In a right triangle, cos (4x) = sin (6x + 10). Find the smaller of the triangle's two
acute angles.
Answer:
Submit Answer
M
attempt 1 out of 3/problem 1 out of max 1
DELL
Therefore, the smaller of the two acute angles is 8°.
How to solve trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. Here are some general steps to solve trigonometry problems:
Understand the problem: Read the problem carefully and identify what is being asked for.
Draw a diagram: Draw a diagram of the triangle and label the sides and angles.
Identify the known values: Identify what is given in the problem, such as the lengths of the sides or the measure of an angle.
Choose the appropriate formula: Choose the formula that relates the known values to the unknown value that you need to find.
Solve for the unknown value: Use algebraic manipulation and/or your calculator to solve for the unknown value.
Check your answer: Check your answer to make sure it makes sense and that it satisfies any given constraints.
Let's start by using the trigonometric identity cos(x) = sin(90° - x) for the left-hand side of the equation:
[tex]cos(4x) =[/tex][tex]sin(90^{0} - 4x)[/tex]
Now we can substitute this into the original equation and simplify:
[tex]sin(90^{0} - 4x) = sin(6x + 10)[/tex]
Using the identity sin(a) = sin(b) implies a = b + 2kπ or a = π - b + 2kπ for some integer k, we can set the angles inside the sine function equal to each other and solve for x:
90° - 4x = 6x + 10 + 2nπ or 90° - 4x = π - (6x + 10) + 2nπ
where n is an integer.
Solving for x in the first equation, we get:
10x = 80° + 2nπ
x = 8° + (2n/10)π
Solving for x in the second equation, we get:
10x = 80° + π + 2nπ
x = (8° + π/10) + (2n/10)π
Since we want the acute angle of the right triangle, which is less than 90°, we only need to consider the values of x that satisfy 0° < x < 22.5°. From the two equations above, we see that x can take on values between 8° and 9° or between 89° and 90°. Therefore, the smaller of the two acute angles is 8°.
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forever quilting is a small company that makes quilting kits priced at $120 each. there is no quantity discount. the costs of the materials that go into each kit total $45. it costs $5 in labor to assemble a kit. the company has monthly expenses of $1,000 for rent and insurance, $200 for heat and electricity, $500 for advertising, and $4,500 for the monthly salary of its owner. last month the company sold 150 kits in a given month, calculate it’s monthly profits
Forever Quilting's monthly profit is $10,250. We can caclculate it in the following manner.
To calculate the company's monthly profit, we need to subtract its total expenses from its total revenue.
Total Revenue = Number of kits sold x Price per kit
Total Revenue = 150 kits x $120 per kit
Total Revenue = $18,000
Total Costs = (Cost of materials per kit + Labor cost per kit) x Number of kits sold + Monthly expenses
Total Costs = ($45 + $5) x 150 kits + $1,000 + $200 + $500 + $4,500
Total Costs = $7,750
Monthly Profit = Total Revenue - Total Costs
Monthly Profit = $18,000 - $7,750
Monthly Profit = $10,250
Therefore, Forever Quilting's monthly profit is $10,250.
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Ect edt A weather center collects rain data for 10 years at two lakes. The amount of annual rainfall for each lake during that time period is shown by the graphs. Annual Rainfall Amounts Lake Warbler Lake Mockingbird + + + + + 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Rainfall (inches) 2 Which statement correctly describes the spreads of the data distributions for the lakes? The spreads of the data distributions are about the same for both lakes. BThe spread of the data distribution for Lake Mockingbird is about 40% greater than the /spread for Lake Warbler. The spread of the data distribution for Lake Mockingbird is 3 inches less than the spread of the data distribution for Lake Warbler. The spread of the data distribution for Lake Mockingbird is 5 inches greater than the spread of the data distribution at Lake Warbler. 3 Which statement is NOT true about the data? A The spreads for the first 25% of the data distributions for both lakes are equal. B The distribution for Lake Mockingbird shows a center that is 3 inches greater than the center of the distribution for Lake Warbler. C The interquartile range of the data distribution for Lake Warbler is about 60% of the interquartile range for Lake Mockingbird. D The data distributions for both lakes appear to be skewed left.
The correct answer is B. The spread of the data distribution for Lake Mockingbird is about 40% greater than the spread for Lake Warbler.
What is the data distribution?
The data distribution refers to the pattern of the data values in a dataset. It describes how the data is spread out, including the range of values, the shape of the distribution, and any clustering or gaps in the data. The data distribution can be described using various statistical measures, such as the mean, median, and standard deviation.
The correct answer to the first question is B: "The spread of the data distribution for Lake Mockingbird is about 40% greater than the spread for Lake Warbler."
For the second question, the statement that is NOT true about the data is B: "The distribution for Lake Mockingbird shows a center that is 3 inches greater than the center of the distribution for Lake Warbler."
hence, The correct answer is B. The spread of the data distribution for Lake Mockingbird is about 40% greater than the spread for Lake Warbler.
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Which of the following is a balance for a single $1856 deposit in an account with an APR of 2.42% that compounds interest quarterly and is invested for six years
The balance of the account after six years with a single $1856 deposit at an APR of 2.42% that compounds interest quarterly would be $2,177.89.
To calculate the balance of the account after six years, we need to use the formula for compound interest:
A = [tex]P(1 + r/n)^(nt)[/tex]
Where:
A = the final amount
P = the principal amount (initial deposit)
r = the annual interest rate as a decimal
n = the number of times the interest is compounded per year
t = the time the money is invested in years
Using the given values:
P = $1856
r = 2.42% = 0.0242
n = 4 (compounded quarterly)
t = 6
Substituting these values in the formula, we get:
A = [tex]1856(1 + 0.0242/4)^(4*6)[/tex]
A = [tex]1856(1.00605)^24[/tex]
A = $2,177.89
Therefore, with a single $1856 contribution over the course of six years at an annual percentage rate of 2.42%, the account balance would be $2,177.89.
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Change numbers from one base to another. Perform base conversions using multiplication expansion and divisions, and distinguish the differences between the two through writing.
Through this activity, you see how the hexadecimal value of color is represented in HTML and practice how to convert among hexadecimal, binary, and decimal values.
Conner took a graphic design class and learned:
Combining red, green, and blue (RGB) light is the standard method of producing color images on screens. In HTML code, the color red is expressed as a hexadecimal #FF 00 00 or a 24-bit color depth (bit is binary digit), which means the browser is showing only red (FF) with no green (00) and no blue (00).
Now Conner got this question on the Liberal Arts Math class:
Q: What is FF equivalent to in Decimals and what is the equivalent in Binary?
He was so confident in his answers since he already knew the letter F is 1111 from his graphic design class.
Below shows how Conner answered the question, but Conner didn't receive full credit. He argued that he was confident with the solution, and also his numbers were the same as the answer key. (Answer key: 255 and 11111111)
Conner's incorrect answer:
#FF0000 converted to base ten (decimal) is: 255 (Incorrect)
#FF0000 converted to base two (binary) is: 11111111 (Incorrect)
1. Conner didn't show the details of the conversions, but that is not the reason why he lost points. Please explain to him why his answer didn't receive full credit. Note: It is not because he didn't show work. Help Conner correct his mistakes. Please show details of the conversions.
2. Show how to convert 255 to the binary 11111111 using divisions. Please show the detailed steps. Be specific with your answer. If work is done on paper, please attach the image file.
3. Describe how you convert a decimal number (base ten) to another base using divisions. Use your own words to provide an instructional description.
Answer:
137 in binary is 10001001
Step-by-step explanation:
Conner's answer did not receive full credit because he did not convert the hexadecimal number #FF0000 to decimal and binary correctly.
While it is true that the letter F represents 1111 in binary, in hexadecimal, FF represents the decimal value 255, not 1111.
Therefore, Conner's answer is incorrect, and he needs to use the correct conversions to get the right answer.
To convert 255 to binary using divisions, we can use the following steps:
Start with the decimal number 255.
Divide 255 by 2, and write down the quotient and remainder. The quotient is 127, and the remainder is 1.
Divide the quotient (127) by 2, and write down the quotient and remainder. The quotient is 63, and the remainder is 1.
Repeat this process of dividing the quotient by 2 and writing down the quotient and remainder until the quotient becomes 0.
The binary equivalent of 255 is the sequence of remainders written in reverse order: 11111111.
Decimal Number Quotient Remainder
255 127 1
127 63 1
63 31 1
31 15 1
15 7 1
7 3 1
3 1 1
1 0 1
Divide 137 by 2. The quotient is 68, and the remainder is 1.
Divide 68 by 2. The quotient is 34, and the remainder is 0.
Divide 34 by 2. The quotient is 17, and the remainder is 0.
Divide 17 by 2. The quotient is 8, and the remainder is 1.
Divide 8 by 2. The quotient is 4, and the remainder is 0.
Divide 4 by 2. The quotient is 2, and the remainder is 0.
Divide 2 by 2. The quotient is 1, and the remainder is 0.
Divide 1 by 2. The quotient is 0, and the remainder is 1.
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15. a = 3, b = 4, C = 40°
18. a = 6, b = 4, C = 60°
26. a=4, b=3, c=6
39. Dimensions of Home Plate The dimensions of home plate at any major league baseball stadium are shown. Find the area of home plate.
The area of this home plate is equal to 216.5 in².
How to determine the area of home plate?In order to determine the area of home plate, we would have to apply the law of cosine:
C² = A² + B² - 2(A)(B)cosθ
Where:
A, B, and C represent the length of side or side length of a given triangle.
By substituting the given side lengths and angle into the law of cosine formula, we have the following;
C² = A² + B² - 2(A)(B)cosθ
17² = 12² + 12² - 2(12)(12)cosθ
284 = 144 + 144 - 288cosθ
1 = -288cosθ
cosθ = (-1/288)
θ = 90.199
For the area of home plate, we have:
Area of home plate = Area of rectangle + Area of triangle
Area of home plate = 17(8.5) + 1/2(12)(12)sin90.199
Area of home plate = 144.5 + 72(0.9999940)
Area of home plate = 216.5 in².
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Three different athletic teams were surveyed about the
number of glasses of water consumed each day. The
results are represented in the segmented bar graph.
Water Consumed by Athletes
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Track
Softball Baseball
<4 Glasses
4-8 Glasses
>8 Glasses
Which statement is true?
About 30% of track athletes consume 8 glasses of
water or less each day.
About 70% of track athletes consume 4 to 8 glasses
of water each day.
About 60% of baseball players consume 4 to 8
glasses of water each day.
About 12% of softball players consume more than 8
glasses of water each day.
After answering the presented question, we can conclude that Softball graphs players drink less than 4 glasses of water, 60% drink 4 to 8 glasses, and 12% drink more than 8 glasses.
What is graphs?Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a relationship between two or more things. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph includes V=1, 2, 3, 5, and E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential growth. A triangle-shaped logarithmic graph.
70% of track athletes drink 4 to 8 glasses of water every day.
We can observe that the blue segment, which represents the number of track athletes who drink 4 to 8 glasses of water each day, accounts for almost 70% of the whole bar. The graph does not support any of the other statements. According to the graph, approximately 25% of track athletes take less than 4 glasses of water, while approximately 5% consume more than 8 glasses. Baseball players drink less than 4 glasses of water, 35% drink 4 to 8 glasses, and 25% drink more than 8 glasses. Softball players drink less than 4 glasses of water, 60% drink 4 to 8 glasses, and 12% drink more than 8 glasses.
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The graph of y = f(x) is shown in red below. Find f(-2).
Answer: about 0.75
Step-by-step explanation:
There is no integer answer, but if you put the x value of -2, you will see the y value is about 0.75
The equation of the piecewise defined function f(x) is below. What is the value of f(1)?
[x²+1, -4
f(x) = -x², 1
3x, x22
f(1) = -2
f(1) = -1
f(1) = 2
f(1) = 3
The second piece of the function applies to x = 1, which is f(x) = -x².
Thus, f(1) = -(1)² = -1. The correct answer is f(1) = -1.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.
To find the value of f(1), we need to determine which piece of the function applies to x = 1.
Since 1 is greater than 0 and less than 2, the second piece of the function applies to x = 1, which is f(x) = -x².
Thus, f(1) = -(1)² = -1.
Therefore, the correct answer is f(1) = -1.
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=
Divide.
O EXPONENTS AND POLYNOMIALS
Dividing a polynomial by a monomial: Multivariate
(12y'u²-32ysu+15y¹uº) ÷ (-4y²u³)
Simplify your answer as much as possible.
0
X
010
Ś
The simplified expression when a polynomial is divided by a monomial is [tex]y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).[/tex]
What is factoring?A polynomial expression can be represented as a product of other, smaller polynomial expressions through the algebraic process of factoring. The process of factoring can be used to simplify expressions and solve problems. A polynomial equation's roots can be found by factoring, as can the common factors in an expression that can be eliminated. Factoring occasionally enables us to spot trends and connections between several expressions.
Depending on the kind of polynomial and the degree of the terms involved, there are several ways to factor. S
For the given expression [tex](12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)[/tex] factor the common term.
[tex](12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)\\-4y^5u^2(3y^2 - 8u^4 - 3y^2u^4) / (-4y^2u^5)[/tex]
Cancelling the -4:
[tex]= y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2)[/tex]
Hence, the simplified expression is [tex]y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).[/tex]
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A box with a square base and open top must have a volume of 13,500 cm^3. Find the dimensions of the box (in cm) that minimize the amount of material used.
There are 2 answer, the height and the sides of the base.
Let the side length of the square base be x cm and the height of the box be h cm. Then the volume of the box is given by:
V = x^2 * h = 13,500 cm^3
We want to minimize the amount of material used, which is the surface area of the box. The surface area A is given by:
A = x^2 + 4xh
We can use the volume equation to solve for h in terms of x:
h = 13,500 / x^2
Substituting this into the surface area equation gives:
A = x^2 + 4x(13,500 / x^2) = x^2 + 54,000 / x
To minimize A, we take the derivative with respect to x and set it equal to zero:
dA/dx = 2x - 54,000 / x^2 = 0
Solving for x, we get:
x^3 = 27,000
x = 30
Substituting this back into the volume equation gives:
h = 13,500 / (30^2) = 15
Therefore, the dimensions of the box that minimize the amount of material used are 30 cm by 30 cm by 15 cm.
Work out the perimeter of this semicircle. Take a to be 3.142
Perimeter of circle is 25.7cm
Define semicircleA semicircle is a two-dimensional geometric shape that is exactly half of a circle. It is formed by taking a diameter of a circle and cutting it in half, so that one half of the circle's circumference is traced out by the resulting arc. The boundary of a semicircle is composed of a curved line called the semicircular arc, which is connected to the two endpoints of the diameter, forming a closed shape.
The area of a semicircle is equal to half of the area of the corresponding circle, while its perimeter is equal to the sum of the diameter and half the circumference of the corresponding circle.
Given
Diameter of semicircle=10cm.
Perimeter of circle=πr+2r
=π×5+2×5
=25.7cm
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Use the polygon tool to graph the feasible region for the following constraints.
x+y≤6
2x+y≤8
x≥0
y≥0
This allows you to visualize all of the possible solutions that meet the Constraint and determine the optimal solution for your problem.
To graph the feasible region for the constraint y≥0, you would start by using the polygon tool in a graphing program or software. This tool allows you to create and manipulate polygons on a coordinate plane.
To create the feasible region for the constraint y≥0, you would draw a horizontal line at y=0 on the coordinate plane. This line represents the boundary between the feasible and infeasible regions. Any point above the line is infeasible, while any point below the line is feasible.
Once you have drawn the horizontal line, you can use the polygon tool to create the feasible region by shading in the area below the line. This region represents all of the possible solutions that meet the constraint y≥0. Any point within this region would satisfy the constraint, while any point outside the region would violate the constraint.
Overall, using the polygon tool to graph the feasible region for the constraint y≥0 is a simple process that involves drawing a horizontal line at y=0 and shading in the area below it. This allows you to visualize all of the possible solutions that meet the constraint and determine the optimal solution for your problem.
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The diameter of a cylindrical construction pipe is 3ft . If the pipe is 16ft long, what is its volume?
(I THINK I USED THE RIGHT CALCULATOR)
Answer: V≈113.1
Step-by-step explanation:
V=πr2h=π·1.52·16≈113.09734
Pls help i need to pass
The total surface area of the square pyramid is 39 ft².
What is the total surface area?The total surface area of a square pyramid can be determined by adding the area of the lateral surfaces and the base together. A square pyramid has four lateral sides and one base.
Total surface area= area of the base + area of the lateral sides
Area of the base = area of a square = length² = 3² = 9 ft²
Area of the lateral sides = 2 x base x height
2 x 3 x 5 = 30 ft²
Total surface area = 30 + 9 = 39 ft²
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y'+x=(x-1)y^+1
Solve
We can use the method of integrating factors to solve the equation.
Y' + x = (x-1)y' + 1
How can we use the integrating factors method here?The integrating factor method is a technique used to solve linear first-order ordinary differential equations.
Find the integrating factor:
The integrating factor is given by:
I(x) = e^(∫x dx) = e^(x^2/2)
Multiply both sides of the equation by the integrating factor I(x)
e^(x^2/2)Y' + xe^(x^2/2) = (x-1)e^(x^2/2)y' + e^(x^2/2)
Let's simplify the left-hand side using the product rule of differentiation
(d/dx)(e^(x^2/2)Y) = e^(x^2/2)Y' + xe^(x^2/2)
Rewrite the equation using the simplified left-hand side
(d/dx)(e^(x^2/2)Y) = (x-1)e^(x^2/2)y' + e^(x^2/2)
Then, Integrate both sides with respect to x
∫(d/dx)(e^(x^2/2)Y) dx = ∫((x-1)e^(x^2/2)y' + e^(x^2/2)) dx
e^(x^2/2)Y = ∫((x-1)e^(x^2/2)y' + e^(x^2/2)) dx
Using integration by substitution and integration by parts, we can evaluate the integral on the right-hand side and simplify the equation:
e^(x^2/2)Y = e^(x^2/2) + C - e^(x^2/2)y + D
where C and D are constants of integration.
We Solve for Y:
Y = 1 - y + Ce^(-x^2/2) + De^(x^2/2)
Therefore, the solution of the given differential equation is:
Y = 1 - y + Ce^(-x^2/2) + De^(x^2/2)
where C and D are constants of integration.
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At what rate of interest will a sum of 10,000 become 12,544 in 2 years if the interest is compounded annually
3. Se tienen los puntos A. M. B, colineales y consecutivos, donde AB = 52 cm y M es punto medio de AB. ¿Cuanto mide el segmento AM?
Answer:
Por lo tanto, el segmento AM mide 26 cm.
Step-by-step explanation:
Como M es el punto medio de AB, entonces AM tiene la misma longitud que MB. Por lo tanto, la longitud de AM es:
AM = MB = AB / 2
Sustituyendo los valores dados, tenemos:
AM = MB = AB / 2 = 52 cm / 2 = 26 cm
Suppose a pendulum is L meters long. The time, f, in seconds that it takes to swing back and forth once is given by t=2.01 √L. If a pendulum is 13.69
meters long, how long does it take to swing back and forth once?
Round your answer to the nearest tenth.
Rounded to the nearest tenth, the approximate duration for one swing of a pendulum with a length of 13.69 meters is 7.7 seconds.
We are given that the time, t, in seconds it takes for a pendulum to swing back and forth once is given by:
t = 2.01√L
where L is the length of the pendulum in meters.
We are asked to find the time it takes for a pendulum of length 13.69 meters to swing back and forth once. So we can substitute L = 13.69 into the equation above to get:
t = 2.01√(13.69) ≈ 2.01 × 3.7 ≈ 7.7
Therefore, the time it takes for a pendulum of length 13.69 meters to swing back and forth once is approximately 7.7 seconds (rounded to the nearest tenth).
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The standard form of rational number of -30/75
The standard form of rational number of -30/75 is -2/5.
The standard form, given is -30/75.
Both numerator and denominator are a multiple of 15,
Hence we divide them by 15,
The result is -2/5 which is its standard form.
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Roger is 5’11”. How much should he weigh in order to have a BMI of 25?
1. What weird food combinations do you really enjoy? 2. What social stigma does society need to get over? 3. What food have you never eaten but would really like to try? 4. What's something you really resent paying for? 5. What would a world populated by clones of you be like? 6. Do you think that aliens exist? 7. What are you currently worried about? 8. Where are some unusual places you've been? 9. Where do you get your news? 10. What are some red flags to watch out for in daily life? 11. What movie can you watch over and over without ever getting tired of? 12. When you are old, what do you think children will ask you to tell stories about? 13. If you could switch two movie characters, what switch would lead to the most inappropriate movies? 14. What inanimate object would be the most annoying if it played loud upbeat music while being used?
Answer:
1. Weird food combinations that people enjoy can vary widely and may include things like peanut butter and pickles, french fries and ice cream, or even hot sauce on popcorn.
2. Society needs to get over many social stigmas, such as those related to mental health, sexuality, gender identity, and race. Breaking down these stigmas can help create a more inclusive and accepting society.
3. Foods that people have never tried but would like to can also vary widely and may include exotic fruits, unusual vegetables, or traditional dishes from different cultures.
4. People may resent paying for a variety of things, such as taxes, healthcare costs, or overpriced products or services.
5. A world populated by clones of one person would likely be very homogenous and lacking in diversity, both in terms of physical appearance and personality traits.
6. The existence of aliens is a topic of debate and speculation. While there is no conclusive evidence that they exist, some people believe that the vastness of the universe suggests that other intelligent life forms could be out there.
7. People may worry about a wide range of things, such as their health, their relationships, their finances, or the state of the world.
8. Unusual places that people have been may include remote locations, abandoned buildings, or unconventional travel destinations.
9. People may get their news from a variety of sources, such as traditional news outlets, social media, or alternative news sources.
10. Red flags to watch out for in daily life can include warning signs of scams, dangerous situations, or manipulative people.
11. Movies that people can watch over and over without getting tired of can vary widely, from classic comedies to action-packed blockbusters.
12. When people are old, children may ask them to tell stories about their childhood, their family history, or significant events they witnessed throughout their lifetime.
13. Switching two movie characters could lead to a variety of inappropriate scenarios, depending on the characters and the plot of the movie.
14. An inanimate object that played loud upbeat music while being used could be annoying in many situations, such as during a quiet study session or while trying to fall asleep.
Valeria is tilling her kitchen wall with two types of traditional hand painted Mexicano tiles. If she uses 56 flower tiles how many sun tiles dose she need to maintain the pattern?
A=28
Therefore, Aditi's mother requires 342 yellow tiles and 57 red tiles for the floral design on the kitchen wall.
What is proportion?Proportion is a statement that two ratios are equal. A ratio is a comparison of two quantities and is written in the form of a fraction. A proportion can be written in the form of a:b = c:d, where a, b, c, and d are numbers. This means that the ratio of a to b is equal to the ratio of c to d. We can also write a proportion as a fraction, where the numerator is the product of the means (ad) and the denominator is the product of the extremes (bc). Proportions are commonly used in mathematics to solve problems involving ratios and rates.
Here,
Since the floral design is made up of yellow and red hexagonal tiles, we need to determine the proportion of yellow tiles and red tiles in the design. Let's assume that the design consists of x yellow tiles and y red tiles. Each flower in the design consists of 7 hexagonal tiles - 6 yellow tiles and 1 red tile. Therefore, the total number of tiles in the floral design is:
Total number of tiles = 57 flowers x 7 tiles per flower
Total number of tiles = 399 tiles
Since each flower consists of 6 yellow tiles and 1 red tile, the total number of yellow tiles in the design is:
Number of yellow tiles = 6 x Number of flowers
Number of yellow tiles = 6 x 57
Number of yellow tiles = 342
Similarly, the total number of red tiles in the design is:
Number of red tiles = 1 x Number of flowers
Number of red tiles = 1 x 57
Number of red tiles = 57
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Complete question:
Aditi's mother is renovating her kitchen. One of the walls of kitchen is entirely made up of tiles. She wants to have a row of floral designs made up of yellow and red hexagonal tiles in the middle of the wall as shown in the adjoining figure. If there are 57 flowers in a row, find out how many yellow-and red-coloured tiles she requires for that wall.
limit comparison test
The formal statement of the Limit Comparison Test are discuss below with ∑bₙ converges, then ∑aₙ converges as well.
Define the Limit Comparison?The Limit Comparison Test is a method used to determine the convergence or divergence of a series.
Suppose we have two series, aₙ and bₙ. If we can find a third series, cₙ, such that the limit of the ratio aₙ/cₙ and bₙ/cₙ both exist and are finite, and the limit of aₙ/cₙ divided by bₙ/cₙ is also finite and non-zero, then the two series aₙ and bₙ will converge or diverge together.
In other words, we can say that if the series aₙ diverges, then bₙ also diverges, and if the series bₙ converges, then aₙ also converges.
Here's the formal statement of the Limit Comparison Test:
Let aₙ and bₙ be two positive series. If there exists a positive series cₙ such that [tex]\lim_{n \to \infty} \frac{a_n}{c_n}[/tex] and [tex]\lim_{n \to \infty} \frac{b_n}{c_n}[/tex] both exist and are finite and positive, then:
(i) If ∑bₙ converges, then ∑aₙ converges as well.
(ii) If ∑aₙ diverges, then ∑bₙ diverges as well.
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Which expression below gives the average rate of change of the function g(x) = -x² - 4x on the interval 6 ≤x≤8?
O [-82-4(8)]-[-6²-4(6)]
8-6
O [-62-4(6)]-[-8²-4(8)]
8-6
8-6
[-82-4(8)]-[-62²-4(6)]
8-6
[-62-4(6)]-[-8²-4(8)]
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Answer:
o=3
Step-by-step explanation:
3+0+3=6
Solve this system of linear equations. Separate
the x- and y-values with a comma.
9x - 19y = 74
3x + 3y = 6
Step-by-step explanation:
We can start by solving the second equation for one of the variables. Let's solve for y:
3x + 3y = 6
3y = 6 - 3x
y = 2 - x
Now we can substitute this expression for y into the first equation:
9x - 19y = 74
9x - 19(2 - x) = 74 (substituting y = 2 - x)
9x - 38 + 19x = 74
28x = 112
x = 4
Now we can use this value to find y:
y = 2 - x
y = 2 - 4
y = -2
Therefore, the solution to the system of equations is x = 4 and y = -2.
Hopes this helps
Given the triangle below, find the angle θ in radians. Round to four decimal places
Answer:
Θ ≈ 41.8103°
Step-by-step explanation:
using the sine ratio in the right triangle
sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{4}{6}[/tex] , then
Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{4}{6}[/tex] ) ≈ 41.8103° ( to 4 decimal places )
WILL MARK BRAINLIEST
a quadratic function is represented by the graph
what is the equation of the axis of symmetry of the function?
what are the coordinates of the vertex of the function
what are the coordinates of the x-intercepts of the function
what are the coordinates of the y intercept of the function
The equation of the axis of symmetry of the quadratic function is given by y = -2x² + 8x - 5.
x = 4 is the x-coordinate of the vertex.
x = 0 and x = 4 are the x-coordinates of the x-intercepts.
y = -5 is the y-coordinate of the y-intercept.
What is quadratic function?A quadratic function has two variables that can be used to model real-world problems. It has a distinct shape of a parabola, which is a symmetrical U-shaped curve.
The coordinates of the vertex of the function can be calculated by taking the derivative of the given equation and setting it equal to 0.
This yields x = 4 as the x-coordinate of the vertex.
Substituting this value in the given equation gives us the y-coordinate of the vertex, which is y = 11.
The coordinates of the x-intercepts of the function can be found by setting y = 0 in the given equation.
This yields x = 0 and x = 4 as the x-coordinates of the x-intercepts. Substituting these values in the given equation gives us the corresponding y-intercepts, which are
y = -5 and y = 0 respectively.
The coordinates of the y-intercept of the function can be found by setting x = 0 in the given equation.
This yields y = -5 as the y-coordinate of the y-intercept.
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Can someone please help me? I have to put this equation in order. I already tried but I was missing something.
I don't think anything is wrong with your values. Since it's an equation, you can see something different and get the right answer.
Need help with HW question 5
The characteristic polynomial of A is λ³ - 4λ² - 3λ + 14. The eigenvalues of A are 2, 1, and 7.
What is rational root theorem?According to the rational root theorem, p is a factor of the constant term and q is a factor of the leading coefficient if a polynomial with integer coefficients has a rational root of p/q, where p and q are integers without any shared factors. As the leading coefficient is 1 and the constant term is 14, the only potential rational roots in this situation are 1, 2, 7, and 14.
The characteristic polynomial of a matrix is given as
det(A - λI)
Here, λ is the eigen value.
det (A - λI)
[tex]\left[\begin{array}{ccc}1 - \lambda&0&1\\2&3 -\lambda&-1\\0&6& \lambda\end{array}\right][/tex]
Taking the determinant we have:
det(A - λI) = (1-λ)[(3-λ)(-λ) - (-1)(6)] - 0[2(-λ) - (-1)(0)] + (-1)[2(6) - (3-λ)(0)]
det(A - λI) = (1-λ)(λ² - 3λ - 6) - (-1)(12) = λ³ - 4λ² - 3λ + 14
Hence, the characteristic polynomial of A is λ³ - 4λ² - 3λ + 14.
The eigen values is the solution of the polynomial.
Using the rational roots of polynomial we have:
λ³ - 4λ² - 3λ + 14. factors as (λ-2)(λ-1)(λ-7)
Hence, the eigenvalues of A are 2, 1, and 7.
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