Function with the domain of [-3, 3] is f(x) = [tex]x^2[/tex]
Define function.A function is a mathematical formula that gives each input value in a set an individual output value. The domain and range are two sets that relate to one another in such a way that each element in the domain has a unique association with the elements in the range.
An equation or collection of rules that indicate how the output is determined depending on the input constitutes a function, which is often denoted by a symbol like f. The independent variable is the value of the inputs, and the dependent variable is the value of the outputs.
Here's an example of a function with the domain of [-3, 3]:
f(x) = [tex]x^2[/tex]
This function maps each value in the interval [-3, 3] to its square. For example, when x = -3, f(x) = [tex](-3)^2[/tex] = 9, and when x = 3, f(x) = [tex](3)^2[/tex] = 9. The graph of this function is a parabola that opens upward and has its vertex at the origin (0,0).
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"Susanna sells a lot for $45,400. She netted $41,428 after paying a broker’s commission. What was her rate of commission? (Hint: Before you find the rate of commission, you must find the amount of commission.)"
The accompanying sample of six measurements was randomly selected from a normally distributed population. Complete parts a through c below. 2, 3, -1.5.1.2 a. Test the null hypothesis that the mean of the population is 3 against the alternative hypothesis, u <3. Use a =0.05. The test statistic is ____(Round to two decimal places as needed.) .
The t-test statistic of the data is -1.23
What is the test statisticTo test the null hypothesis that the mean of the population is 3 against the alternative hypothesis, u <3 with a significance level of 0.05, we can use a one-tailed t-test since the sample size is small and the population standard deviation is unknown.
The formula for the t-test statistic is:
t = (x(bar) - μ) / (s / √n)
Where:
x(bar) = sample mean
μ = population mean (null hypothesis)
s = sample standard deviation
n = sample size
Given the sample of six measurements: 2, 3, -1.5, 1.2
First, we need to calculate the sample mean, sample standard deviation, and t-test statistic.
Sample mean (x(bar)) = (2 + 3 - 1.5 + 1.2) / 4 = 1.93
Sample standard deviation (s) = √[(∑(x - x(bar))^2) / (n - 1)]
= √[((2 - 1.93)^2 + (3 - 1.93)^2 + (-1.5 - 1.93)^2 + (1.2 - 1.93)^2 + / (4 - 1)]
= 1.92
t-test statistic = (x(bar) - μ) / (s / √n)
= (1.93 - 3) / (1.92 / √5)
= -1.23 (rounded to two decimal places)
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Choose the function whose graph is given by:
IN
OA. y = sec(x) +2
B. y = sec (2x)
OC. y = 2sec(-x)
OD. y = 2csc(-x)
12s
J
35+
Answer:
C
Step-by-step explanation:
If you start by picking a point to plug in you can check easily to see what works.
Lets start with x=pi. If we plug that into all the answer choices,
A. sec(pi/2)+2 = does not exist
B. 1/2sec(2pi) = 1/2
C. 2sec(pi/2) = does not exist
D. 2csc(pi/2) = 1
So, since at pi there is a vertical asymptote it should not exist. So, A or C.
Then pick x = 0, y must be 2.
A. sec(0) +2 = 1+2 = 3
C. 2sec(0) = 2
So, C must be the answer.
When using the number line you represent subtraction of a negative number with an arrow going to the ______.
PLS HELP IM SO CONFUSED
Answer:
When using the number line, you represent subtraction of a negative number with an arrow going to the right. The direction of the arrow indicates the movement of the number line towards the positive side, which is the opposite of the direction of a negative number. Subtraction of a negative number is equivalent to addition of a positive number, so the arrow going to the right represents the addition of the absolute value of the negative number. For example, if you are subtracting -5 from 10, you can represent this on a number line by starting at 10 and drawing an arrow to the right that goes 5 units, ending at 15.
Answer:
When using the number line to represent subtraction of a negative number, you would represent it with an arrow going to the right (or in the positive direction).
For example, let's say you want to represent the following subtraction on a number line:
5 - (-3)
You can start at 5 on the number line and then move to the left by 3 units, since you are subtracting a negative number. However, instead of leaving the arrow pointing to the left to represent the subtraction, you can turn it around and point it to the right, which is the positive direction. This means that you end up at a point that is 8 units to the right of 0 on the number line, which represents the answer of 8.
So, the arrow would go to the right to show the subtraction of a negative number on the number line.
Solve the equation :step by step
f/24 = 27
f =
Answer:
f = 648
Step-by-step explanation:
[tex]\frac{f}{24} =27[/tex]
Multiply both sides by 24
[tex]f=648[/tex]
Which of the following is the proper name for the figure below?
Answer:
Δ JKE
Step-by-step explanation:
the figure is a triangle and is named using its vertices.
the vertices are J, K, E
to name the triangle start with any vertex , then in clockwise/ anticlockwise order the other 2 vertices. in this case starting with J , then clockwise for K and E.
in this case then the figure is Δ JKE
8x/8 simplified into a decimal
Step-by-step explanation:
8/8 in decimal form is equal to 1. To simplify 8/8 to a decimal, you divide the numerator (8) by the denominator (8). This is equal to 1. Therefore, 8/8 simplified into a decimal is 1.
find the equilibrium quantity and equilibrium price for the demand and supply functions
supply p= 0.2q²+0.4q+1.8
Demand p = -0.1q²-0.2q+9
Answer:
Step-by-step explanation:
To find the equilibrium quantity and equilibrium price for the demand and supply functions, we need to find the point where the quantity demanded and the quantity supplied are equal. This point is known as the equilibrium point and is represented by the intersection of the demand and supply curves.
The demand function is given by p = -0.1q²-0.2q+9, and the supply function is given by p = 0.2q²+0.4q+1.8.
To find the equilibrium quantity, we need to set the quantity demanded equal to the quantity supplied:
-0.1q²-0.2q+9 = 0.2q²+0.4q+1.8
Simplifying and rearranging the terms, we get:
0.3q² + 0.6q - 7.2 = 0
Using the quadratic formula, we can solve for q:
q = (-0.6 ± √(0.6² - 4(0.3)(-7.2))) / (2(0.3))
q = (-0.6 ± √(0.6² + 8.64)) / 0.6
q = (-0.6 ± √9.36) / 0.6
q = (-0.6 ± 3.06) / 0.6
q = 4.6, -5.0
Since the quantity cannot be negative, the equilibrium quantity is q = 4.6.
To find the equilibrium price, we can substitute the equilibrium quantity into either the demand or supply function:
p = 0.2q²+0.4q+1.8
p = 0.2(4.6)²+0.4(4.6)+1.8
p = 7.82
Therefore, the equilibrium quantity is 4.6 units and the equilibrium price is $7.82.
a study was conducted that resulted in the following relative frequency histogram. determine whether or not the histogram indicates that a normal distribution could be used as a model for the variable.
If the bars of a histogram roughly follow a symmetrical bell or hill shape, then the distribution is approximately normally distributed.
What is Histogram?Histogram a diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.
Given is relative frequency histogram.
The histogram is not given, so will discussion the property that tells whether the histogram indicates a normal distribution or not.If the bars roughly follow a symmetrical bell or hill shape, then the distribution is approximately normally distributed.Therefore, if the bars of a histogram roughly follow a symmetrical bell or hill shape, then the distribution is approximately normally distributed.
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The three side lengths of four triangles are given. Which triangle is a right triangle? Triangle 1: 13‾‾‾√ 13 , 6, 7 Triangle 2: 7, 8, 13 Triangle 3: 10, 11, 12 Triangle 4: 10‾‾‾√ 10 , 9, 8
The triangle whose sides are √13, 6, and 7, is a right triangle.
What is the right triangle?
A right triangle is defined as a triangle with one right angle or two perpendicular sides. The longest side of a right triangle is called the hypotenuse.
Pythagorean Theorem :
The square on the hypotenuse is equal to the total of the squares on the legs of a right triangle.
Mathematically, let r be the length of the hypotenuse of a right triangle. Again let p, q be the lengths of other sides of this triangle. By the Pythagorean Theorem,
r² = p² + q².
How to solve this problem?
We just check which triangle's sides follow the above theorem.
Option A (Triangle with sides √13, 6, and 7 ):
13 + 36 = 49
i.e. (√13)² + 6² = 7²
This triangle's sides follow the Pythagorean Theorem.
So, the triangle with sides √13, 6, and 7 is a right triangle.
Option B (Triangle with sides 7, 8, and 13 ):
49 + 64 ≠ 169
i.e. 7² + 8² ≠ 13²
This triangle's sides do not follow the Pythagorean Theorem.
So, the triangle with sides 7, 8, and 13 is not a right triangle.
Option C (Triangle with sides 10, 11, and 12 ):
100 + 121 ≠ 144
i.e. 10² + 11² ≠ 12²
This triangle's sides do not follow the Pythagorean Theorem.
So, the triangle with sides 10, 11, and 12 is not a right triangle.
Option D (Triangle with sides √10, 9, and 8 ):
10 + 64 ≠ 81
i.e. (√10)² + 8² ≠ 9²
This triangle's sides do not follow the Pythagorean Theorem.
So, the triangle with sides √10, 9, and 8 is not a right triangle.
Therefore the triangle whose sides are √13, 6, and 7, is a right triangle. So, option A is correct.
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Sb please help me Will give thanks and try to award brainliest
Answer:
3
Step-by-step explanation:
∠LMN = ∠BMN + ∠LMB (linear angles)
59x + 3 = 160 + (-1 + 7x)
59x - 7x = 160 - 1 - 3
52x = 156
x = 156/52 = 3
Identify the rational function whose graph is given below. Note the graph has an x-intercept at x=2 and a y-intercept at y=−2/3.
Therefore, the rational function whose graph has an x-intercept at x=2.
What is function?In mathematics, a function is a rule that assigns to each input value from a set (called the domain) exactly one output value from another set (called the range). In other words, a function is a relationship between two sets of numbers, such that for each input value there is a unique output value. Functions are commonly denoted by an equation that defines the relationship between the input and output variables. For example, the equation y = f(x) defines a function f, where x is the input variable and y is the output variable.
Here,
To identify the rational function whose graph is given below, we need to determine its equation. We know that the graph has an x-intercept at x=2 and a y-intercept at y=−2/3.
We also know that the function is a rational function, which means it can be written as a ratio of two polynomials. The general form of a rational function is:
f(x) = p(x)/q(x)
where p(x) and q(x) are polynomials, and q(x) cannot be zero.
To find the specific equation of the function whose graph is shown, we can use the information about the intercepts to write down two points that are on the graph. We can use these points to set up a system of equations that we can solve for the coefficients of the polynomials p(x) and q(x).
Using the x-intercept, we know that the point (2,0) is on the graph. Using the y-intercept, we know that the point (0,-2/3) is on the graph. So we can set up the following system of equations:
p(2)/q(2) = 0
p(0)/q(0) = -2/3
Since the denominator of a rational function cannot be zero, we know that q(2) and q(0) cannot be zero. This allows us to set up a third equation:
q(x) ≠ 0
Now we can use algebra to solve for the coefficients of p(x) and q(x). We can start by writing the rational function in general form:
f(x) = p(x)/q(x)
and then multiplying both sides by q(x):
f(x)q(x) = p(x)
We can now substitute x=2 and x=0 to get two equations:
f(2)q(2) = p(2) = 0
f(0)q(0) = p(0) = -2/3
We also have the equation q(x) ≠ 0. This means that the denominator cannot have any factors that would make it equal to zero, so we can assume that q(x) has a linear factor of (x - 2), since we know that the graph has an x-intercept at x=2. We can then write:
q(x) = a(x - 2)
where a is some constant.
Now we can substitute this expression for q(x) into the equation f(x)q(x) = p(x) and simplify:
f(x)q(x) = p(x)
f(x)a(x - 2) = p(x)
We can now substitute x=0 and use the equation we found for p(0):
f(0)a(-2) = -2/3
f(0) = 1/3a
Next, we can substitute x=2 and use the equation we found for p(2):
f(2)a(0) = 0
f(2) = 0
Finally, we can substitute these values for f(0) and f(2) into the general form of the rational function and simplify:
f(x) = p(x)/q(x)
f(x) = p(x)/(a(x - 2))
We know that p(x) = f(x)q(x) from the equation we derived earlier, so we can substitute this into the equation above:
f(x) = f(x)(x - 2)/a(x - 2)
We can now cancel the f(x) terms from both sides and simplify:
1 = (x - 2)/a
a = x - 2
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The function f(x) is defined as f(x) = One-third(6)x. Which table of values could be used to graph g(x), a reflection of f(x) across the x-axis? A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, one-third, 2, 12. The third column is labeled g (x) with entries 12, 2, one-third, one-eighteenth, StartFraction 1 Over 108 EndFraction. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, 0, 2, 12. The third column is labeled g (x) with entries 12, 2, 0, one-eighteenth, StartFraction 1 Over 108 EndFraction. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, one-third, 2, 12. The third column is labeled g (x) with entries negative StartFraction 1 Over 108 EndFraction, negative one-eighteenth, negative one-third, negative 2, negative 12. A 3-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries StartFraction 1 Over 108 EndFraction, One-eighteenth, 0, 2, 12. The third column is labeled g (x) with entries negative StartFraction 1 Over 108 EndFraction, negative one-eighteenth, negative one-third, negative 2, negative 12.
The table that is used to graph g(x) is given by table 3 and 4.
What is reflection?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation.
Given that, the function is:
f(x) = 1/3(6x) = 2x
f(x) = 2x
g(x) is the reflection of f(x) across the x-axis.
According to the rule of reflection, the reflection on x-axis is given as:
(x, y) → (x, -y)
Here, the y coordinated of the graph of g(x) has the same value but the opposite sign.
This is satisfied by the table 3 and 4.
Hence, the table that is used to graph g(x) is given by table 3 and 4.
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Need help asap. Whoever helps gets 25 points
The value of the indicated trigonometric ratio cosβ is equal to 11/12.
How to determine the value of cosβ?From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:
Opposite side = 2√23.Hypotenuse = 24Adjacent side = 22.In order to determine the magnitude of cosβ, we would apply the law of cosine because the given side lengths represent the adjacent side and hypotenuse of a right-angled triangle.
cos(θ) = Adj/Hyp
Where:
Adj represents the adjacent side of a right-angled triangle.Hyp represents the hypotenuse of a right-angled triangle.θ represents the angle.Therefore, we have the following cosine trigonometric function:
cosβ = 22/24
cosβ = 11/12
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What is the slope of the line that passes through the point (6.24) and the origina
KINA
m=4
SEES
m
m=0
m = undefined
Answer:
slope = 4
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (6, 24 ) and (x₂, y₂ ) = (0, 0 )
m = [tex]\frac{0-24}{0-6}[/tex] = [tex]\frac{-24}{-6}[/tex] = 4
Find the value of ƒ (6).
y = f(x)
Answer:
The value of ƒ (6) is the value of y.
Step-by-step explanation:
Given: y = f(x)
Step 1: Substitute x = 6 into the equation.
y = f(6)
Step 2: Solve for y.
y = f(6)
Help Help Help Help Help Help (Just yes or no, I don’t need explanation)
Answer:
No
Step-by-step explanation:
The y intercept is 7. For it to be proportional it has to go through (0,0).
Answer:
Yes
Step-by-step explanation:
PLEASE HELP
match each transformation with its coordinates
1) A(1,2),A'(-1,2) : a reflection across the y-axis
2) A(1,2), A'(-2,1): a rotation 270⁰ clockwise around the origin
3) A(1,2), A'(-1,4): a translation of 2 units left and 2 unit up
4) A(1,2),A'(-1,-2): a rotation 180⁰ around the origin
5) A(1,2),A'(-3,-7): a translation of 4 units left and 9 units down
What is the transformation of a point?
The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.
The given point is A(1,2).
The rule of a rotation 180⁰ around the origin is (x,y)→(−x,−y).
Therefore, A(1,2)→A'(-1,-2).
A rule of translation of 2 units left and 2 unit up is (x,y)→(x-2,y+2)
Therefore, A(1,2)→A'(1-2,2+2) = A'(-1,4).
The rule of a reflection across the y-axis is (x,y)→(−x,y).
Therefore, A(1,2)→A'(-1,2)
A rule of translation of 4 units left and 9 units down is (x,y)→(x-4,y-9)
Therefore, A(1,2)→A'(1-4,2-9) = A'(-3,-7).
The rule of a rotation 270⁰ clockwise around the origin is (x,y)→(-y,x)
Therefore, A(1,2)→A'(-2,1)
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Answer:
Step-by-step explanation:
An old truck has a fuel efficiency of 12 mpg. What is the cost of gasoline if the truck uses 5 gallons to drive 60 miles?
The cost of gasoline if the truck uses 5 gallons to drive 60 miles is $18.70
How to determine the cost of gasoline if the truck uses 5 gallons to drive 60 miles?To calculate the cost of gasoline for the old truck, we can use the following formula:
Cost of gasoline = Price per gallon × Number of gallons used
Given that
Price per gallon = 3.74
Number of gallons used = 5 gallons
We have
Cost of gasoline = $3.74/gallon × 5 gallons
Evaluate
Cost = $18.70
Hence, the cost is $18.70
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Complete question
An old truck has a fuel efficiency of 12 mpg. What is the cost of gasoline if the truck uses 5 gallons to drive 60 miles if the gasoline costs $3.74 per gallon
Let A = {a, s, i, m, o, v}
How many partitions are possible for this set?
Answer:
Step-by-step explanation:
The number of partitions possible for a set A with n elements is given by the Bell number, denoted as Bn.
For a set A = {a, s, i, m, o, v} with 6 elements, the number of partitions possible is given by the 6th Bell number, which can be computed as follows:
B6 = ∑k=1 to 6 {6 choose k} * Sk
where Sk is the Stirling number of the second kind, which counts the number of ways to partition a set of n elements into k non-empty subsets.
Using this formula, we can compute the Bell number for n = 6 as follows:
B6 = {6 choose 1} * S1 + {6 choose 2} * S2 + {6 choose 3} * S3 + {6 choose 4} * S4 + {6 choose 5} * S5 + {6 choose 6} * S6
S1 = 1, S2 = 15, S3 = 25, S4 = 10, S5 = 1, S6 = 0 (using a table of Stirling numbers)
B6 = (6 choose 1) * 1 + (6 choose 2) * 15 + (6 choose 3) * 25 + (6 choose 4) * 10 + (6 choose 5) * 1 + (6 choose 6) * 0
= 1 + 90 + 200 + 150 + 6 + 1
= 448
Therefore, there are 448 possible partitions of the set A = {a, s, i, m, o, v}.
Someone please help me :(
Explain in detail the process/steps you would use to factor 6x^2-11x+4. Explain how you can prove your answer is correct. Then show your work for checking your answer.
Answer:
(2x-1)(3x-4)
Step-by-step explanation:
6x²-11x+4
Now we will split the middle term so when we add the digits it will give the original number back but when we multiply them, it will give the sum of the first and the last digit
6x²-11x+4
6x²-3x-8x+4
Now you can that if we add -3 and -8, we get -11 back but if we multiple them, we get the sum of 6 and 4 (the first and the last digits), which is 24
Now we will simplify the values
3x(2x-1) - 4(2x-1)
Simplifying further, we get
(2x-1) (3x-4) which is the answer
PLSS ANSWER QUICKY I BEG YALL
The discounted price per yard for ribbons and for fabrics is A. Ribbon costs $ 1. 50 per yard and fabric costs $ 5. 75 per yard.
How to find the discounted price ?You can find the discounted price by using the options and then multiplying the prices given, by the purchases of Gwen and Penelope to find out which price is right.
If the discounted price of ribbons were $ 1.50 per yard and the fabric was $ 5. 75 per yard, then the cost to Gwen would be:
= ( 1. 50 x 6 ) + ( 10 x 5. 75 )
= $ 66. 50
For Penelope :
= ( 1. 50 x 5 ) + ( 8 x 5. 75 )
= $ 53. 50
These are the amounts spent so these are the discounted prices.
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Can someone explain to me why I got this question wrong? The reasoning for my answer (2, 3) for the vertex is because in the setup for the equation f(x) = a( x - h ) + k, x is subtracted from h. If h was negative, it would be adding instead because it'd be a negative and a negative. So I know h is positive. Am I misunderstanding the question? Will give brainliest!
Kevin's error is that he incorrectly identified the vertex of the parabola as (3, 2) instead of (2, 3), which resulted to the parabola opens downward. The correct vertex is at (2, 3) and the parabola opens upward.
Correcting an Error in Identifying the Vertex and Direction of a Parabola.You are correct that the vertex of the parabola can be determined using the equation f(x) = a(x - h)² + k, where the vertex is at (h, k). In this case, we have f(x) = -(x-2)² + 3, so the vertex can be found by setting x - 2 = 0, which gives x = 2. Plugging this value into the equation,
we get f(2) = -(2-2)² + 3 = 3, so the vertex is at (2, 3).
However, your reasoning for why h is positive is not correct. The expression x - h represents the horizontal distance from the vertex to any point on the parabola. So if x is greater than h, then the expression x - h will be positive, and if x is less than h, then the expression x - h will be negative. In this case, the vertex is at (2, 3), so we have h = 2. This means that any point to the right of the vertex will have a positive value of x - h, while any point to the left of the vertex will have a negative value of x - h.
Therefore, the correct explanation of Kevin's error is that he incorrectly identified the vertex as (3, 2) instead of (2, 3), and as a result, he also incorrectly concluded that the parabola opens downward. In fact, the parabola opens upward because the coefficient of the x² term, -1, is negative.
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In Exercises 1 to 8, find the limit of each sequence that converges; if the sequence diverges, explain why 4. z" = Log ( 1 + θ fixed α fixed {i-co-C)-is nC)} fised θ fixed
The given sequence is
[tex]z_n = log(1 + (θ/(α + {i*cos(π/2) - i*sin(π/2)}))^n)[/tex]
First, we need to simplify the expression inside the log. The term [tex]{i*cos(π/2) - i*sin(π/2)}[/tex] can be simplified to 0, since cos(π/2) = 0 and sin(π/2) = 1.
Therefore, the expression inside the log becomes [tex](1 + (\theta/\alpha)^n)[/tex].
Now, we need to find the limit of this sequence as n approaches ∞.
If θ/α is less than 1, then (θ/α)^n will approach 0 as n approaches infinity, and the limit of the sequence will be log(1) = 0.
If θ/α is greater than 1, then (θ/α)^n will approach infinity as n approaches infinity, and the limit of the sequence will be log(infinity) = infinity.
If θ/α is equal to 1, then (θ/α)^n will always be 1, and the limit of the sequence will be log(2).
Therefore, the limit of the sequence depends on the values of θ and α. If θ/α < 1, the limit is 0. If θ/α > 1, the limit is infinity. If θ/α = 1, the limit is log(2).
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a search and rescue pilot is flying over a section of forest. The angle of depression to two clearings is 32 degrees and 56 degrees respectively. According to her co-pilot, the two clearings are 5.7km apart. find the distance from airplane to clearing A, rounded to nearest hundredth of a kilometre
Let's call the position of the plane "P", and the positions of clearing A and clearing B "A" and "B", respectively. We want to find the distance from the plane to clearing A.
First, draw a diagram. The angle of depression to clearing A means that the line from the plane to clearing A makes a 32 degree angle with the horizontal. Similarly, the angle of depression to clearing B means that the line from the plane to clearing B makes a 56 degree angle with the horizontal. We know that the distance between clearings A and B is 5.7 km.
Now, we can use trigonometry to find the distance from the plane to clearing A. Let's call this distance "d". We can set up the following equation:
tan(32) = d/x
where x is the horizontal distance from the plane to clearing A. We can rearrange this equation to solve for d:
d = x tan(32)
Similarly, we can set up an equation for the distance from the plane to clearing B:
tan(56) = (x + 5.7) / d
We can rearrange this equation to solve for d:
d = (x + 5.7) / tan(56)
Now we can set the two expressions for d equal to each other and solve for x:
x tan(32) = (x + 5.7) / tan(56)
x tan(32) tan(56) = x + 5.7
x (0.6561) = x + 5.7
0.6561 x = x + 5.7
-0.3439 x = 5.7
x = -5.7 / 0.3439
x ≈ -16.57
Since the distance from the plane to clearing A is a positive distance, we can ignore the negative solution. Therefore, the distance from the plane to clearing A is approximately:
d = x tan(32) ≈ (-16.57) tan(32) ≈ 9.18 km
Rounding this to the nearest hundredth of a kilometer gives:
d ≈ 9.18 km
Therefore, the distance from the plane to clearing A is approximately 9.18 km.
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Consider the following points.
(−2,−3),(3,3)
and (3,−3)
Step 2 of 2 : What is the area of the triangle? (Hint: Make use of the midpoint formula if the triangle is isosceles.)
The area of the triangle is equal to half the product of the two base lengths (6) multiplied by the height (6), or 18.
What is area?Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.
The area of the triangle can be determined by using the midpoint formula, which states that the area of an isosceles triangle is equal to half the product of the two base lengths multiplied by the height.
In this case, the midpoint of the triangle is (3,0). This means that the triangle's base lengths are equal to 6 (the difference between the x coordinates of the midpoint and the two endpoints, 3-(-3)) and the height is equal to 6 (the difference between the y coordinates of the midpoint and the two endpoints, 3-(-3)).
Therefore, the area of the triangle is equal to half the product of the two base lengths (6) multiplied by the height (6), or 18.
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Write an equation for a rational function with:
Vertical asymptotes at x = -2 and x = -6
x intercepts at x = 5 and x = -5
Horizontal asymptote at y = 3
y=
The equation of rational function is f(x) = 3 - (5/2)(x - 5)(x + 1) / ((x + 2)(x + 6))
What is the equation of rational functionOne possible equation for a rational function with the given properties is:
f(x) = 3 + (k(x + 5)(x - 5)) / ((x + 2)(x + 6))
Here, k is a constant that determines the vertical scale of the function. We choose the factor (x + 5)(x - 5) in the numerator to make the x-intercepts at x = 5 and x = -5. We choose the factors (x + 2) and (x + 6) in the denominator to make the vertical asymptotes at x = -2 and x = -6. We choose the constant term 3 in the equation to make the horizontal asymptote at y = 3.
To determine the value of k, we can use one of the x-intercepts, say x = 5. Substituting x = 5 into the equation and setting the result to 0 (since the function has an x-intercept at x = 5) gives:
0 = 3 + (k(5 + 5)(5 - 5)) / ((5 + 2)(5 + 6))
Simplifying the right-hand side, we get:
0 = 3 + 0 / (7 * 11)
0 = 3
This equation is not true, which means that we have made a mistake somewhere. The mistake is in assuming that the x-intercepts occur at x = 5 and x = -5. Instead, we should have x-intercepts at x = 5 and x = -1, which are the roots of the numerator (x - 5)(x + 1). So we need to adjust the numerator in the equation to (x - 5)(x + 1) in order to get the correct x-intercepts.
The correct equation for the rational function is:
f(x) = 3 + (k(x - 5)(x + 1)) / ((x + 2)(x + 6))
To determine the value of k, we can use the other x-intercept, x = -1. Substituting x = -1 into the equation and setting the result to 0 gives:
0 = 3 + (k(-1 - 5)(-1 + 1)) / ((-1 + 2)(-1 + 6))
Simplifying the right-hand side, we get:
0 = 3 + 6k / 5
Multiplying both sides by 5, we get:
0 = 15 + 6k
Solving for k, we get:
k = -15 / 6 = -5/2
So the final equation for the rational function is:
f(x) = 3 - (5/2)(x - 5)(x + 1) / ((x + 2)(x + 6))
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Please help me solve this
All of the solutions of the given system of linear inequalities above include the following:
A. (0, 3).
C. (6, 2)
E. (0, -1)
What is an ordered pair?In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph of a system of linear inequalities.
In this scenario, we can reasonably infer and logically deduce that the solution to the given system of linear inequalities is the shaded region and it lies in both quadrant I and quadrant IV with the following ordered pairs:
Ordered pair = 0, 3).
Ordered pair = (6, 2)
Ordered pair = (0, -1)
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Which is a correct classification for this triangle?
Answer: Obtuse Triangle
Step-by-step explanation:
63 + 22 = 85
180 - 85 = 95
Since the unknown angle is over 90 degrees, it is an obtuse triangle.
A laptop computer that you want to purchase was originally priced at $750. You will receive a 20% student
discount, and the sales tax rate is 8%. How much money will you pay for the laptop? Round to the nearest cent
if needed.
The amount paid with discount for the laptop is $ 660.
What is discount?Discount is the amount of money removed from the price of an object being sold.
What is amount paid?Amount paid is the total cost of an item.
How to find how much you will pay for the laptop?Since laptop computer that you want to purchase was originally priced at $750. You will receive a 20% student discount, and the sales tax rate is 8%.
First, we need to know how much discount is given.
Since there is a 20 % discount, the amount of discount removed is 20% × $750 = 0.2 × % 750 = $ 150
Also, there is a sales tax rate of 8%. So, the amount of sales tax added is 8% × $750 = 0.08 × $ 750 = $ 60
So, the total amount paid is T = price - discount + tax
= $ 750 - $ 150 + $ 60
= $ 660
So, the amount paid is $ 660.
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