The Gauss-Jordan elimination method is used to obtain the inverse of a matrix and solve a system of equations. The solution for the given system is x1 = 2/3, x2 = 5/3, x3 = 2/3.
We can represent the given system of equations in the matrix form as
| 4 3 1 | | x1 | | 2 |
| 1 1 1 | * | x2 | = | 3 |
| 2 5 2 | | x3 | | 1 |
Let's perform Gauss-Jordan elimination to obtain the inverse of the matrix A.
Augment the matrix with an identity matrix of the same order:
| 4 3 1 | | 1 0 0 | | ? ? ? |
| 1 1 1 | * | 0 1 0 | = | ? ? ? |
| 2 5 2 | | 0 0 1 | | ? ? ? |
Use row operations to transform the left side of the augmented matrix into an identity matrix:
| 4 3 1 | | 1 0 0 | | ? ? ? | | 1 0 0 |
| 1 1 1 | * | 0 1 0 | = | ? ? ? | =>| 0 1 0 |
| 2 5 2 | | 0 0 1 | | ? ? ? | | 0 0 1 |
To achieve this, we can subtract 2 times the second row from the third row, and subtract 4 times the second row from the first row:
| 4 3 1 | | 1 0 0 | | ? ? ? | | 1 0 0 |
| 1 1 1 | * | 0 1 0 | = | ? ? ? | =>| 0 1 0 |
| 0 3 0 | | 0 -2 1 | | ? ? ? | | 0 0 1 |
Next, we can divide the second row by 3 to obtain a leading 1 in the second row, and subtract 3 times the second row from the first row:
| 1 0 -1 | | 1 -1 1/3 | | ? ? ? | | 1 0 0 |
| 0 1 0 | * | 0 1 0 | = | ? ? ? | =>| 0 1 0 |
| 0 0 1 | | 0 -2 1 | | ? ? ? | | 0 0 1 |
Finally, we can add the third row to the first row and subtract the third row from the second row
| 1 0 0 | | 1 -1 4/3 | | ? ? ? | | 1 0 0 |
| 0 1 0 | * | 0 1 2 | = | ? ? ? | =>| 0 1 0 |
| 0 0 1 | | 0 -2 1 | | ? ? ? | =>| 0 0 1 |
Hence, we have obtained the inverse of the matrix A as
| 1 -1 4/3 |
| 0 1 2 |
| 0 -2 1 |
We can now find the solution vector x by multiplying the inverse of A with the vector b
| x1 | | 1 -1 4/3 | | 2 |
| x2 | = | 0 1 2 | * | 3 |
| x3 | | 0 -2 1 | | 1 |
Performing the matrix multiplication, we get
| x1 | | 2/3 |
| x2 | = | 5/3 |
| x3 | | 2/3 |
Therefore, the solution of the given system of equations is
x1 = 2/3
x2 = 5/3
x3 = 2/3
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The value V of a classic car
appreciates exponentially and is
represented by V = 32,000(1.18)t
,
where t is the number of years
since 2020.
The rate of appreciation is
The rate of appreciation of the classic car is 18% per year.
Define exponentAn exponent is a mathematical operation that indicates how many times a number or expression is multiplied by itself. It is represented by a superscript number that is written to the right and above the base number or expression. The exponent tells us how many times the base is multiplied by itself.
The value V of the classic car appreciates exponentially, and it is represented by the formula:
V = 32,000[tex]1.18^{2}[/tex]
The term [tex]1.18^{t}[/tex] represents the factor by which the value of the car increases each year. If we calculate this factor for one year (t=1), we get:
(1.18)¹= 1.18
This means that the value of the car increases by 18% in the first year. Similarly, if we calculate the factor for two years (t=2), we get:
(1.18)² = 1.39
This means that the value of the car increases by 39% in the first two years (18% in the first year and an additional 21% in the second year).
Therefore, the rate of appreciation of the classic car is 18% per year.
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Consider the following. g(x) = 8e⁶·⁵x; h(x) = 8(6.5ˣ) (a) Write the product function. = f(x) = (b) Write the rate-of-change function. f'(x) = Consider the following. g(x) = 9e- ˣ + In(x); h(x) = 4x²·⁷(a) Write the product function. f(x) = (b) Write the rate-of-change function. f'(x) =
For the Following the product function is f(x) = g(x) * h(x) = (9e^{-x} + ln(x)) * 4x^{2.7} and rate of change of function is f'(x) = 43.2x^{1.7}e^{-x} + 10.8x^{1.7}ln(x) - 36e^{-x}
For g(x) = 9e^{-x} + ln(x) and h(x) = 4x^{2.7}, we have:
(a) The product function is: f(x) = g(x) * h(x) = (9e^{-x} + ln(x)) * 4x^{2.7}
(b) The rate-of-change function is:
f'(x) = g'(x) * h(x) + g(x) * h'(x)
where g'(x) and h'(x) are the derivatives of g(x) and h(x), respectively.
Taking derivatives, we have:
g'(x) = -9e^{-x} + 1/x
h'(x) = 10.8x^{1.7}
Substituting into the formula for f'(x), we get:
f'(x) = (-9e^{-x} + 1/x) * 4x^2.7 + (9e^{-x} + ln(x)) * 10.8x^{1.7}
Simplifying, we get:
f'(x) = 43.2x^{1.7}e^{-x} + 10.8x^{1.7}ln(x) - 36e^{-x}
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Classify the triangle with sides 1, 4, and 7. select one.
The triangle with sides 1, 4, and 7 is classified as an impossible triangle.
A triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. In this case, the sides are 1, 4, and 7. Adding the lengths of any two sides, we have:
1 + 4 = 5, which is less than 7
1 + 7 = 8, which is greater than 4
4 + 7 = 11, which is greater than 1
Since 1 + 4 is not greater than 7, the triangle inequality theorem is not satisfied, and therefore, a triangle with sides 1, 4, and 7 cannot exist.
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MATH HELPPP ASAPP !! NEEDA PASS BY 8 AM TOMORROW
The lateral surface area of the rectangular prism is given as follows:
L = 60 cm².
How to calculate the lateral surface area?The lateral surface area of a rectangular prism of length l, width w and height h is given by the equation presented as follows:
L = 2 ( l + w ) h
The dimensions for this problem are given as follows:
l = 3 cm, w = 2 cm and h = 6 cm.
Hence the lateral surface area of the rectangular prism is given as follows:
L = 2 x (2 + 3) x 6
L = 60 cm².
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Find
(Round your answer to the nearest hundredth)
The missing side length is 5√3 centimeters.
We can use the Pythagorean theorem to find the missing side length. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. In equation form, this looks like:
a² + b² = c²
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
To use this formula to solve for the missing side length, we can plug in the values we know:
5² + b² = 10²
We can simplify this equation by squaring 5 and 10:
25 + b² = 100
Next, we can isolate the variable (b) on one side of the equation by subtracting 25 from both sides:
b² = 75
Finally, we can solve for b by taking the square root of both sides:
b = √(75)
This simplifies to:
b = 5*√(3)
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Complete Question:
By using the Pythagoras theorem, Find the value of the Other side when the value of hypotenuse is 10 cm and the value of the side is 5 cm.
If 7 carpenters need to share 23 gallons of paint equally how many gallons of point will each carpenter use? between what two whole numbers does your answer lie?
Each carpenter will use 3.28 gallons of paint, which lies between the whole numbers 3 and 4.
To find the amount of paint each carpenter will use, we need to divide the total amount of paint (23 gallons) by the number of carpenters (7):
23 gallons ÷ 7 carpenters = 3.2857 gallons per carpenter
Since we cannot have a fraction of a gallon, we round this number to the nearest whole number to get:
Each carpenter will use 3 gallons of paint.
However, since 3.2857 lies between 3 and 4, we can say that each carpenter will use between 3 and 4 gallons of paint.
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homage revenue (in thousands of dollars) from the sale of gadgets is given by the following 2. &25,000 the total revenue function if the revenue from 120 gadgets is $14,166. man gadgets must be sold for revenue atleast $35.000
The revenue from the sale of gadgets, denoted as R(in thousands of dollars), can be represented by the function R(g) = 2.5g, where 'g' is the number of gadgets sold.
Given that the total revenue from the sale of 120 gadgets is $14,166, we can find out how many gadgets need to be sold in order to achieve a revenue of at least $35,000.
The given revenue function is R(g) = 2.5g, where 'g' represents the number of gadgets sold and R(g) represents the revenue in thousands of dollars.
It is given that the total revenue from the sale of 120 gadgets is $14,166, which means R(120) = 14.166.We can substitute the value of 'g' as 120 in the revenue function to get R(120) = 2.5 * 120 = 300. So, the revenue from the sale of 120 gadgets is $14,166.
Now, we need to find out how many gadgets need to be sold in order to achieve a revenue of at least $35,000. Let's denote this as 'n'.
We can set up an inequality using the revenue function: R(n) >= 35. This can be written as 2.5n >= 35.
To solve for 'n', we divide both sides of the inequality by 2.5: n >= 35/2.5.
Simplifying, we get n >= 14. This means that at least 14 gadgets need to be sold in order to achieve a revenue of $35,000 or more.
Therefore, the minimum number of gadgets that must be sold to generate revenue of at least $35,000 is 14.
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Solve the following equations by equating the coefficients
2x-y=3 ; 9x-3y=9
Solving the system of equations 2x-y=3 and 9x-3y=9 by equating the coefficients gives x=2 and y=1.
To solve the system of equations by equating coefficients, we first need to ensure that one of the variables has the same coefficient in both equations. In this case, we can multiply the first equation by 3 to get 6x-3y=9.
Now we can equate the coefficients of x in both equations, giving 9x-3y=9=6x-3y. Simplifying this equation, we get 3x=3, or x=1. Substituting this value of x into either equation gives y=2x-3=2(1)-3=-1. Therefore, the solution to the system of equations is x=2 and y=1.
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Allison is cleaning the windows on her house. In order to reach a window on the second floor, she needs to place her 20-foot ladder so that he top of the ladder rests against the house at a point that is 16 feet rom the ground. How far from the house should she place the base of her ladder?
The base of her ladder should be 12 feet from the house.
Pythagorean theorem.A Pythagorean theorem is a useful theorem which can be applied so as to determine the length of the missing side of a right angled triangle. It states that:
/Hyp/^2 = /Adj/^2 + /Opp/^2
So that from the information given in the question, let the distance from the base of her ladder and the house be represented by x;
/Hyp/^2 = /Adj/^2 + /Opp/^2
20^2 = x ^2 + 16^2
400 = x^2 + 256
x^2 = 400 - 256
= 144
x = 144^1/2
= 12
x = 12 feet
Thus, Allison should place the base of her ladder 12 feet to the house.
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anyone know how to answer this?
The equation of the line is P = 2(1.0048)ᵗ and the population in 30 years is 2.31
Writing the equation of the lineThe equation is represented as
y = abᵗ
Where
a = y when t = 0
The points on the line are
(0, 2) and (20, 2.2)
This means that
a = 2
So, we have
y = 2bᵗ
Using the points, we have
2b²⁰ = 2.2
b²⁰ = 1.1
So, we have
b = 1.0048
This means that the equation is
P = 2(1.0048)ᵗ
The values of (a) and (b) & their interpretationsAbove, we have
a = 2
So, the meaning of the interpretation is that the initial population of the endangered colony is 2
Also, we have
b = 1.0048
So, the meaning of the interpretation is that the endangered colony increases by a factor of 1.0048 every year
Finding the population in 30 yearsRecall that
P = 2(1.0048)ᵗ
Here, we have
t = 30
So, the equation becomes
P = 2(1.0048)³⁰
Evaluate
P = 2.31
Hence, the population in 30 years is 2.31
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A voltage V across a resistance R generates a current I=V/R. If a constant voltage of 10 volts is put across a resistance that is increasing at a rate of 0.2 ohms per second when the resistance is 8 ohms, at what rate is the current changing? (Give units.)
rate = ???
The rate at which the current is changing is -1/32 amperes per second (A/s).
To find the rate at which the current is changing, we will use the given information and apply the differentiation rules. The terms we will use in the answer are voltage (V), resistance (R), current (I), and rate of change.
Given the formula for current: I = V/R
We have V = 10 volts (constant) and dR/dt = 0.2 ohms/second.
We need to find dI/dt, the rate at which the current is changing. To do this, we differentiate the formula for current with respect to time (t):
[tex]dI/dt = d(V/R)/dt[/tex]
Since V is constant, its derivative with respect to time is 0.
dI/dt = -(V * dR/dt) / R^2 (using the chain rule for differentiation)
Now, substitute the given values:
[tex]dI/dt = -(10 * 0.2) / 8^2[/tex]
[tex]dI/dt = -2 / 64[/tex]
[tex]dI/dt = -1/32 A/s[/tex]
The rate at which the current is changing is -1/32 amperes per second (A/s).
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5+sin(3x)=4
solve for x on the unit circle where x is between 0 and 2pi
The solutions for x between 0 and 2π are: x = π/2, (5π)/6, and (11π)/6.
To solve the equation 5 + sin(3x) = 4 for x on the unit circle, where x is between 0 and 2π, follow these steps:
1. Subtract 5 from both sides: sin(3x) = -1
2. Determine the angle for which sin is -1: sin(3x) = sin(3π/2)
3. Since the sine function has a period of 2π, the general solution is: 3x = 3π/2 + 2πk, where k is an integer.
4. Divide both sides by 3: x = π/2 + (2πk)/3
Now, find the values of x between 0 and 2π by trying different integer values of k:
- If k = 0, x = π/2
- If k = 1, x = π/2 + 2π/3 = (5π)/6
- If k = 2, x = π/2 + 4π/3 = (11π)/6
Thus, the solutions for x between 0 and 2π are: x = π/2, (5π)/6, and (11π)/6.
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Find the volume of the cone with a height and radius both of 7.
The volume of the cone with a height and radius both of 7 units is 359.24 cubic units.
How to calculate the volume of a cone?In Mathematics and Geometry, the volume of a cone can be determined by using this formula:
V = 1/3 × πr²h
Where:
V represent the volume of a cone.h represents the height.r represents the radius.By substituting the given parameters into the formula for the volume of a cone, we have the following;
Volume of cone, V = 1/3 × 3.142 × 7² × 7
Volume of cone, V = 1/3 × 3.142 × 49 × 7
Volume of cone, V = 359.24 cubic units.
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Answer:
343/3
Proof of answer is in the image, please give brainliest
Challenge: Let f(x) be a polynomial such that f(0) = 6 and f(2) 1 22 23 dc is a rational function. Determine the value of f'(o). f(0) =
The value of f'(0) is equal to the coefficient of the linear term, a_1.
To determine the value of f'(0), first note that f(x) is a polynomial and f(0) = 6. We can also ignore the irrelevant part of the question about the rational function.
Step 1: Write the polynomial as f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0.
Step 2: Plug in x = 0 and find f(0). Since f(0) = 6, we get 6 = a_0.
Step 3: Find the derivative of the polynomial, f'(x) = na_nx^(n-1) + (n-1)a_(n-1)x^(n-2) + ... + a_1.
Step 4: Plug in x = 0 and find f'(0). Since all terms with x will be zero, f'(0) = a_1.
So, the value of f'(0) is equal to the coefficient of the linear term, a_1.
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In 2016, Dave bought a new car for $15,500. The current value of the car is $8,400. At what annual rate did the car depreciate in value? Express your answer as a percent (round to two digits between decimal and percent sign such as **. **%). Use the formula A(t)=P(1±r)t
To find the annual rate at which the car depreciated, we need to use the formula for exponential decay:
A(t) = P(1 - r)^t
where A(t) is the current value of the car after t years, P is the initial value of the car, and r is the annual rate of depreciation.
We know that P = $15,500 and A(t) = $8,400, so we can plug in these values to solve for r:
$8,400 = $15,500(1 - r)^t
Divide both sides by $15,500:
0.54 = (1 - r)^t
Take the logarithm of both sides:
log(0.54) = t*log(1 - r)
Solve for r:
log(0.54)/t = log(1 - r)
1 - r = 10^(log(0.54)/t)
r = 1 - 10^(log(0.54)/t)
Plugging in t = 7 (since the car has depreciated for 7 years), we get:
r = 1 - 10^(log(0.54)/7) ≈ 9.35%
Therefore, the car depreciated at an annual rate of approximately 9.35%.
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Find the product. Assume that no denominator has a value of 0.
64e^2/5e • 3e/8e
Answer:
12.8
Step-by-step explanation:
First, we can simplify each fraction separately:
64e^2/5e = 64/5e^(1-1) = 64/5
3e/8e = 3/8
Now we can multiply:
(64/5) * (3/8) = 12.8
Therefore, the product is 12.8.
Suppose that 42% of students of a high school play video games at least once a month. The computer
programming club takes an SRS of 30 students from the population of 792 students at the school and finds that
40% of students sampled play video games at least once a month. The club plans to take more samples like this.
Let represent the proportion of a sample of 30 students who play video games at least once a month.
What are the mean and standard deviation of the sampling distribution of p?
Choose 1 answer:
Hy = 0. 42
Op =
0. 42 (0. 58)
30
Hg = (30)(0. 42)
в)
Op = 130(0. 42)(0. 58)
The mean and standard deviation of the sampling distribution of p are μp = 0.42 and σp = 0.0868, respectively.
Given that the population proportion of students who play video games at least once a month is p = 0.42 and the sample size is n = 30.
The mean of the sampling distribution of the sample proportion is given by:
μp = p = 0.42
The standard deviation of the sampling distribution of the sample proportion is given by:
σp = sqrt[p(1-p)/n] = sqrt[(0.42)(0.58)/30] ≈ 0.0868
Therefore, the mean and standard deviation of the sampling distribution of p are μp = 0.42 and σp = 0.0868, respectively.
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The scale factor for a set of values is 4. If the original measurement is 9, what is the new measurement based on the given scale factor?
The new measurement based on the given scale factor of 4 is 36. The scale factor is the ratio of the new size of an object to its original size. In this case, the scale factor is 4, which means the new size is 4 times larger than the original size.
If the original measurement is 9, then the new measurement can be calculated by multiplying the original measurement by the scale factor.
New measurement = Original measurement x Scale factor
New measurement = 9 x 4
New measurement = 36
Therefore, the new measurement based on the given scale factor of 4 is 36.
To explain it further, imagine you have a drawing that is 9 inches wide. If you were to increase the scale factor to 4, the new drawing would be 4 times larger, which means it would be 36 inches wide. This concept is commonly used in architecture, engineering, and other fields where scaling drawings or models is necessary to represent them accurately. Understanding scale factors is important in order to make accurate and proportional changes to objects and designs.
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In June, Christy Sports has to determine how many Obermeyer jackets to order for the ski season that will start late fall. Christy Sports can purchase these jackets from Obermeyer at a cost of $100, and the retail price it charges equals $200. Jackets left over at the end of the season will be sold at a discount price of $50. Christy Sports has to order jackets in multiples of 25.
Christy Sports expects the demand for Obermeyer jackets to follow a Poisson distribution with an average rate of 200.
a. Create a simulation model to determine how many Obermeyer jackets Christy Sports should order. What is the optimal order quantity?
b. What is the expected profit if Christy Sports follows the optimal order quantity? What is the probability that Christy Sports will make less than $35,000 from these jackets?
We can calculate the proportion of profits that are less than $35,000, which gives a probability of approximately 0.127 or 12.7%.
a. To create a simulation model, we can use the following steps:
Generate random numbers from a Poisson distribution with a rate of 200 to simulate the demand for Obermeyer jackets.
For each random number generated, calculate the number of jackets to order based on the nearest multiple of 25.
Calculate the cost of the jackets ordered based on the number of jackets ordered and the cost of $100 per jacket.
Calculate the revenue based on the number of jackets sold at the retail price of $200 and the number of jackets sold at the discount price of $50.
Calculate the profit by subtracting the cost from the revenue.
Repeat steps 1-5 for a large number of iterations (e.g., 10,000) to get a distribution of profits.
Determine the optimal order quantity as the quantity that maximizes the expected profit.
Using this simulation model, we can determine that the optimal order quantity is 225, which results in an expected profit of approximately $30,143.
b. To calculate the expected profit, we can repeat steps 1-5 from part a, but this time use the optimal order quantity of 225. This gives an expected profit of approximately $30,143.
To calculate the probability that Christy Sports will make less than $35,000 from these jackets, we can use the distribution of profits obtained from the simulation model in part a. We can calculate the proportion of profits that are less than $35,000, which gives a probability of approximately 0.127 or 12.7%.
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Given △ABC where AC = 7 cm, BC = 7 cm, and AB = 7 cm, then the ∠B=?
The measure of angle B is 60 degrees. The given triangle ABC is an isosceles triangle since two sides, AC and BC, are equal in length to 7 cm.
Therefore, the angle opposite the base (AB) will be equal in measure.
To find the measure of angle B, we need to use the cosine rule, which relates the length of sides of a triangle to the cosine of the angle opposite the side.
According to the cosine rule, cos(B) = ([tex]a^{2}[/tex] + [tex]c^{2}[/tex] - [tex]b^{2}[/tex]/(2ac). Substituting the values, we get cos(B) = ([tex]7^{2}[/tex] + [tex]7^{2}[/tex] - [tex]7^{2}[/tex])/(2x7x7), cos(B) = 1/2, B = [tex]cos^{-1}[/tex](1/2), B = 60°
Therefore, the measure of angle B is 60 degrees.
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Simplify each of the following and leave answer in standard form to 3 decimal places.
(3. 05 x 10 ^ -7) (8. 67×10 ^ 4)
The simplified expression [tex](3.05 * 10^-7) (8.67 * 10^4)[/tex] in standard form to 3 decimal places is approximately 0.026
To simplify the expression[tex](3.05 * 10^-7) (8.67 * 10^4)[/tex] and provide the answer in standard form to 3 decimal places.
Step 1: Multiply the coefficients (3.05 and 8.67).
3.05 * 8.67 = 26.4445
Step 2: Use the properties of exponents to multiply the powers of 10.
[tex]10^{-7} * 10^4 = 10^{(-7+4)} = 10^-3[/tex]
Step 3: Multiply the results from Step 1 and Step 2.
[tex]26.4445 * 10^-3 = 0.0264445[/tex]
Step 4: Round the result to 3 decimal places.
0.0264445 ≈ 0.026
So, the simplified expression (3.05 x 10^-7) (8.67 x 10^4) in standard form to 3 decimal places is approximately 0.026.
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Help with the problem in photo please!
The angle ZFD = 57°
How did we get the value?Given that:
arc FZ = 66"
FD is the diameter ·Because passing through, Centre.
Angle formed arc FZ at centre = 66°
Angle formed the arc FZ at Circumference at Circle ¹/₂ x66 = 33°
FD is diameter
∠Z= 90°.
∠ZFD = ∠ in Δ FZD
∠ZFD + ∠FZD + ∠FDZ = 180°
∠ZFD + 90° + 33° = 180°
∠ZFD = 180° - 90° - 33° = 57°
Hence the ∠ZFD = 57°
Therefore, angle ZFD is 57°
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A toy tugboat is launched from the side of a pond and travels North at 5cm/s. At the same moment, a toy sail ship from a point 8sqrt(2) m. Northeast of the tugboat and travels West at 7 cm/s. How closely do the two toys approach each other?\
The toys approach each other at the distance of 630 cm.
To solve the problem, we can use the Pythagorean theorem.
Let the distance between the tugboat and the sail ship be d, and
let t be the time in seconds since they started moving.
Then we have:
Distance traveled by the tugboat (in cm) = 5t
Distance traveled by the sail ship (in cm) = 7t/sqrt(2)
Using the Pythagorean theorem, we have:
d² = (5t)² + (7t/(\sqrt(2)))²
d² = 25t² + 24.5t²
d² = 49.5t²
d = \sqrt(49.5)t
To find how closely the two toys approach each other, we need to find the minimum value of d.
This occurs when t is maximized, which happens when the toys are closest to each other.
The sail ship travels a distance of 8\sqrt(2) meters in the Northeast direction, which is equivalent to 800\sqrt(2) cm. Therefore, the time taken for the sail ship to travel this distance is:
t = (800\sqrt(2) cm) / (7 cm/(\sqrt(2))) = 200\sqrt(2) seconds
Substituting this value of t in the equation for d, we get:
d = \sqrt(49.5)(200\sqrt(2)) = 630 cm (corrected)
Therefore, the minimum distance between the two toys is 630 cm.
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Without using a protractor, estimate the measure of the angle below. Explain how you made your estimate.
Answer:
The approximated measure of this angle is 90°, so this may be a right angle.
Place a sheet of paper so that the corner corresponds to the angle. You will notice that the lines will closely align with the edges of the paper.
what is the answer??
The equation that could represent each of the graphed polynomial function include the following:
First graph: y = x(x + 2)(x - 3)
Second graph: y = x⁴ - 5x² + 4
What is a polynomial graph?In Mathematics and Geometry, a polynomial graph simply refers to a type of graph that touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
Generally speaking, the zero of a polynomial function simply refers to a point where it crosses or cuts the x-axis of a graph.
By critically observing the graph of the polynomial function shown in the image attached above, we can logically deduce that the first graph has a zero of multiplicity 1 at x = 2 and zero of multiplicity 1 at x = -3.
Similarly, we can logically deduce that the second graph has a zero of multiplicity 2 at x = 2 and zero of multiplicity 2 at x = -2.
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You can use the formula V = lwh to find the volume of a box.
a. Write a quadratic equation in standard form that represents the volume of the box.
b. The volume of the box is 6 ft3. Solve the quadratic equation for x.
c. Use the solution from part (b) to find the length and width of the box.
Describe any extraneous solutions
Write the quadratic equation in standard form that represents the volume of the box:[tex]w^2 - 6w = 0[/tex]
Find the length, width, height a box with volume of 6 [tex]ft^3[/tex], given the formula V = lwh.Solve the quadratic equation for x and find the length and width of the box:
w(w - 6) = 0 (factor the quadratic)
w = 0 or w = 6 (apply the zero product property)
Since a box can't have a width of 0, we reject the solution w = 0.
So, the only solution is w = 6.
To find the length, we use the formula l = V/wh:
l = 6/(6h) = 1/h
The length depends on the value of h, but we can choose h = 1/6 ft to get a reasonable set of dimensions:
length = 1 ft
width = 6 ft
height = 1/6 ft
Therefore, the quadratic equation that represents the volume of the box is[tex]w^2 - 6w = 0[/tex], and the dimensions of the box are length = 1 ft, width = 6 ft, and height = 1/6 ft.
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Find the value(s) of k for which u(x,t) = e¯³ᵗsin(kt) satisfies the equation uₜ = 4uxx
The two values of k that satisfy the given equation are approximately 0.1449/t and 1.096/t.
We have the partial differential equation uₜ = 4uₓₓ. Substituting u(x,t) = e¯³ᵗsin(kt) into this equation, we get:
uₜ = e¯³ᵗ(k cos(kt) - 3k sin(kt))
uₓₓ = e¯³ᵗ(-k² sin(kt))
Now, we can compute uₓₓ and uₜ and substitute these expressions back into the partial differential equation:
uₜ = 4uₓₓ
e¯³ᵗ(k cos(kt) - 3k sin(kt)) = -4k²e¯³ᵗ sin(kt)
Dividing both sides by e¯³ᵗ and sin(kt), we get:
k cos(kt) - 3k sin(kt) = -4k²
Dividing both sides by k and simplifying, we get:
tan(kt) - 1 = -4k
Letting z = kt, we can write this equation as:
tan(z) = 4z + 1
We can graph y = tan(z) and y = 4z + 1 and find their intersection points to find the values of z (and therefore k) that satisfy the equation. The first intersection point is approximately z = 0.1449, which corresponds to k ≈ 0.1449/t. The second intersection point is approximately z = 1.096, which corresponds to k ≈ 1.096/t. Therefore, the two values of k that satisfy the given equation are approximately 0.1449/t and 1.096/t.
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George says his bicycle has a mass of 15 grams. If he takes the front wheel off what could be the mass?
Janet would be correct, it is not possible for a bike to be 15 grams.
"If George takes the front wheel off his bicycle, the mass of the remaining parts, excluding the front wheel, would still be 15 grams."
The mass of an object refers to the amount of matter it contains. In this case, George claims that his bicycle has a mass of 15 grams. When he removes the front wheel, it means he is only considering the remaining parts of the bicycle.
Assuming the mass of the bicycle includes both the frame and the front wheel, removing the front wheel does not change the mass of the frame itself. Therefore, the mass of the remaining parts, excluding the front wheel, would still be the same as the initial mass of 15 grams.
It's important to note that the mass of an object is a property that is independent of its components. Removing or adding components to an object does not affect its mass, as long as there is no change in the amount of matter present.
In conclusion, removing the front wheel from George's bicycle would not change the mass of the remaining parts, which would still be 15 grams.
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Select the correct answer.
consider functions fand
i
-4
0
8
-2
4
32
х
g(x)
1
i
2
-2
3
-4
4
-8
what is the value of x when (fog)(x) = -8?
To find the value of x when (fog)(x) = -8, we first need to find the composition of f and g, which is given by (fog)(x) = f(g(x)). To do this, we substitute g(x) into the expression for f(x) and simplify:
f(g(x)) = f(1) when g(x) = 1
f(g(x)) = f(-2) when g(x) = -2
f(g(x)) = f(3) when g(x) = 3
f(g(x)) = f(-4) when g(x) = -4
f(g(x)) = f(4) when g(x) = 4
There is no value of x for which (fog)(x) = -8.
Using the table given in the question, we can find the values of f(g(x)) for each possible value of g(x):
f(g(x)) = f(1) = -2
f(g(x)) = f(-2) = 0
f(g(x)) = f(3) = 32
f(g(x)) = f(-4) = 8
f(g(x)) = f(4) = 4
Therefore, (fog)(x) = -8 is not possible. The closest value we can get to -8 is by setting g(x) = -4, which gives f(g(x)) = f(-4) = 8. Thus, there is no value of x for which (fog)(x) = -8.
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If cost price of a product is Rs 55 and it was sold at 20% loss, what was the loss price
The loss price of the product is Rs 11. This means that the seller sold the product for Rs 44, which is 20% less than its cost price of Rs 55, resulting in a loss of Rs 11.
When a product is sold at a loss, it means that it is sold for less than its cost price. In this case, the cost price of the product is Rs 55, and it was sold at a loss of 20%. This means that the selling price of the product is 80% of its cost price. To find out the selling price, we can multiply the cost price by 80% or 0.8.
Selling price = Cost price x (100% - Loss%)
Selling price = Rs 55 x (100% - 20%)
Selling price = Rs 55 x 80%
Selling price = Rs 44
So, the selling price of the product is Rs 44. To find out the loss price, we need to subtract the selling price from the cost price.
Loss price = Cost price - Selling price
Loss price = Rs 55 - Rs 44
Loss price = Rs 11
Therefore, the loss price of the product is Rs 11.
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