Answer:
To find the 9th term of a geometric sequence, we can use the formula:
an = a1 * r^(n-1)
where:
an = the nth term of the sequence
a1 = the first term of the sequence
r = the common ratio of the sequence
n = the term number we want to find
In this case, we are given that the common ratio is 2/3, the first term is 6, and we want to find the 9th term. So we can plug in those values and get:
a9 = 6 * (2/3)^(9-1)
Simplifying the exponent, we get:
a9 = 6 * (2/3)^8
Using a calculator, we can evaluate the exponent:
a9 = 6 * 0.015625
Multiplying, we get:
a9 = 0.09375
Therefore, the 9th term of the geometric sequence is 0.09375.
Step-by-step explanation:
here's a step-by-step explanation:
We are given the first term of the geometric sequence, a1 = 6, and the common ratio, r = 2/3. We need to find the 9th term, which we can do using the formula:
an = a1 * r^(n-1)
where n is the term number we want to find.
Step 1: Substitute the given values into the formula
a9 = 6 * (2/3)^(9-1)
Step 2: Simplify the exponent
a9 = 6 * (2/3)^8
The exponent 9-1 simplifies to 8.
Step 3: Evaluate the exponent
a9 = 6 * 0.015625
We can use a calculator to evaluate (2/3)^8, which is 0.015625.
Step 4: Multiply to find the 9th term
a9 = 0.09375
Multiplying 6 by 0.015625 gives us the 9th term of the geometric sequence, which is 0.09375.
Therefore, the 9th term of the geometric sequence whose common ratio is 2/3 and whose first term is 6 is 0.09375.
The suspension cable that supports a footbridge hangs in the shape of a parabola. The height h, in feet, of the cable above the bridge is given by the function
h(x) = 0.25x ^ 2 - 0.8x + 30, 0 < x < 3.2
where x is the distance in feet measured from the left tower toward the right tower. What is the minimum height of the cable above the bridge? (Round your answer to two decimal places.)
Step-by-step explanation:
The height of the cable above the bridge is given by the function:
h(x) = 0.25x^2 - 0.8x + 30
To find the minimum height of the cable above the bridge, we need to find the vertex of the parabola, which is the lowest point.
The x-coordinate of the vertex is given by:
x = -b / 2a
where a = 0.25 and b = -0.8. Substituting these values, we get:
x = -(-0.8) / 2(0.25) = 1.6
So the vertex is at x = 1.6.
To find the height of the cable at the vertex, we substitute x = 1.6 into the equation for h(x):
h(1.6) = 0.25(1.6)^2 - 0.8(1.6) + 30 = 29.48
Therefore, the minimum height of the cable above the bridge is approximately 29.48 feet (rounded to two decimal places).
HELP ME ASAP I NEED A NUMERICAL ANSWER
Owen's Muffin Extravaganza recorded how many of each type of muffin it recently sold.
bran muffins 25
blueberry muffins 12
poppy seed muffins 3
chocolate chip muffins 10
Considering this data, how many of the next 16 muffins sold would you expect to be bran muffins?
After answering the given query, we can state that Therefore, we can function anticipate that 8 to 16 of the upcoming pastries will be bran muffins.
what is function?Mathematicians research numbers, their variations, equations, associated structures, shapes, and possible configurations of these. The relationship between a group of inputs, each of which has a corresponding outcome, is referred to as a "function." A function is a relationship between inputs and outputs where each input results in a unique, distinct output. Each function has a domain, codomain, or scope assigned to it. Functions are commonly denoted by the letter f. (x). An cross is entered. On functions, one-to-one capabilities, so several capabilities, in capabilities, and on functions are the four main categories of available functions.
We must determine the percentage of muffins that were bran muffins in the prior sales in order to determine how many of the subsequent 16 muffins sold would be bran muffins.
In the prior auction, the following amount of muffins were sold in total:
25 + 12 + 3 + 10 = 50
The percentage of muffins that were wheat muffins is as follows:
25/50 = 0.5
This indicates that wheat muffins accounted for 50% of all sales.
This ratio can be used to make a forecast about how many bran muffins will be sold over the course of the following 16 muffins. Therefore, we anticipate that roughly 50% of the subsequent 16 batches of muffins sold will be wheat muffins:
0.5 x 16 = 8
Therefore, we can anticipate that 8 to 16 of the upcoming pastries will be bran muffins.
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Question 5) [6 Points]
Find the answer to each of the following counting problems:
The U.S. Senate Appropriations Committee has 29 members and a subcommittee is to be
formed by randomly selecting 5 of its members. How many different committees could be
formed?
●
If 25 people start a race, in how many different ways can the top 2 finishers be determined?
Companies who stocks are listed on the NASDAQ stock exchange have their company name
represented by either four or five letters (repetition of letters is allowed). What is the maximum
number of companies that can be listed on the NASDAQ?
Using permutation and combination we can find the total number of companies listed = 12,338,352
What is permutation and combination?A permutation is a methodical arrangement of things or numbers. Combinations let you choose things or numbers from a collection without worrying about the order in which they were gathered.
N (5 member) =₂₉C₅29!/5!(29-5)!=118755
The total number of firms that can be listed on NASDAQ if the company names can be either 4 or 5 letters and the letters can repeat themselves is: 4 letter names = 26 x 26 x 26 x 26 = 264 = 456,976
5 letter names equal 26, 26, 26, 26, 26 = 11,881,376.
Total number of companies listed = 456,976 + 11,881,376 = 12,338,352
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) Using matrix method solve the following simultaneous equations 1x + 4y = 9 2x – 3y = 7
Answer: To solve the system of equations using the matrix method, we first need to set up the corresponding coefficient matrix and augmented matrix:
Coefficient matrix:
[1 4]
[2 -3]
Augmented matrix:
[1 4 | 9]
[2 -3 | 7]
To solve the system using matrix method, we perform row operations on the augmented matrix to get it into row echelon form, and then back substitute to obtain the solutions.
Performing row operations:
Multiply the first row by 2 and subtract the result from the second row:
[1 4 | 9]
[0 -11| -11]
Divide the second row by -11:
[1 4 | 9]
[0 1 | 1]
Subtract 4 times the second row from the first row:
[1 0 | 5]
[0 1 | 1]
The row echelon form of the augmented matrix is:
[1 0 | 5]
[0 1 | 1]
Therefore, the solution is x = 5 and y = 1.
So the solution of the system of equations is x = 5 and y = 1.
Step-by-step explanation:
60 POINTS PLSS
Why is the quotient of three divided by one-fifth different from the quotient of one-fifth divided by three? Tell a story that could describe each situation.
HELP ASAP
After answering the presented question, we can conclude that They are equation still pleased with the quantity of pizza they received, although it is less than in the previous scenario.
What is Quotient?A quotient refers to the result obtained when one quantity is divided by another. For example, if you have 10 apples and you want to divide them equally among 2 people, each person would get 5 apples. The quotient in this case is 5, which represents the number of apples that each person would receive.
The quotient can be expressed in different forms, depending on the situation. If you are dividing two integers, the quotient can be a whole number (also known as an integer quotient) or a fraction (also known as a rational quotient). For example, if you divide 10 by 3, the quotient is 3 with a remainder of 1, which can be expressed as [tex]3 + 1/3[/tex] or as the fraction 10/3.
In algebra, the quotient can also refer to the result obtained when dividing two algebraic expressions. For example, if you divide [tex]x^2 + 3x + 2[/tex] by [tex]x + 1,[/tex] the quotient is [tex]x + 2[/tex], which represents the quotient of the division.
The concept of quotient is also used in other areas of mathematics, such as in modular arithmetic and in group theory, where it refers to the result of dividing one element of a group or a ring by another.
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What referents would you use to estimate the length, in both SI units and imperial units, of the Victoria (Old Traffic) Bridge in Saskatoon? Explain how you could measure the length in both units.
Step-by-step explanation:
The Victoria (Old Traffic) Bridge in Saskatoon, Canada, has a length of approximately 230 meters (755 feet). To estimate the length of the bridge in both SI and imperial units, you can use the following referents:
SI Units:
To estimate the length of the bridge in SI units, you can use meters as the referent. The length of the Victoria Bridge can be measured using a distance measuring device such as a surveyor's wheel, a laser distance meter, or a tape measure. You can start at one end of the bridge and measure the distance to the other end. This will give you an accurate measurement of the length of the bridge in meters.
Imperial Units:
To estimate the length of the bridge in imperial units, you can use feet as the referent. You can use a tape measure or a distance measuring wheel that measures in feet. You can start at one end of the bridge and measure the distance to the other end. This will give you an accurate measurement of the length of the bridge in feet.
To convert the length from meters to feet or vice versa, you can use the following conversion factors:
1 meter = 3.28 feet
1 foot = 0.3048 meters
Therefore, to convert the length of the Victoria Bridge from meters to feet, you can multiply the length in meters by 3.28. For example, 230 meters x 3.28 = 754.4 feet (rounded to the nearest tenth).
To convert the length of the Victoria Bridge from feet to meters, you can multiply the length in feet by 0.3048. For example, 755 feet x 0.3048 = 230.1 meters (rounded to the nearest tenth).
What is the area of this trapezoid?
Enter your answer in the box.
Answer:
80
Step-by-step explanation:
Jaylon works for a concrete company
His customer would be him to pour a new driveway. The concrete must be 3/4 fr deep.
Look at the drawing and calculate the number of cubic feet of concrete he will need to bring to the job.
Answer:
volume = length × width × depth
Assuming that the driveway has a rectangular shape, you can measure the length and width of the area to be covered and multiply by the depth of 3/4 ft (which is 0.75 ft) to get the volume in cubic feet.
For example, if the driveway is 20 ft long and 10 ft wide, the volume of concrete needed would be:
volume = length × width × depth
= 20 ft × 10 ft × 0.75 ft
= 150 cubic feet
Use the quadratic formula f(x)=3x2−18x+23
to determine the coordinates of the vertex of the best-fitting parabola. Write the exact answer. Do not round.
Answer:
108x^2 +23
Step-by-step explanation:
i think...
3x×2×18x+23
108x×x+23
final answer: 108^2 +23
please helpppp asap thank you !!:)
[tex]f(-11) = 3(-11)^{2} - 5 = 3(11)^{2} - 5 = 3(121) - 5 = 363-5= \bf 358[/tex]
Answer:D
Step-by-step explanation:
if x==-11
then,
f(-11) means you should write -11 in every x you see.
[tex]f(-11)=3*(-11)^{2} -5=3*121-5=363-5=358[/tex]
Devon wants to plant 84 tomato plants in his garden.
He wants to put 7 plants in each row. How many rows
will he need?
Marilou,a buyer of lot,pays Php10,000 every month for ten years.If money is 8%compoundef annually,how much is the cash value of the lot?
Answer:1,200,000
Step-by-step explanation:
The ratio of men to women at the picnic is 4:5,if there are 819 people, how many men are there in the picnic
There are 364 men at the picnic
Describe Equation?Equations can be written in many forms, but they all have the same basic structure: an expression on the left-hand side of the equals sign, and an expression on the right-hand side of the equals sign, with the equals sign itself indicating that the two expressions are equal.
Equations can be solved using a variety of techniques, including algebraic manipulation, substitution, and graphing. The goal of solving an equation is to find the values of the variables that make the equation true. In some cases, there may be multiple solutions to an equation, or no solutions at all.
Let the number of men be 4x, and the number of women be 5x.
According to the problem, the total number of people is 819, so:
4x + 5x = 819
Simplifying and solving for x, we get:
9x = 819
x = 91
Therefore, the number of men at the picnic is:
4x = 4(91) = 364
So there are 364 men at the picnic.
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In triangle ABC, the length of side AB is 16 inches and the length of side BC is 25 inches. Which of the following could be the length
of side AC?
A. 29 inches
B. 46 inches
C. 43 inches
D. 7 inches
After answering the presented question, we can conclude that triangle Therefore, the answer is A. 29 inches, since it falls within this range.
What precisely is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.
So, for triangle ABC with sides AB, BC, and AC, we have:
[tex]AB + BC > AC\\16 + 25 > AC\\41 > AC\\BC + AC > AB\\25 + AC > 16\\AC > -9 \\AB + AC > BC\\16 + AC > 25\\AC > 9\\[/tex]
So, the possible lengths of side AC are between 9 and 41 inches.
Therefore, the answer is A. 29 inches, since it falls within this range.
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if i had 1000 apples and gave 39 away
how many wouldd i have left
Answer:
1000-39=961
so 961 apples are left.
Divide 240g in the ratio 5: 3: 4.method
To divide 240g in the ratio 5:3:4, we need to find out the total number of parts of the ratio:
5 + 3 + 4 = 12
Now, we can find the value of one part of the ratio by dividing the total quantity by the total number of parts:
240g ÷ 12 = 20g
So, one part of the ratio is equal to 20g.
To find the quantities of each part of the ratio, we multiply the value of one part by the respective ratio number:
5 parts x 20g = 100g (for the first part)
3 parts x 20g = 60g (for the second part)
4 parts x 20g = 80g (for the third part)
Therefore, the quantities of 240g divided in the ratio 5:3:4 are 100g, 60g, and 80g respectively.
Find the length of side � x in simplest radical form with a rational denominator. 30° 60° x 2
The length οf side x can be any value, as lοng as it is nοt 0.
We can use the trigοnοmetric ratiοs fοr 30°-60°-90° triangles tο sοlve fοr the value οf x.
In a 30°-60°-90° triangle, the sides are in the ratiο:
1 : √3 : 2
In this case, we have the side οppοsite the 60° angle (which is the lοnger leg) equal tο x√3 and the side οppοsite the 30° angle (which is the shοrter leg) equal tο x.
Sο we can set up the fοllοwing equatiοn:
x√3 = 2x sin 60°
Simplifying the right side:
sin 60° = √3/2
2x sin 60° = 2x(√3/2) = x√3
Substituting back intο the equatiοn:
x√3 = x√3
This is true fοr any value οf x, as lοng as x is nοt equal tο 0. Therefοre, the length οf side x can be any value, as lοng as it is nοt 0.
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The following events occur for The Turner Corporation during 2024 and 2025, its first two years of operations.
June 12, 2024 Provide services to customers on account for $35,000.
September 17, 2024 Receive $20,000 from customers on account.
December 31, 2024 Estimate that 40% of accounts receivable at the end of the year will not be received.
March 4, 2025 Provide services to customers on account for $50,000.
May 20, 2025 Receive $10,000 from customers for services provided in 2024.
July 2, 2025 Write off the remaining amounts owed from services provided in 2024.
October 19, 2025 Receive $40,000 from customers for services provided in 2025.
December 31, 2025 Estimate that 40% of accounts receivable at the end of the year will not be received.
Required:
1. Record transactions for each date.
2. Post transactions to the following accounts: Cash, Accounts Receivable, and Allowance for Uncollectible Accounts.
3. Calculate net accounts receivable reported in the balance sheet at the end of 2024 and 2025
How to calculate
July 2, 2025 Write off the remaining amounts owed from services provided in 2024.
Net accounts receivable is calculated by subtracting allowance for uncollectible from gross accounts receivable.
1- The journal entries are used to record the business transactions.
2- Ledger accounts are used to summarize thee recorded transactions.
3- Net accounts receivable (2024) = 8,640
Net accounts receivable (2025) = 4,280
1. The Turner Corporation's transactions are recorded as follows:
Date Account Title Debit Credit Journal Entries
Accounts Receivable $35,000 on June 12, 2024
$35,000 in revenue from services
Cash $20,000, September 17, 2024
$20,000 in accounts receivable
Bad Debt Cost $5,760 as of December 31, 2024
Uncollectible Allowance: $5,760
Accounts Receivable $46,400 on March 4, 2025
$46,400 in revenue from services
Cash $10,000, May 20, 2025
$10,000 in Accounts Receivable
Allowance for Uncollectible $4,400 on July 2, 2025
$4,400 in Accounts Receivable
On October 19, 2025, the cash value is $40,000.
$40,000 in accounts receivable
Bad Debts Cost $2,400 on December 31, 2025
Uncollectible Allowance: $2,400
2. The following is the procedure for posting transactions to the chosen accounts:
Account Titles Debit Credit Cash Account Date Account Titles Debit Credit
Accounts Receivable $17,000 on September 17, 2024
Accounts Receivable $10,000 on May 20, 2025
The date is October 19, 2025 $37,000 in accounts receivable
Date Account Titles Debit Credit Accounts Receivable
Service Revenue of $31,400 on June 12, 2024
17th of September, 2024, $17,000 cash
$46,400 in service revenue on March 4, 2025
$10,000 cash, May 20, 2025
Allowance for Uncollectible Accounts $4,400 on July 2, 2025
On October 19, 2025, a cash payment of $37,000 is made.
Balance $9,400 on December 31, 202 $77,800
Provision for Uncollectible Accounts
Debit Credit Date Account Titles
Bad debt expense of $5,760 as of December 31, 2024
Accounts Receivable $4,400 on July 2, 2025
Bad Debts Cost $2,400 as of December 31, 2025
Balance of $3,760 at the end of December 2025
3. The balance sheet net accounts receivable at the end of 2024 and 2025 include:
Net accounts receivable = $8,640 in 2024
Net accounts receivable = $5,640 in 2025.
Transaction Analysis: Accounts Receivable $31,400 on June 12, 2024 $31,400 in service revenue September 17, 2024, $17,000 Cash Accounts Receivable $17,000
Bad Debt Cost $5,760 as of December 31, 2024 Provision for Uncollectible Accounts $5,760 ($31,400 minus $17,000 multiplied by 40%)
Accounts Receivable $50,000 on March 4, 2025 $50,000 in service revenue
May 20, 2025, $10,000 Cash Accounts $10,000 is available for receipt.
Allowance for Uncollectible Accounts $4,400 Accounts Receivable $4,400 July 2, 2025
The date is October 19, 2025. $37,000 in cash and accounts Receivable: $37,000
Bad Debts Cost $2,400 on December 31, 2025 Uncollectible Accounts Allowance $2,400
Net Accounts Receivable: $8,640 in 2024 ($14,400 - $5,760)
2025: $5,640 ($9,400 - $3,760).
HELPP i dont understand either of these questions
What is the part in the equation “45 is 15% of what number”
Answer:
the number is 300
Step-by-step explanation:
just look it up next time
Answer:
300
Step-by-step explanation:
let x be the number
then, 15% of x = 45
[tex] \frac{15}{100} \times x \: = 45 \\ x \: = 45 \times \frac{100}{15} [/tex]
x = 300
pls mrk me brainliest
can someone please help me
please show work
The arc length and area of each circle sector is:
Case 1: s = 121π / 12 yd, A = 1331π / 24 yd²
Case 2: s = 35π / 3 in, A = 245π / 3 in²
Case 3: s = 17π / 6 ft, A = 17π / 4 ft²
Case 4: s = 11π / 2 in, A = 33π / 2 in²
Case 5: s = 116π / 9 yd, A = 928π / 9 yd²
Case 6: s = 13π / 12 ft, A = 13π / 8 ft²
How to determine the arc length and the area of a circle sector
In this problem we need to determine the arc length (s), in yards or inches, and the area (A), in square yards or square inches, of a circle sector, whose formulas are listed below:
Arc length
s = (θ / 180) · π · r
Area
A = 0.5 · (θ / 180) · π · r²
Where:
θ - Measure of the central angle, in degrees. r - Radius, in yards or inches.Now we proceed to determine the arc length and the area for each case:
Case 1 (r = 11 yd, θ = 165°)
s = (165 / 180) · π · 11
s = 121π / 12 yd
A = 0.5 · (165 / 180) · π · 11²
A = 1331π / 24 yd²
Case 2 (r = 14 in, θ = 150°)
s = (150 / 180) · π · 14
s = 35π / 3 in
A = 0.5 · (150 / 180) · π · 14²
A = 245π / 3 in²
Case 3 (r = 3 ft, θ = 170°)
s = (170 / 180) · π · 3
s = 17π / 6 ft
A = 0.5 · (170 / 180) · π · 3²
A = 17π / 4 ft²
Case 4 (r = 6 in, θ = 165°)
s = (165 / 180) · π · 6
s = 11π / 2 in
A = 0.5 · (165 / 180) · π · 6²
A = 33π / 2 in²
Case 5 (r = 16 yd, θ = 145°)
s = (145 / 180) · π · 16
s = 116π / 9 yd
A = 0.5 · (145 / 180) · π · 16²
A = 928π / 9 yd²
Case 6 (r = 3 ft, θ = 65°)
s = (65 / 180) · π · 3
s = 13π / 12 ft
A = 0.5 · (65 / 180) · π · 3²
A = 13π / 8 ft²
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NEED HELP ASSIGNMENT DUE IN AN HOUR WOULD BE MUCH APPRECIATED!
point z is the circumcenter of triangle tub what is the value of uv
The measure of angle ZUB is 32.8°.
What precisely is a triangle?A triangle is a closed, double-symmetrical object composed of three line segments known as sides that intersect at three points known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides.
Triangles are classified as acute (all angles are less than 90 degrees), okay (one angle is equal to 90 degrees), or orbicular (all angles are greater than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighborhood, b is the triangle's base, and h is the triangle's height.
Since the angles given are 90 degrees and 57.2 yοu can add thοse tοgether then subtract them frοm 180 tο find the answer.
180 - 90 + 57.2 = 32.8
Thus,
32.8° is the answer.
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Complete question:
Point Z is the circumcenter of ΔTUV.
Point Z is the circumcenter of triangle T U V. Lines are drawn from each point of the triangle to point Z. Lines are drawn from point Z to each side to form right angles and line segments Z A, Z B, and Z C. The line segments cut the sides into 2 equal parts. Angle Z T B is 32.8 degrees and angle B Z U is 57.2 degrees.
What is m Angle ZUB?
23.7°
32.8°
33.5°
57.2°
Given the function I need to evaluate question a)
Answer:
a) p(-6) = 30
b) c = -2 ,1
Step-by-step explanation:
[tex]p(c)=c^2+c[/tex]
a) Evaluate p(-6)
This mean input -6 into the equation to solve for p(-6) =
[tex]p(-6)=(-6)^2+(-6)\\\\p(-6)=36-6\\\\p(-6)=30\\[/tex]
(b) Solve for p(c) = 2.
[tex]p(c)=c^2+c\\\\2=c^2+c\\\\c^2+c=2\\\\c^2+c-2=0\\\\Factoring\\(c+2)(c-1)=0\\(c+2)=0,(c-1)=0\\c = -2 , 1[/tex]
work out the question
23 - 81 =
The mathematical expression 23 - √81 has a value of 14 when evaluated, mathematically
How to evaluate the expressionGiven the following expression
23 - √81
The expression 23 - √81 involves finding the difference between the number 23 and the square root of 81.
We know that the square root of 81 is 9, so we can simplify the expression to:
23 - √81 = 23 - 9
Evaluate the difference
23 - √81 = 14
Therefore, the value of the expression is 14.
In evaluating expressions like these, it is important to be familiar with basic arithmetic operations and the rules of exponents and radicals.
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If cos 55° = p determine the value of cos 5° in terms of p.
Answer:
Step-by-step explanation:
We can use the identity for the cosine of the sum of two angles:
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
In this case, we can write:
cos(60°) = cos(55° + 5°) = cos(55°)cos(5°) - sin(55°)sin(5°)
We know that cos(60°) = 1/2, and we also know that cos(55°) = p. We can solve for cos(5°):
1/2 = p cos(5°) - sin(55°)sin(5°)
sin(55°)sin(5°) = p cos(5°) - 1/2
We also know that sin²(55°) + cos²(55°) = 1, so:
sin²(55°) = 1 - cos²(55°) = 1 - p²
Substituting this into the previous equation:
(1 - p²)sin(5°)² = p cos(5°) - 1/2
Rearranging and factoring:
p cos(5°) = 1/2 - (1 - p²)sin(5°)²
Using the fact that sin²(5°) + cos²(5°) = 1, we can substitute cos²(5°) = 1 - sin²(5°):
p cos(5°) = 1/2 - (1 - p²)(1 - cos²(5°))
Simplifying:
p cos(5°) = 1/2 - (1 - p²) + (1 - p²)cos²(5°)
p cos(5°) = 1 - 2p² + (2p² - 1)cos²(5°)
Solving for cos²(5°):
cos²(5°) = (1 - p cos(5°) + 2p²) / (2p² - 1)
Substituting the value we found for p, cos²(55°) = p²:
cos²(5°) = (1 - p cos(5°) + 2cos²(55°)) / (2cos²(55°) - 1)
Finally, substituting p = cos(55°):
cos²(5°) = (1 - cos²(55°) cos(5°) + 2cos²(55°)) / (2cos²(55°) - 1)
cos²(5°) = (2cos²(55°) - cos²(55°) cos(5°) + 1) / (2cos²(55°) - 1)
cos²(5°) = (cos²(55°) + 1) / (2cos²(55°) - 1)
Therefore, the value of cos 5° in terms of p = cos 55° is:
cos 5° = ±sqrt[(cos²(55°) + 1) / (2cos²(55°) - 1)]
Note that the sign of the square root is determined by the quadrant in which 5° lies. Since 5° is in the first quadrant, cos 5° is positive.
Solve the differential equation with
the given initial condition.
Dy/dx=3x/√y
(0,1)
The solution to the differential equation dy/dx = 3x/√(y) with initial condition (0,1) is y = ((9/4) × x² + 1)^(2/3).
Describe differential equation?Differential equations are used to model a wide variety of physical, biological, and economic systems, including the motion of objects under the influence of forces, the spread of disease in a population, and the behavior of financial markets.
There are many different types of differential equations, including ordinary differential equations (ODEs) and partial differential equations (PDEs). ODEs involve a single independent variable and its derivatives, while PDEs involve multiple independent variables and their derivatives.
To solve the differential equation dy/dx = 3x/√(y), we can separate the variables by multiplying both sides by √(y) and dividing both sides by 3x:
dy/dx = 3x/√(y)
√(y) dy/dx = 3x
√(y) dy = 3x dx
Integrating both sides:
∫√(y) dy = ∫3x dx
(2/3)*y^(3/2) = (3/2)*x² + C
where C is the constant of integration.
To find the value of C, we can use the initial condition (0,1), which means y=1 when x=0:
(2/3)*y^(3/2) = (3/2)*x² + C
(2/3)*1^(3/2) = (3/2)*0² + C
C = (2/3)
Substituting C = 2/3 back into the equation, we get:
(2/3)×y^(3/2) = (3/2) × x² + 2/3
y^(3/2) = (9/4) × x² + 1
y = ((9/4) × x² + 1)^(2/3)
Therefore, the solution to the differential equation dy/dx = 3x/√(y) with initial condition (0,1) is y = ((9/4) × x² + 1)^(2/3).
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x + 5 < 2
the solution is ??
Answer:
x < -3
Step-by-step explanation:
x + 5 < 2
x < -3
So, the answer is x < -3
I will mark you brainiest!
A) 3
B) 6
C) 9
D) 12
The value of x, considering the similar triangles, is given as follows:
B) 6.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.Considering that the triangles for this problem are similar, the proportional relationship for the side lengths is given as follows:
9/3 = 12/4 = x/2.
Since the constant is of 3, the value of x is obtained with cross multiplication as follows:
x/2 = 3
x = 6.
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Compare the given measures.
The angles in the triangles when compared are:
First pair: m∠2 > m∠1Second pair: m∠L > m∠DThird pair: m∠1 > m∠2How to compare the angles in the trianglesThe triangle inequality theorem implies that
The largest angle in a triangle is opposite to the longest side of the triangle.
Using the above as a guide, we have the following comparison of angles:
First pair: m∠2 > m∠1Second pair: m∠L > m∠DThird pair: m∠1 > m∠2The above comparison are true because the angles before the inequality symbol opposite a side length greater than the lengths faced by the other angle
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Which pizza can represent 3/4 of a pizza remaining?
Answer:
Step-by-step explanation:
C.