The inverse function of f, what is the value of (ƒ-¹)' (-4) -1/16 ∓ i/(8√3)
We know that the point (1,-4) is on the graph of f, so we can use this information to find the value of x for which f(x) = -4:
-4 = -x³ + 3x² + (6x)
-x³ + 3x² + 6x + 4 = 0
We can solve this equation using various methods, such as graphing, factoring, or using the cubic formula. One possible method is to use synthetic division to test factors of the constant term (4) and find one that gives a remainder of zero. By testing -1 as a factor, we get:
-1 | 1 -3 6 4
-1 4 -10
1 -4 10 -6
Therefore, the equation can be factored as:
-(x + 1)(x² - 4x + 6) = 0
Using the quadratic formula or completing the square, we can find the roots of the quadratic factor:
x = 2 ± √2i
Since the function f is not one-to-one, we must restrict its domain to make it invertible. One possible domain is x ≤ 2, so the inverse function f⁻¹(x) is:
f⁻¹(x) = 1 ± √(1 - 2x)/x
Note that there are two possible values for f⁻¹(-4), one for each branch of the inverse function. To find the value of (f⁻¹)'(-4), we need to take the derivative of the inverse function at x = -4:
(f⁻¹)'(x) = -1/x² ∓ √(1 - 2x)/2x³
(f⁻¹)'(-4) = -1/16 ∓ i/(8√3)
Therefore, the value of (f⁻¹)'(-4) is either -1/16 - i/(8√3) or -1/16 + i/(8√3), depending on which branch of the inverse function we choose.
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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.
The time taken for healthy Canadian adults to complete a logic problem is believed to have a mean 40 seconds. It is of interest to investigate whether UBC students perform better on average than healthy adult Canadians, so the logic problem is given to a sample of 80 UBC students, and their times to solution are recorded. The sample mean and standard deviation are 36 seconds and 17 seconds.
Part a) What is/are the parameters of interest relevant to this hypothesis test? Choose all parameters that you use to set up the null and alternative hypotheses, as well as those referenced in the assumptions and derivation of the relevant test statistic. Hint: A value (number) by itself is not a parameter.
A. 80
B. 40 seconds
C. The mean time for the 80 UBC students to complete the logic problem.
D. The mean time for all UBC students to complete the logic problem.
E. None of the above
Part b) In testing a hypothesis about a parameter of interest, what would your null hypothesis be?
The mean time taken to solve the logic problem by healthy Canadian adults is 40 seconds.
The mean time taken to solve the logic problem by healthy Canadian adults is greater than 40 seconds.
The mean time taken to solve the logic problem by healthy Canadian adults is less than 40 seconds.
The mean time taken to solve the logic problem by healthy Canadian adults is different from 40 seconds.
The mean time taken to solve the logic problem by UBC students is greater than 40 seconds.
The mean time taken to solve the logic problem by UBC students is less than 40 seconds.
The mean time taken to solve the logic problem by UBC students is different from 40 seconds.
The mean time taken to solve the logic problem by UBC students is 40 seconds.
Part c) You would take the alternative hypothesis to be:
one-sided, left-tailed
two-sided.
one-sided, right-tailed.
it does not matter whether we take a one-sided or two-sided alternative.
Part d) Compute the test statistic (Please round your answer to three decimal places):
Part e) Assume all necessary conditions are met (random sampling, independence samples, large enough sample size). Which of the following approximate the sampling distribution of the test statistic in Part d:
Normal distribution
t-distribution
Part f) Suppose that, based on data collected, you reject the null hypothesis. Which of the following could you conclude? Note: Read these carefully. I know they all sound the same, but they are all saying different things.
There is sufficient evidence to suggest the mean time taken to solve the logic problem by UBC students is less than the mean time for healthy adult Canadians.
There is sufficient evidence to suggest the mean time taken to solve the logic problem by UBC students is the same as the mean time for healthy adult Canadians.
There is sufficient evidence to suggest the mean time taken to solve the logic problem by UBC students is greater than the mean time for healthy adult Canadians.
There is insufficient evidence to suggest the mean time taken to solve the logic problem by UBC students is the same as the mean time for healthy adult Canadians.
There is insufficient evidence to suggest the mean time taken to solve the logic problem by UBC students is less than the mean time for healthy adult Canadians.
There is insufficient evidence to suggest the mean time taken to solve the logic problem by UBC students is greater than the mean time for healthy adult Canadians.
Part g) Suppose that, based on data collected, you decide that UBC students perform better on average than healthy adult Canadians. Note: Read these carefully. I know they all sound the same, but they are all saying different things.
it is possible that you are making a Type I error.
it is possible that you are making a Type II error.
it is certainly correct that UBC students perform better on average than healthy adult Canadians.
it is certainly incorrect that UBC students perform better on average than healthy adult Canadians.
there must have been a problem with the way the sample was obtained.
Part h) Suppose that, based on the data collected, you obtain a P
-value of 0.02 (confirm this using the t-table). This means:
the sample of UBC students performed relatively better, if indeed the true mean time taken to solve the logic problem by all UBC students is 40 seconds.
there is a 2% chance that UBC students perform better on average than healthy adult Canadians.
there is a 2% chance that UBC students perform worse on average than healthy adult Canadians.
the probability of UBC students performing as well or better is 0.02, if indeed the true mean time taken to solve the logic problem by all UBC students is 40 seconds.
the probability of UBC students performing as well or worse is 0.02, if indeed the true mean time taken to solve the logic problem by all UBC students is 40 seconds.
the sample of UBC students performed relatively worse, if indeed the true mean time taken to solve the logic problem by all UBC students is 40 seconds.
a) 40 seconds is hypothesized mean b) mean time to solve problem by UBC students = 40 sec is null hypothesis c) Alternative hypothesis is time taken is different from 40 sec d) t = -2.353 h) 2% sample mean
Part a) The following variables are significant to this hypothesis test:
B. The null hypothesis is based on the assumption that it will take healthy Canadian adults an average of 40 seconds to solve the logic puzzle.
D. The test statistic is calculated using the sample mean, which is the average time it took the 80 UBC students to solve the logic puzzle.
D. Based on our sample data, we wish to determine the mean time it takes for all UBC students to complete the logic problem.
Part b) The null hypothesis would be that it took UBC students an average of 40 seconds to solve the logic puzzle.
The alternate hypothesis (part c) is that students at UBC take longer than 40 seconds on average to answer the logic puzzle (two-sided alternative).
Part d) You can compute the test statistic as:
t = [tex]\sqrt{sample size} / (sample standard deviation / hypothesised mean) / (sample mean - hypothesised mean)[/tex]
[tex]t = (36 - 40) / (17 / \sqrt{80} )[/tex]
t = -2.353
Part e) The normal distribution can be used to approximate the sampling distribution of the test statistic because the sample size is high (n = 80).
Part f) If we reject the null hypothesis, we can draw the conclusion that there is enough evidence to support the idea that UBC students took longer on average than healthy adult Canadians to solve the logic puzzle.
Part g) It's feasible that we are committing a Type I error if we determine that UBC students perform on average better than healthy adult Canadians (rejecting the null hypothesis when it is actually true).
Part h) If the null hypothesis is correct, a p-value of 0.02 indicates that there is a 0.02 chance of receiving a sample mean that is as severe as the one we observed (or more extreme). In other words, there is only a 2% probability of observing a sample mean that is as different from 40 seconds (or more different) as the one we obtained, if the true mean time taken to solve the logic problem by all UBC students is 40 seconds. Hence, at a significance level of 0.05 but not at a significance level of 0.01 we would reject the null hypothesis.
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Which number line shows ï > 7? A B 0 1 2 3 4 5 6 7 8 9 10 * 0 1 2 3 4 5 6 7 8 9 10 OF A → B Submit
Answer:
The number line that shows ï > 7 would be from 8 to 10, as the symbol > means greater than. So the correct answer is B. Submit B.
Find all integer solutions of
x+y=3
3xy-z*z=9
In conclusion, the integer solutions of the given system of equations are [tex]$(x, y, z) = (1, 2, 0)$ and $(x, y, z) = (-1, 4, 0)$.[/tex]
What is the integer?An integer is a positive, negative, or zero-valued whole number. It is a number without a fractional or decimal component.
To find all integer solutions of the given system of equations:
[tex]x + y &= 3 \[/tex]
[tex]3xy - z^2 &= 9[/tex]
We can start by solving the first equation for one of the variables. Let's solve for y in terms of x:
[tex]x + y &= 3 \[/tex]
[tex]y &= 3 - x[/tex]
Now we substitute this expression for y into the second equation:
[tex]3xy - z^2 &= 9 \[/tex]
[tex]3x(3-x) - z^2 &= 9 \quad \text{Substituting } y = 3-x \[/tex]
[tex]9x - 3x^2 - z^2 &= 9 \[/tex]
[tex]3x^2 + z^2 &= 9x - 9 \[/tex]
[tex]3x^2 - 9x + z^2 &= -9 \quad \text{(1)}[/tex]
Now we will examine equation (1) for integer solutions.
Case 1: [tex]z= 0[/tex]
If then equation (1) becomes:
[tex]3x^2 - 9x &= -9 \quad \text{(1a)} \[/tex]
[tex]3x(x-3) &= -9[/tex]
Since we are looking for integer solutions, 3x and x-3 must have opposite signs. The possible pairs of factors of -9 with opposite signs are (3,-3) and (-3,3). So we have two possible sets of equations to solve:
The discriminant is negative, there are no integer solutions. Therefore, there are no integer solutions for the original system of equations when [tex]z \neq 0.[/tex]
In conclusion, the integer solutions of the given system of equations are [tex]$(x, y, z) = (1, 2, 0)$ and $(x, y, z) = (-1, 4, 0)$.[/tex]
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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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. Translate parallelogram ABCD 2 units down and plot it. 2. Translate rhombus EFGH 2 units to the left, 4 units down, and plot it. 3. If the coordinates of the vertices of a square LMNO are L(-5,-5), M(-5,-2), N(-2,-2). What are the coordinates for O? 4. If the coordinates of the vertices of a triangle XYZ are X (2,1), Y(4,4) and Z(5,2). Translate the triangle XYZ 4 units down. What are the new coordinates? 5. Write the coordinates down for the following points:
Answer:
To translate a shape, we need to move all its vertices by the same amount in the same direction. Here are the answers to the three parts of the question:
1. To translate parallelogram ABCD 2 units down, we need to subtract 2 from the y-coordinates of all its vertices. Let's say the original coordinates of the vertices are A(a,b), B(c,d), C(e,f), and D(g,h). Then the new coordinates of the vertices will be A'(a,b-2), B'(c,d-2), C'(e,f-2), and D'(g,h-2). Plot these new vertices to get the translated parallelogram.
2. To translate rhombus EFGH 2 units to the left and 4 units down, we need to subtract 2 from the x-coordinates and 4 from the y-coordinates of all its vertices. Let's say the original coordinates of the vertices are E(a,b), F(c,d), G(e,f), and H(g,h). Then the new coordinates of the vertices will be E'(a-2,b-4), F'(c-2,d-4), G'(e-2,f-4), and H'(g-2,h-4). Plot these new vertices to get the translated rhombus.
3. If the coordinates of the vertices of a square LMNO are L(-5,-5), M(-5,5), N(5,5), and O(5,-5), and we want to translate it 3 units to the right and 2 units up, we need to add 3 to the x-coordinates and subtract 2 from the y-coordinates of all its vertices. The new coordinates of the vertices will be L'(-2,-7), M'(-2,3), N'(8,3), and O'(8,-7). Plot these new vertices to get the translated square.
A line segment is shown on the coordinate grid.
Select all of the numbers that are included within the range of the line segment.
Without the specific details or an image of the line segment on the coordinate grid, I'm unable to provide you with the specific numbers included in the range.
To help you generally, a line segment is a part of a line with two endpoints, and it is located on a coordinate grid, which is a two-dimensional plane formed by the intersection of horizontal and vertical lines (x and y axes).
To determine the range of the line segment, you need to identify the y-coordinates of the two endpoints.
The range includes all the y-coordinates between those two points, inclusive of the endpoints. To find the range, observe the line segment and note the y-coordinates of both endpoints. Then, list all the numbers (whole or fractional) between those values, including the endpoints themselves.
Once you have the necessary details or an image of the line segment, feel free to ask again, and I'll be happy to help you identify the numbers within the range.
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Candice makes bracelets that contain 2 oval-shaped beads and 8 circular-shaped beads.
She has 32 oval-shaped beads and 38 circular-shaped beads.
How many bracelets can she make?
Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation.
Slope = 4, passing through (-7,6)
Type the point-slope form of the equation of the line.
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
Type the slope-intercept form of the equation of the line.
(Use integers or simplified fractions for any numbers in the equation.)
Answer:
y = 7x + 10
Step-by-step explanation:
Use your point-slope form: y- y1 = m (x - x1) to substitute the given information.
y - 6 = 7(x - (-4))
Then simplify.
y - 6 = 7(x + 4)
Next, distribute the 7 into the parenthesis which will give you the point-slope form.
y - 6 = 7x + 28
In order to write it in slope-intercept form, add 6 to both sides.
y - 6 + 6 = 7x + 4 + 6
Then simplify to write the equation in slope-intercept form.
y = 7x + 10
Someone help me with this pls!!!
Answer:
8. A) 3.75
9. B) 5.00
Let S be the set R^2. Define addition and multiplication operations on S as follows: for all real numbers a,b,c,d,
(a,b)+(c,d) := (a+c,b+d), (a,b)·(c,d):=(bd−ad−bc,ac−ad−bc).
(a) Prove the right distributive law for S.
(b) What is the multiplicative identity element for S? Explain how you found it. (c)Using (b), prove the multiplicative identity law for S.
(a) The right distributive law is proven for S.For S, this is expressed as (a,b)·(c,d)=(a,b)·(c,d)=(a·c,a·d+b·c).
(a,b)·(c,d)=(bd−ad−bc,ac−ad−bc)=(a·c,a·d+b·c).
(b) we can deduce that x=1 and y=0. Hence, the multiplicative identity element for S is (1,0).
(c) For S, this is expressed as (a,b)·(1,0)=(a,b). Let (a,b) be an arbitrary element in S. The multiplicative identity law is proven for S.
What is distributive law?The right distributive law states that the product of a scalar and a vector is equal to the sum of the products of the scalar with each component of the vector.
(a) For S, this is expressed as (a,b)·(c,d)=(a,b)·(c,d)=(a·c,a·d+b·c).
To prove this, we need to show that (a,b)·(c,d)=(a·c,a·d+b·c).
Let (a,b) and (c,d) be two arbitrary elements in S. Then,
(a,b)·(c,d)=(bd−ad−bc,ac−ad−bc)
=(a·c,a·d+b·c).
Therefore, the right distributive law is proven for S.
(b) The multiplicative identity element for S is (1,0). To find this, we need to find a pair of elements (x,y) such that (a,b)·(x,y)=(a,b).
Let (x,y) be an arbitrary pair of elements in S. Then,
(a,b)·(x,y)=(ax−by,ay+bx)
=(a,b).
From this, we can deduce that x=1 and y=0. Hence, the multiplicative identity element for S is (1,0).
(c) The multiplicative identity law states that the product of a scalar and the multiplicative identity element is equal to the scalar itself. For S, this is expressed as (a,b)·(1,0)=(a,b).
To prove this, we need to show that (a,b)·(1,0)=(a,b).
Let (a,b) be an arbitrary element in S. Then,
(a,b)·(1,0)=(a·1−b·0,a·0+b·1)
=(a,b).
Therefore, the multiplicative identity law is proven for S.
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The product of eight and two, minus the product of three and four
Answer:
4
Step-by-step explanation:
The product of eight and two is 8 x 2 = 16.
The product of three and four is 3 x 4 = 12.
So, the expression "the product of eight and two, minus the product of three and four" can be written as:
16 - 12 = 4
Therefore, the answer is 4.
The Bells obtain a 30 year $110,000 conventional mortgage at 10% on a house selling for $130,000 their monthly mortgage payment including principal and interest is $957 determine the total amount they will pay for their house 
Answer:
what is 5+17894874298748
Answer:
Therefore, the total amount the Bells will pay for their house is $344,520.
Step-by-step explanation:
We can start by using the information about the monthly mortgage payment to calculate the total number of payments they will make over the 30-year term:
30 years × 12 months/year = 360 months
So the Bells will make 360 monthly payments of $957. To find the total amount they will pay for the house, we need to multiply the monthly payment by the number of payments:
$957/month × 360 months = $344,520
Therefore, the total amount the Bells will pay for their house is $344,520.
Give me the brainiest. thanks
Luther Williams’ charge account statement shows an unpaid balance of $3,987.11. The monthly finance charge is 1.75 percent of the unpaid balance. What is the new account balance? Show your work.
By adding the monthly finance charge to the unpaid balance, the new account balance is $4,056.91.
What is addition?
Addition is a mathematical operation that involves combining two or more numbers to produce a sum or total. It is commonly denoted by the plus sign (+) and is one of the four basic arithmetic operations.
To find the new account balance, we need to add the monthly finance charge to the unpaid balance.
First, we need to calculate the monthly finance charge:
Monthly finance charge = 1.75% of unpaid balance
= 0.0175 * $3,987.11
= $69.80
Next, we add the monthly finance charge to the unpaid balance:
New account balance = Unpaid balance + Monthly finance charge
= $3,987.11 + $69.80
= $4,056.91
Therefore, the new account balance is $4,056.91.
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I just want to know the answer of that question
Answer:
I think a
good luck
have a good day
Help with math problems
The value of the equation are 1. (-2√3 + 2)(√3 - 5) = -16 + 8√3 2. (5 - 4√5)(-2 + √5) = -30 + 21√. 3. (-2 - 3√5)(5 - √5) = -5 - 17√5. 4. (√5 - √3)(√5 + √3) = 2.
What are expressions and equations?An expression is a mathematical sentence without the equal sign that can include variables, operators, and integers. Although it can be appraised or simplified, there isn't a single perfect answer. An expression is, for instance, 3x + 2y.
A mathematical statement that has an equal sign and expresses the equivalence of two expressions is called an equation, on the other hand. To determine the values of variables that meet an equality, equations can be solved. One equation is 3x + 2y = 7, for instance.
1. Multiplying (-2√3 + 2)(√3 - 5), we get:
= -2√3 × √3 + (-2√3 × -5) + (2 × √3) + (2 × -5)
= -2√(3 × 3) + 10√3 - 2√3 - 10
= -2(3) + 8√3 - 10
= -16 + 8√3
Therefore, (-2√3 + 2)(√3 - 5) = -16 + 8√3.
2. Multiplying (5 - 4√5)(-2 + √5), we get:
= 5(-2) + 5√5 + (-4√5)(-2) + (-4√5)(√5)
= -10 + 13√5 + 8√5 - 4(5)
= -30 + 21√5
Therefore, (5 - 4√5)(-2 + √5) = -30 + 21√5.
3. Multiplying (-2 - 3√5)(5 - √5), we get:
= (-2 × 5) + (-2 × √5) + (-3√5 × 5) + (-3√5 × -√5)
= -10 - 2√5 - 15√5 + 3(5)
= -5 - 17√5
Therefore, (-2 - 3√5)(5 - √5) = -5 - 17√5.
4. Multiplying (√5 - √3)(√5 + √3), we get:
= (√5 × √5) - (√3 × √3)
= 5 - 3
= 2
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Roger is 5’11”. How much should he weigh in order to have a BMI of 25?
You are fencing in a rectangular area of a garden you have only 150 feet of fence do you want the length of the garden to be at least 40 feet you want the width of the garden to be at least 5 feet what is a graph showing the possible dimensions your garden could have? What vegetables will you use? What will they represent? How many inequalities do you need to write?
Answer:
Length ≥ 40
Width ≥ 5
Perimeter = 2 × (Length + Width)
2 × (Length + Width) ≤ 150
Step-by-step explanation:
To create a graph showing the possible dimensions of the garden, we need to plot the length and width of the rectangular area on the x and y axes, respectively. Since we want the length to be at least 40 feet and the width to be at least 5 feet, we can represent these constraints by the following inequalities:
Length ≥ 40
Width ≥ 5
We also know that the total length of fencing available is 150 feet, which means that the perimeter of the rectangular area must be less than or equal to 150 feet. The perimeter of a rectangle is given by:
Perimeter = 2 × (Length + Width)
So, we can write the inequality representing the perimeter as:
2 × (Length + Width) ≤ 150
To graph the possible dimensions of the garden, we can plot the points that satisfy all three inequalities on the x-y plane.
Regarding the vegetables, it is not clear what vegetables the user would like to plant in the garden. As such, we cannot provide a specific answer to this question.
In summary, we need to write three inequalities to represent the constraints in the problem, and we can graph the solution space using these inequalities.
Lulu observes that when she dilates a quadrilateral from a center of dilation outside the
quadrilateral, the corresponding sides of the original figure and its dilated image are
parallel. Which statement best explains why this occurs?
As a result, the original figure's corresponding sides and those of its enlarged image are parallel.
what is quadrilateral ?A quadrilateral is a closed, two-dimensional form in geometry that has four straight sides. Four sides, four edges, and four angles make up the polygonal shape. The total of a quadrilateral's internal angles is 360 degrees. Kites, squares, rectangles, parallelograms, and trapezoids are examples of quadrilaterals.
given
Each side of the original figure is expanded to meet the dilation scale factor when a quadrilateral is dilated from an outer centre of dilation, and the sides of the dilated image are parallel.
Parallel lines continue to be parallel after scaling because dilatation scales each side of the quadrilateral by a constant factor.
As a result, the original figure's corresponding sides and those of its enlarged image are parallel.
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Victoria is 5 years older than her brother Elliot. Let k represent Elliot's age. Identify the expression that can be used to find Victoria's age.
Answer:
k+5
Step-by-step explanation:
k= Elliot
Victoria is 5 years older than Elliot
=k+5
Solve the systems by elimination.
2x + 4y = -16
-2x + 2y = -2
Answer: (-2,-3)
Step-by-step explanation:
Simplify |x/3| if x>0
Answer: -31x
Step-by-step explanation:
|x|31 becomes -x31 which is -31x
On Monday, Tuesday, and Wednesday, Cheryl ran 1 miles each day. On Thursday, she ran 2 miles. On Friday,
she ran 3 miles.
How many miles, in total, did Cheryl run for those five days?
Write your answer as a decimal.
Cheryl ran a total of 8 miles in five days.
1 + 1 + 1 + 2 + 3 = 8
Written as a decimal, this is 8.0 miles.
For f(x)=3x2 +x2,find: {x: f(x)=0}
By answering the presented question, we may conclude that Therefore, the solution set to the equation f(x) = 0 is {0}.
what is function?In mathematics, a function seems to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.
the equation:
[tex]3x^2 + x^2 = 0\\4x^2 = 0\\x^2 = 0\\x = 0[/tex]
Therefore, the solution set to the equation f(x) = 0 is {0}.
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which functions are symmetric with respect to the origin? y=arcsinx and y=arccosx
Function[tex]y = arcsin(x)[/tex]is symmetric with respect to the origin, while function [tex]y = arccos(x)[/tex] is not. This is as inverse sine function is an odd function, while inverse cosine function is an even function.
If [tex]f(-x) = -f(x)[/tex] for all values of x in the function's domain, then the function is symmetric with regard to the origin. In other words, a function is said to be symmetric with regard to the origin if it passes through the origin and has the same shape on each side of the y-axis.
We must substitute -x for x in each function and simplify to find out if the functions [tex]y = arcsin(x)[/tex] and [tex]y = arccos(x)[/tex] are symmetric with respect to the origin.
According to the equation [tex]y = arcsin(x)[/tex], we get:
[tex]-arcsin = arcsin(-x) (x)[/tex]
Because it is odd, the function[tex]y = arcsin(x)[/tex] is symmetric with respect to the origin.
According to the equation [tex]y = arccos(x)[/tex]:
[tex]x(-arccos) = -arccos (x)[/tex]
Because it is not odd, the function[tex]y = arccos(x)[/tex] is not symmetric with respect to the origin.
In conclusion, [tex]y = arccos(x)[/tex]is not symmetric with regard to the origin, but [tex]y = arcsin(x[/tex] is. Due to the fact that the inverse cosine function is an even function, whereas the inverse sine function is an odd function, this is the case.
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The value of an industrial embroidery machine is decreasing according to the function defined by:
V(t) = 11,700(3)^-0.15
Where t is the number of years since the machine was purchased. What does the y-intercept represent?
A. The value of the machine after 3 years
B. The amount of time it takes for the value of the machine to reach zero
C. The rate at which the value of the machine depreciates
D. The original value of the machine
I think it is A. The value of the machine after 3 years
What do you think?
Jennifer pours 1/3 quart of milk equally into 4 glasses. How much milk, in quarts, does Jennifer pour into each glass?
Answer:
1 ⅓
Step-by-step explanation:
there 4 glasses and you put ⅓ in each one therefore 4 x ⅓ = 1 ⅓
A shopkeeper had 4 handbags which were of the same cost price. He sold 3 of them at 40% more than the cost price. He sold the fourth handbag at cost price. He received $260 altogether. Find the cost price of each handbag.
The line of its elements from the upper left corner to the lower right of the second order determinant is called?
NEED IMMEDIATELY: The circumference of a circular garden is 65.94 feet what is the diameter of the garden is 3.14 for pie and do not round your answer 
pi x 2r = circ
2r = circ/pi
r = circ /(2 x pi) = 65.94/(2 x 3.14) = 10.5 feet