 + ∠2 = 90°
∠1 + ∠2 = 90° - ∠A/2 ---(equation 2)
Then one need to Substitute (2) in (1), So:
∠BOC + 90° - ∠A/2 = 180°
∠BOC - ∠A/2 = 180° - 90°
∠BOC - ∠A/2 = 90°
Hence , ∠BOC = 90° + ∠A/2
Therefore, from the above, we care able to prove that BOC = 90° + A/2.
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1/3 +1/6 in fraction form
Answers
[tex]\Large\texttt{Answer}[/tex]
[tex]\bf{\cfrac{1}{2}}[/tex]
[tex]\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}[/tex]
[tex]\Large\texttt{Process}[/tex]
Do you remember that we cannot add fractions when they have unlike denominators? We can onyl add fractions as long as they have the same denominator!
So here's the big idea: fractions must have the same denominator.
If we multiply the first fraction by 2, then both fractions will have the same denominator. *
* Why 2??
- Because:
We need to find the least common multiple of 3 and 6, which is 6. Next, what should 3 be multiplied by to result in 6? That's right, 2.
Also, we can only multiply the denominator by 2 as long as we multiply the numerator by 2!
So that's why we multiply the whole fraction by 2
[tex]\bf{\cfrac{1\times2}{3\times2}+\cfrac{1}{6}}[/tex]
Watch what happens
[tex]\bf{\cfrac{2}{6}+\cfrac{1}{6}}[/tex]
Add the numerators
[tex]\bf{\cfrac{2+1}{6}}[/tex]
[tex]\bf{\cfrac{3}{6}}[/tex]
Simplifying the fractions
[tex]\bf{\cfrac{3\div3}{6\div3}}[/tex]
[tex]\bf{\cfrac{1}{2}}[/tex]
Hope that helped
Answer: 1 / 2
Step-by-step explanation:
Given information
[tex]\frac{1}{3} ~+~\frac{1}{6}[/tex]
Convert the denominator (3, 6) into the same common denominator
Least Common Multiple (LCM) of 3 and 6 = 6
[tex]=\frac{1~*~2}{3~*~2} ~+~\frac{1}{6}[/tex]
[tex]=\frac{2}{6} ~+~\frac{1}{6}[/tex]
Combine two fractions
[tex]=\frac{2~+~1}{6}[/tex]
[tex]=\frac{3}{6}[/tex]
Simplify the fraction by dividing 3 on both numerator and denominator
[tex]=\frac{3~/~3}{6~/~3}[/tex]
[tex]=\Large\boxed{\frac{1}{2} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
nvm no need liao
The curve y = ax^n, where a and n are constants, passes through the points (2.25, 27), (4, 64) and (6.25, p). Without using logarithms, calculate the value of a, of n and of p.
Answers
a. The value of n is 3/2
b. The value of a is 8.
c. The value of p is 125
The curve is an exponential function
What is an exponential function?An exponential function is a function of the form y = axⁿ where a and n are constants
a. How to find the value of n?
Since y = axⁿ where a and n are constants, passes through the points (2.25, 27), (4, 64) and (6.25, p), substituting these points into the equation, we have
y = axⁿ
27 = a(2.25)ⁿ (1)
64 = a(4)ⁿ (2)
P = a(6.25)ⁿ (3)
Dividing (2) by (1), we have
64/27 = a(4)ⁿ/a(2.25)ⁿ
4³/3³ = (4 ÷ 2¹/₄)ⁿ
4³/3³ = (4 ÷ ⁹/₄)ⁿ
4³/3³ = (4 × 4/9)ⁿ
4³/3³ = (16/9)ⁿ
4³/3³ = (4²/3²)ⁿ
(4/3)³ = (4/3)²ⁿ
Equating exponents, we have
2n = 3
n = 3/2
The value of n is 3/2
b. What is the value of a?Using equation (2)
64 = a(4)ⁿ
a = 64/(4)ⁿ
substituting n = 3/2 into the equation, we have
[tex]a = \frac{64}{4^{\frac{3}{2} } } \\= \frac{64}{(\sqrt{4 } )^{3} } \\= \frac{64}{2^{3} } \\= \frac{64}{8} \\= 8[/tex]
So, the value of a is 8.
c. What is the value of p.Using equation (3), we have
P = a(6.25)ⁿ (3)
substituting the values of a and n into the equation,we have
[tex]P = 8(6.25)^{\frac{3}{2} } \\= 8(\sqrt{6.25}) ^{3} \\= 8(2.5}) ^{3} \\= 8(15.625})\\= 125[/tex]
The value of p is 125
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