The equation of the line passing through A and B is y = (4/5)x - (2/5).
What is the line example's equation?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. The y-axis intercept is denoted by the number c. A straight line with gradient m and intercept c on the y-axis has the equation y = mx + c.
The point-slope form of a linear equation can be used to find the equation of the line passing through points A and B:
y - y1 = m(x - x1) (x - x1)
where m denotes the slope of the line, (x1, y1) denotes the coordinates of point A or B, and (x, y) denotes the coordinates of any other point on the line.
To calculate the slope, we can use points A (3, 2) and B (8, 6).
m = (y2 - y1) / (x2 - x1) = (6 - 2) / (8 - 3)\s= 4 / 5
So the equation for the line connecting A and B is:
y - 2 = (4/5)(x - 3) (x - 3)
This equation can be simplified by multiplying both sides by 5:
5y - 10 = 4x - 12
Then we can rearrange it to form the slope-intercept equation, y = mx + b:
5y = 4x - 2
y = (4/5)x - (2/5)
As a result, the equation for the line connecting A and B is y = (4/5)x - (2/5).
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Work out the size of angle x. 79°) 35
Answer: 66
Step-by-step explanation:
all 3 of them should equal to 180
so 79+35 is 114
180-114 will give us the answer which is 66
What is the maximum number of students to whom 48 apples, 60 bananas and and 96 guavas can be distributed equally? Also find the shares of each fruit.
Answer:
The maximum number of students to whom 48 apples, 60 bananas, and 96 guavas can be distributed equally is 20. Each student will receive 2 apples, 3 bananas, and 4 guavas.
How do you write 0.38 as a percentage?
Write your answer using a percent sign (%).
Answer:
38%
Step-by-step explanation:
I learned in class on Friday.
Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator.
[tex]0.38\times \dfrac{100}{100}[/tex]
[tex]= (0.38 \times 100) \times \dfrac{1}{100} =\dfrac{38}{100}[/tex]
Write in percentage notation: 38%
can someone help me? please
evalute the following function h(x)=3x2+ax-1 for h(3) and find the value for a.
Answer:
Step-by-step explanation:
[tex]h(3)=3\times 3^2+3a-1 \rightarrow h(3)=26+3a[/tex]
But we cannot find [tex]a[/tex] unless we are told what [tex]h(3)[/tex] equals.
The table shows some points on the graph of exponential function g(x)
0 1 2 3 4 g(x) 1 3 9 27 81 What is the range of g?
the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.
How to solve and what is graph?
The range of a function refers to the set of all possible output values. Looking at the table, we can see that the output values of g(x) increase rapidly as x increases.
In fact, the output values of g(x) are the result of raising 3 to the power of x, which means that g(x) can never be negative. Therefore, the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.
A graph is a visual representation of data or mathematical functions. It is a diagram made up of points, lines, and curves that show the relationship between different variables or data points.
Graphs are used to display and analyze data, to illustrate trends and patterns, and to communicate complex information in an easily understandable way. There are many different types of graphs, including bar graphs, line graphs, pie charts, scatter plots, and more, each suited to different types of data and analysis.
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Question 20 (2 points)
Suppose a survey was given to students at WCC and it asked them if they voted for
the Democrat or Republican in the last election. Results of the survey are shown
below:
Democrat Republican
Male. 50. 75
Female. 125. 50
If a student from the survey is selected at random, what is the probability they voted
for the republican?
75/50
50/75
75/300
125/300
Answer:
The table given provides the number of male and female students who voted for each party, but it does not give the total number of students in the survey. To find the probability of selecting a student who voted for the Republican party, we need to know the total number of students who participated in the survey.
The total number of students in the survey is:
50 + 75 + 125 + 50 = 300
The number of students who voted for the Republican party is:
75 + 50 = 125
Therefore, the probability of selecting a student who voted for the Republican party is:
125/300 = 0.4167 (rounded to four decimal places)
So, the answer is option D: 125/300
(please mark my answer as brainliest)
the circumference of a circle is 4.8m. Calculate the area of the circle
Answer:
A≈1.83m²
Step-by-step explanation:
Using the formulas
A=πr2C=2πr
Solving forAA=C24π=4.824·π≈1.83346m²
Answer:
1.83 (approximate)
Step-by-step explanation:
First, we need to find the radius of the circle.
Using the formula:
[tex]C=2 \pi r[/tex]
We have to reorganize terms:
[tex]r=\frac{C}{2\pi}[/tex]
[tex]\frac{4.8}{2 \times \pi}[/tex]
r ≈ 0.76
Now we have the radius and the circumference in order to find the area.
Use the formulas:
[tex]A= \pi r^2[/tex]
[tex]C=2 \pi r[/tex]
A = C^2/4[tex]\pi[/tex] = 4.8^2 / 4 * pi = 1.83
Question 13 (2 points)
Suppose you flip a coin and then roll a die. You record your result. What is the
probability you flip heads or roll a 3?
1/2
3/4
7/12
1
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
we have 2 possible cases for the coin and 6 possible cases for the die.
so, we have 2×6 = 12 combined possible cases :
heads, 1
heads, 2
heads, 3
heads, 4
heads, 5
heads, 6
tails, 1
tails, 2
tails, 3
tails, 4
tails, 5
tails, 6
out of these 12 cases, which ones (how many) are desired ?
all first 6 plus (tails, 3) = 7 cases
so, the correct probability is
7/12
formally that is calculated :
1/2 × 6/6 + 1/2 × 1/6 = 6/12 + 1/12 = 7/12
the probability to get heads combined with the probability to roll anything on the die, plus the probability to get tails combined with the probability to roll 3.
Help pleaseeee!!
On January 1, 2014, the federal minimum wage was $7.25 per hour. Which graph has a slope that best represents this rate?
The horizontal line at $7.25 on the y-axis of the graph is the one with a slope that most accurately depicts the federal minimum wage of $7.25 per hour as of January 1, 2014.
Which federal minimum wage was the highest?Although it varies from state to state, the federally mandated minimum wage in the United States is $7.25 per hour. The District of Columbia had the highest minimum wage in the US as of January 1, 2023, at 16.50 dollars per hour.
How are minimum wages determined?The variable dearness allowance (VDA) component, which takes into account inflationary trends, such as an increase or fall in the Consumer Price Index (CPI), and, if applicable, the housing rent, are included in the computation of the monthly minimum salary.
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The graph of y = 5x2 is
Answer:
................................
f(x)
g(x)
=6x−4
=3x
2
−2x−10
Escribe (g∘f)(x) como una expresión en términos de x.
Answer:
g(x)
=6x−4
=3x
2
−2x−10
Escribe (g∘f)(x) como una expresión en términos de x.
Step-by-step explanation:
Primero necesitamos conocer la función f(x). Luego podemos sustituir f(x) en g(x) para obtener (g∘f)(x).
Como la función f(x) no se proporcionó en la pregunta, asumiré que f(x) es:
f(x) = x^2 - 2x + 1
Entonces, podemos sustituir f(x) en g(x) de la siguiente manera:
g(f(x)) = 6f(x) - 4
= 6(x^2 - 2x + 1) - 4 (sustituyendo f(x))
= 6x^2 - 12x + 2
Por lo tanto, (g∘f)(x) = 6x^2 - 12x + 2.
Use a triple integral to find the volume of the solid bounded below by the cone z = vx2 + y2 and bounded above by the sphere x2 + y2 + z2 = 18. (0.0.V18) x?+y+z=18 cubic units The volume of the solid is (Type an exact answer.)
The volume of the solid is given by the equation V = 36π (√2 - 1) using the triple integral.
A three-dimensional object's volume in three-dimensional space may be determined using the triple integral. The three-variable function is represented by the triple integral. If in space is a closed region, the region's entire volume may be expressed as V = Ddv, which is equivalent to V = D d x d y d z.
Cone: z = [tex]\sqrt{x^2+y^2}[/tex]
sphere: x² + y² + z² = 18
Here, we will use cylindrical coordinates to evaluate volume:
x = rcosθ , y = rsinθ, z = z
so, z = [tex]\sqrt{r^2cos^2\theta+r^2sin^2\theta} =r[/tex]
z = [tex]\sqrt{18-(x^2+y^2)} =\sqrt{18-r^2}[/tex]
r = [tex]\sqrt{18-r^2}[/tex]
r = 3
Finding limits,
[tex]Volume = \int\limits^2_0 \int\limits^3_0\int\limits^a_r {rdzdrd\theta} \, \\\\= \int\limits^2_0 \int\limits^3_0rz \ drd\theta\\\\= \int\limits^2_0 \int\limits^3_0 r(\sqrt{18-r^2}-r ) \ drd\theta\\\\[/tex]
Now, we have
[tex]\int\limits^3_0 {r\sqrt{18-r^2} } \, dr = -(9-18\sqrt{2} ) = 18\sqrt{2} -9[/tex]
Now the integral becomes,
Volume = 2π [(18√2-9) - 9]
= 2π x 18√2 - 18
V = 36π (√2 - 1)
Therefore, the volume of the solid is given by V = 36π (√2 - 1).
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What does the point (5, 10) represent on the
graph?
Answer:
It means the point x = 5 and y = 10
Answer: The place 5 units right and 10 units up from the center of the graph (the origin).
Step-by-step explanation:
Starting at the origin, the 5 represents moving right 5, and the 10 represents going up 5.
How many proper subsets are in {2,4,6,8...100}
Answer:
159 proper subsets.
Step-by-step explanation:
Given a set {2, 4, 6, 8...100}, how many proper subsets are there?
First, find how many subsets there are in 2 - 10:
That's 16.
Then because there are 10 10s in 100, multiply by 10:
16 x 10 = 160
Finally, because it says proper subsets, subtract by 1:
160 - 1 = 159 proper subsets.
Therefore, there are 159 proper subsets in {2, 4, 6, 8...100}
the formula for converting degrees fahrenheit (F) to degrees Kelvin is K= 5/9 (F = 459.67) Solve for F, terms of K
The formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.
What is degrees Fahrenheit and degrees Kelvin?Degrees Kelvin and Degrees Fahrenheit are two temperature measuring measures that are widely used across the globe. While Kelvin is an international standard unit of measurement, Fahrenheit is mostly used in the United States.
The fact that they measure temperature on distinct scales explains the difference between degrees Fahrenheit (F) and degrees Kelvin (K). Whereas Kelvin is based on a scale of 100 degrees between the freezing and boiling temperatures of water at normal atmospheric pressure, Fahrenheit is based on a scale of 180 degrees between these extremes.
Given that, K = 5/9 (F - 459.67).
To obtain F in term of K we isolate the value of F as follows:
K = 5/9 (F - 459.67)
Multiplying both sides by 9/5, we get:
(9/5) K = F - 459.67
Adding 459.67 to both sides, we get:
F = (9/5) K + 459.67
Hence, the formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.
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Which of the following is true regarding cross-sectional data sets? Check all that apply. The data consist of a sample of multiple individuals. It can be assumed that the data were obtained through a random sampling of the underlying population. These data require attention to the frequency at which they are collected (weekly, monthly, yearly, etc.). The data are collected at approximately the same point in time.
The correct options are:
The data contain a sample of multiple individuals.
The data are collected are approximately at the same point in time.
Cross-sectional data sets are a type of research design used in statistical analysis. They consist of a sample of multiple individuals or entities observed at a single point in time. One of the characteristics of cross-sectional data sets is that they do not involve any observation or measurement over time, making them different from longitudinal or time-series data sets.
One advantage of cross-sectional data sets is that they are relatively easy and inexpensive to collect. It can be assumed that the data were obtained through a random sampling of the underlying population, making them representative of the larger population. However, these data require attention to the frequency at which they are collected (weekly, monthly, yearly, etc.), as the timing of data collection can impact the results.
Overall, cross-sectional data sets can provide a snapshot of a population or phenomenon at a specific point in time, making them useful for a wide range of research questions in social, economic, and political sciences.
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TRUE/FALSE. Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" Ris a linear transformation. If Ic.B = Tç, e then B = E = C.
Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" R is a linear transformation. If Ic.B = Tç, e then B = E = C.
The above statement is True.
In mathematics, and more specifically in linear algebra, a linear map (also called a linear map, a linear transformation, a vector space homomorphism, or in some cases a linear function) is a map between two vector spaces V → W, which performs the conservation of operations on vectors. Addition and scalar multiplication. The same names and definitions are also used for the more general case of modules over rings; see the homomorphism of modules.
A linear map is called a linear isomorphism if it is a bijection. In the case V=W, the linear map is called linear automorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily that V = W, where V is the space of functions, which is a common convention in functional analysis.
Sometimes the term linear function has the same meaning as linear map, but not in analysis.
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locate the absolute extrema of the function
on the closed interval
Answer:
To find the integral of f(x) = 2x + 5/3 over the interval [0, 5], we can use the definite integral formula:
∫[a,b] f(x) dx = F(b) - F(a)
where F(x) is the antiderivative of f(x).
First, we find the antiderivative of f(x):
F(x) = x^2 + (5/3)x + C
where C is the constant of integration.
Next, we evaluate F(5) and F(0):
F(5) = 5^2 + (5/3)(5) + C = 25 + (25/3) + C
F(0) = 0^2 + (5/3)(0) + C = 0 + 0 + C
Subtracting F(0) from F(5), we get:
∫[0,5] f(x) dx = F(5) - F(0)
= 25 + (25/3) + C - C
= 25 + (25/3)
= 100/3
Therefore, the definite integral of f(x) = 2x + 5/3 over the interval [0, 5] is 100/3.
(a)A Chinese restaurant offers 10 different lunch specials. Each weekday for one week, Fiona goes to the restaurant and selects a lunch special. How many different ways are there for her to select her lunches for the week? Note that which lunch she orders on which day matters, so the following two selections are considered different.One possible selection:Mon: Kung pao chickenTues: Beef with broccoliWed: Kung pao chickenThurs: Moo shu porkFri: Beef with broccoliA different selection:Mon: Beef with broccoliTues: Kung pao chickenWed: Kung pao chickenThurs: Moo shu porkFri: Beef with broccoli(b)Now suppose that in addition to selecting her main course, she also selects between water or tea for her drink. How many ways are there for her to select her lunches?
(a) There are 100,000 different ways for Fiona to select her lunches for the week.
(b) There are 200,000 different ways for Fiona to select her lunches and drinks for the week.
(a) Since Fiona selects one lunch special each day, there are 10 options for Monday, 10 options for Tuesday, and so on, for a total of 10 options for each of the 5 weekdays. Therefore, the total number of ways for Fiona to select her lunches for the week is:
10 × 10 × 10 × 10 × 10 = 10^5 = 100,000
(b) In addition to the 10 lunch specials, Fiona now has 2 options for her drink, either water or tea. So for each of the 100,000 possible lunch selections from part (a), there are 2 possible drink options. Therefore, the total number of ways for Fiona to select her lunches and drinks for the week is:
100,000 × 2 = 200,000
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$9,300 is invested in an account earning 8.9% interest (APR), compounded daily. Write a function showing the value of the account after � t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
The function for the value of the account after t years can be written as:
V(t) = 93000(1.08900365)t
The coefficient of 1.08900365 is the annual growth rate (APR) compounded daily. After rounding to four decimal places, it becomes 1.0890.
The percentage of growth per year (APY) is 8.90%. This is the same as APR, but expressed as a percentage.
2) The table shows the number of minority officers in the U.S. military in 2000.
Army
Marines
Air Force Total
9162
1341
4282
18309
2105
914
1518
7269
4075
599
3823
11150
15342
2854
9623
36728
Assume that one person will be randomly selected from the group described in the table. Find the
probability of selecting an officer who is in the Navy, given that the officer is African American. (Do
not reduce.)
3524
A)
8909
African Americans
Hispanic Americans
Other Minorities
Total
B)
Navy
3524
2732
2653
8909
8909
18,309
C).
3524
18,309
3542
14785
D).
2)
The probability of selecting an officer who is in the Navy given that the officer is African American is 0.192.
What is the probability?Probability calculates the likelihood that an event would happen. The likelihood that an event would occur has a value that lies between 0 and 1 or 0 and 100. The more likely an event would happen, the closer the probability value would be to 1 or 100.
The probability of selecting an officer who is in the Navy given that the officer is African American = number of African Americans that are in the Navy / total number of African Americans
Total number of African Americans = 9162 + 3524 + 1341 + 4282 = 18,309
The probability = 3524 / 18,309 = 0.192
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what is the answer?
?
No, there is not enough information
Yes, because of the intermediate value theorem
Because g(x) is continuous on the interval, we can see that the correct option is the last one (counting from the top)
Does the value c exists in the given interval?Here we have the function g(x), and we know that it is continuous on the interval [1, 6], and that:
g(1) = 18
g(6) = 11
If it is continuous, then g(x) covers all the values between 18 and 11 in the given interval, this means that there must exist a value c in the given interval such that when we evaluat g(x) in that value c, we get the outcome 12, and we know this by the intermediate value theorem.
So the correct optionis the last one.
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your friend claims the geometric mean of 4 and 9 is 6, and then labels the triangle, as shown. is your friend correct? explain your reasoning.
The correct option is -C: No, 6 is the geometric mean of 4 and 9, however if the altitude is 6, then the hypotenuse is the geometric mean of the two segments.
Explain about the geometric mean?An average technique multiplies several values and determines the number's root is known as the geometric mean. You locate the nth root for their product for a collection of n numbers. This descriptive statistic can be used to sum up your data.
Mean Geometric The square root of the product of two numbers is the geometric mean amongst them. The geometric mean of two positive numbers an as well as b is the positive number x as in percentage Cross multiplication results in x² = ab,.
For the given question.
geometric mean of a and b :
From the drawn diagram.
a = 4
b = 9
x = √ab
x = √9*4
x = 6
geometric mean: 6
Applying the altitude rule:
h² = x.y
6² = 9*4
36 = 36
Thus, the geometric mean calculated by friend is correct but the marking on the diagram is wrong.
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there are 24total customers seated at 4 tables in a restaurant each table is the same size and has the same number of customers tell whether each statement is truth or false
Interpret the slope of this function in the context of the situation. Use complete sentences.
Jennifer is painting an office complex. One wing has a large reception area with several equal-sized offices. Before painting, she must put tape on the baseboards. The amount of tape needed is given by the equation, y=12x+25 where y is total number of meters of tape, and x is the number of offices.
The slope of the function is 12. Because of the slope, Jennifer will require 12 extra meters of tape for each additional office she needs to tape the baseboards in.
What is slope?A line's slope on a graph is its steepness or inclination. It may be derived from any two locations on a line by dividing the vertical change (rise) by the horizontal change (run). Positive, negative, zero, or undefinable slopes are all possible for lines. A line on a graph with a positive slope is growing as you travel from left to right, while one with a negative slope is declining. A line has a slope of zero when it is horizontal and a slope of infinity when it is vertical.
The given function is y = 12x + 25.
The standard equation of the line is given as:
y = mx + b
where, m is the slope.
Comparing the equation with the given equation the slope of the function is 12.
Because of the slope, Jennifer will require 12 extra metres of tape for each additional office she needs to tape the baseboards in. In other words, if more offices need to be painted, the amount of sellotape required also grows linearly.
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What is the end behavior of the polynomial function?
Answer: D. As x → -∞, y → -∞.
Step-by-step explanation:
The graph shows the function approaching negative infinity on the x-axis (left side). When the x-axis is decreasing, the y-axis is also decreasing towards negative infinity.
Below is the graph of a trigonometric function. It has a minimum point at
(1, 1.5) and an amplitude of 1.5. What is the midline equation of the function?
The midline equation of the function is y = 1.5.
What is amplitude of trigonometric functions?The gap between a trigonometric function's highest and least values is known as its amplitude. The difference between the greatest and minimum numbers is, in other words, divided by two. For instance, the amplitude is A in the equation y = A sin(Bx) + C. The amplitude, also known as the average value of the function across a period, denotes the "height" of the function above and below the midline. It gauges the magnitude or intensity of the oscillation of the function's representation of. The oscillation is more prominent and subtler depending on the amplitude, which ranges from higher to lower values.
Given that, the function has minimum point at (1, 1.5) and an amplitude of 1.5.
Using the definition of the amplitude the midline is the given amplitude.
Hence, the midline equation of the function is y = 1.5.
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Answer:
3
Step-by-step explanation:
Khan Academy
Please answer the attached question
The values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.
How are radicals solved?Equations containing radicals can be made simpler by solving the resultant equation after squaring both sides of the equation to remove the radical. Nonetheless, caution must be exercised to guarantee that any solutions found are reliable and adhere to any variables' limitations.
The given equation is [tex](e - 2\sqrt{3} )^2[/tex] = f - 20√3.
Expanding the left side of the equation we have:
[tex](e - 2\sqrt{3} )^2[/tex] = (e - 2√3)(e - 2√3)
= [tex]e^2[/tex] - 2e√3 - 2e√3 + 12
= [tex]e^2[/tex] - 4e√3 + 12
Substituting back in the function
[tex]e^2[/tex] - 4e√3 + 12 = f - 20√3
[tex]e^2[/tex] - 4e√3 - f + 20√3 - 12 = 0
Using the quadratic formula:
e = [4√3 ± √(16*3 + 4(f - 20√3 + 12))] / 2
e = [4√3 ± √(4f - 64√3)] / 2
e = 2√3 ± √(f - 16√3)
Now for,
(e - 2√3)² = f - 20√3
(2√3 + √(f - 16√3) - 2√3)² = f - 20√3
f - 20√3 = f - 16√3
f = 4√3
Hence, the values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.
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find the standard form of the equation of the ellipse having foci (2,0) and (2,6) and a major axis of length 8
The standard form of the equation of the ellipse is (x - 2)^2 / 4 + (y - 3)^2 / 7 = 1
To find the standard form of the equation of the ellipse, we first need to determine some of its properties.
The foci of the ellipse are given as (2, 0) and (2, 6). This tells us that the center of the ellipse is at the point (2, 3), which is the midpoint of the line segment connecting the foci.
The major axis of the ellipse is given as a length of 8. Since the major axis is the longest dimension of the ellipse, we can assume that the length of the major axis is 2a = 8, so a = 4.
Next, we need to determine the length of the minor axis. We know that the distance between the foci is 2c = 6, so c = 3. Since c is the distance from the center of the ellipse to each focus, we can use the Pythagorean theorem to find the length of the minor axis
b^2 = a^2 - c^2
b^2 = 4^2 - 3^2
b^2 = 7
b = sqrt(7)
Now we have all the information we need to write the standard form of the equation of the ellipse. The standard form is
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
where (h, k) is the center of the ellipse. Plugging in the values we found, we get
(x - 2)^2 / 4 + (y - 3)^2 / 7 = 1
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What is the period of f(x)=secx?
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period of f(x)=secx:
Therefore , the solution of the given problem of function comes out to be f(x) = sec(x) has a period of 2. 2 is the answer.
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Here,
=> F(x) = sec(x) has a 2 phase.
Because the secant function is periodic, its values recur after a predetermined amount of time.
This interval's length is equal to the secant function's duration.
The formula for the secant function is
=> sec(x) = 1/cos.(x).
The cosine function repeats its values every 2 units of x, which is known as its period.
Consequently, the secant function has a period of 2 as well.
Therefore, f(x) = sec(x) has a period of 2. 2 is the answer.
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