So, given the plane curve r(t) = -ti - ln(cos t)j, we obtain T, N, and kappa:
T(t) = -i + tan(t)j
N(t) = sec^2(t) j
kappa(t) = sec^2(t)
What is vector?A vector is a matrix that has only one row or one column. A row vector is a matrix with only one row. Example Because it only contains one row, the matrix is a row vector. A column vector is a matrix with only one column. If all of the scalars in a matrix are real-valued, it is indicated using uppercase boldface letters, such as A R m n. That is, the matrix exists in a real-valued vector space with m n dimensions. As a result, matrices are just vectors expressed in a two-dimensional table-like format.
Here,
The position vector of the curve is given by:
r(t) = -ti - ln(cos t)j, -π/2 < t < π/2
Differentiating the position vector, we get the tangent vector:
T(t) = dr/dt = -i + tan(t)j
The normal vector is given by:
N(t) = T'(t) = sec^2(t) j
Finally, the curvature is given by:
kappa(t) = ||T'(t)|| = sec^2(t)
So, we have T, N, and kappa for the plane curve r(t) = -ti - ln(cos t)j:
T(t) = -i + tan(t)j
N(t) = sec^2(t) j
kappa(t) = sec^2(t)
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The surface area of a sphere is found using the formula SA=4², where r is the radius. If the surface area of a
sphere is 144π square feet, what is the radius, in feet?
A. 6
B. 12
C. 18
D. 36
Answer:
A
Step-by-step explanation:
Surface area of sphere is 4 pi r^2
144 pi = 4 pi r^2
144 pi / (4 pi) = r^2
36 = r^2
r = 6 ft
pls help it urgent ty
Answer: A. 2/5 or 0.4 and B. 5/2 or 2.5 or 2 1/2
Step-by-step explanation: I'm a personal math calculator
PLEASE PLEASE HELP whats the origin of the number zero (pls give me interesting info its for a math project)
Please Brainliest
The origin of the number zero is believed to be ancient India, where it was invented as a placeholder in the decimal system around the 5th century CE. The concept of zero as a number in its own right was a revolutionary idea that greatly advanced mathematical understanding and allowed for much more efficient mathematical calculation. From India, the use of zero spread to the Islamic world and eventually to the West. The modern representation of zero as a circle or a digit was introduced in the 13th century in India.
How do you solve a spring equation?
Hooke's Law states that when a spring is extended, the force is proportional to how much longer it is than its equilibrium length. The spring constant can be calculated using the formula k = -F/x.
What is a spring equation?Hooke aimed to show how a spring's elasticity and the forces acting on it are related.
According to Hooke's Law, a spring's extension is proportional to the load placed on it.
As long as the load does not exceed the material's elastic limit, a variety of materials will adhere to this rule.
F = k(x - x0), where x represents the spring's displacement from equilibrium and k is the spring constant.
The negative sign indicates that the force represented by the spring is a restorative force and operates in the opposite direction.
According to Hooke's Law, when a spring is stretched, the force applied is proportional to the lengthening from the equilibrium length.
The formula k = -F/x, where k is the spring constant, can be used to get the spring constant. F stands for force, and x is for the variation in spring length.
Therefore, Hooke's Law states that when a spring is extended, the force is proportional to how much longer it is than its equilibrium length. The spring constant can be calculated using the formula k = -F/x.
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Select the correct answer. A parabola declines through (negative 2, 4), (negative 1 point 5, 2), (negative 1, 1), (0, 0) and rises through (1, 1), (1 point 5, 2) and (2, 4) on the x y coordinate plane. The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = (x + 1)2? A parabola declines through (negative 2, 5), (negative 1 point 5, 3), (negative 1, 2), (0, 1) and rises through (1, 2), (1 point 5, 3) and (2, 5) on the x y coordinate plane. W. A parabola declines through (negative 2, 3), (negative 1 point 5, 1), (1, 0), (0, negative 1) and rises through (1, 1), (1 point 5, 1) and (2, 2) on the x y coordinate plane. X. A parabola declines through (negative 3, 4), (negative 2 point 5, 2), (negative 2, 1), (negative 1, 0), (0, 1), (0 point 5, 2) and (1, 4) on the x y coordinate plane. Y. A parabola declines through (negative 1, 4), (negative 0 point 5, 2), (0, 1) and (1, 0) and rises through (2, 1), (2 point 5, 2) and (3, 4) on the x y coordinate plane. Z. A. W B. X C. Y D. Z Reset Next
The parabola function has a minimum value of -4.
How to determine the maximum or the minimum?The given parameters are:
Declines through (-5,-2), (-3,-4)
Rises through (-2, -3), (-1, -2), (0, 0), (0, 2) and (1, 4)
Because the parabola declines before it rises, it means that the function has a minimum
From the point of decline;
-4 is less than -2
Hence, the parabola function has a minimum value of -4.
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Six friends went to a movie and spent $9 per ticket. They also purchased a small bag of popcorn each. If the friends spend a total of $82.50, how much does each small bag of popcorn cost?
Hello!
If six friends went to a movie and spent $9 per each ticket and also purchased a small bag of popcorn each with them spending a total of $82.50, the cost of each small bag of popcorn costs $4.75.
Step-by-step explanation:
[tex]6[/tex] × [tex]9=54[/tex]
[tex]82.50-54=28.50[/tex]
[tex]28.50[/tex] ÷ [tex]6=4.75[/tex]
Hope this helps!
The target weight of a bag of potatoes is 10 pounds. The weight of each bag can differ from this value by
at most 0.75 pounds. Write and solve an absolute-value inequality to find the range of acceptable
weights. Graph the solutions.
O lt - 10l ≤ 0.75
The range of acceptable weights is t ≥ 9.25 AND t ≤ 10.75.
O lt-10l ≤ 0.75
The range of acceptable weights is t ≥ 9.25.
O It-10l ≤ 0.75
The range of acceptable weights is t ≤ 9.25 OR t≥ 10.75.
O lt -10l < 0.75
The range of acceptable weights is t > 9.25 AND t < 10.75
The inequality is (a) lt - 10l ≤ 0.75
The range of acceptable weights is t ≥ 9.25 AND t ≤ 10.75.
How to determine the rangeThe range of acceptable weights for a bag of potatoes can be found by writing an absolute value inequality as follows:
|w - 10| ≤ 0.75
Where
Difference = At most 0.75 poundsTarget = 10 poundsExpanding the absolute value:
-0.75 ≤ w - 10 ≤ 0.75
Solving for w:
9.25 ≤ w ≤ 10.75
The range of acceptable weights for a bag of potatoes is 9.25 to 10.75 pounds.
The number line is attached
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Triangle DHG is a scale drawing of triangle AFB. Use a ruler. Measure and label the side lengths of triangle AFB and triangle DHG. What scale factor was used to make triangle DHG?
Divide the length of the longest side of triangle AFB by the longest side of triangle DHG to find the scale factor.
Triangle AFB: A=4 cm, B=5 cm, F=7 cm
Triangle DHG: D=2.8 cm, H=3.5 cm, G=4.9 cm
Scale factor = 7/4.9 = 1.43
Step by explanation
Step 1: Draw triangle AFB on a piece of paper.
Step 2: Measure the side lengths of triangle AFB and record them.
Step 3: Draw a second triangle, DHG, on the paper.
Step 4: Measure the side lengths of triangle DHG and record them.
Step 5: Divide the length of the longest side of triangle AFB by the longest side of triangle DHG to find the scale factor.
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let a and w . determine if w is in col(a). is w in nul(a)?
Yes, w is in col(a) since w can be written as a linear equationof the columns in a. No, w is not in nul(a) since w cannot be written as a linear combination of the columns in a with all scalar coefficients being zero.
Yes, w is in col(a) since w can be written as a linear combination of the columns in a. A linear combination of two or more vectors is a vector that can be expressed as a sum of those vectors, with each vector scaled by a scalar (or coefficient). By expressing w as a linear combination of the columns in a, we are saying that w can be expressed as a sum of those columns, with each column scaled by a scalar.
No, w is not in nul(a) since w cannot be written as a linear combination of the columns in a with all scalar coefficients being zero. In other words, w cannot be expressed as a sum of the columns in a such that all coefficients are zero. This is the definition of nul(a): a subspace in which all linear combinations of the columns in a have a coefficient of zero. Since w cannot meet this requirement, then it is not in nul(a).
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explain the difference between the key words 'of' and 'more than' when dealing with percentages. how are their meanings related?
The words ‘of’ and ‘more than’ are often used in conjunction with percentages. The word ‘of’ is usually used to refer to a portion or part of a whole. For example, ‘50% of the population’ means that half of the population is being referred to.
In comparison, ‘more than’ is used to refer to a number that is higher than the one that is being referred to. For instance, ‘more than 50% of the population’ means that more than half of the population is being referred to.
The two words are related in that they both refer to a number or percentage, but their meanings differ. The word ‘of’ is used to refer to a portion of a number or percentage, while ‘more than’ is used to refer to a number or percentage that is higher than the one being referred to.
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Guess the value of the limit (if it exists) by evaluating the function at the given numbers.
lim x→−5
x2 − 5x
x2 − 25
,
x = −4.5, −4.9, −4.95, −4.99, −4.999, −4.9999, −5.5, −5.1, −5.05, −5.01, −5.001, −5.0001
The value of the limit for the given function [tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex] = 1/2.
What is L'hospital rule?A general technique for assessing indeterminate forms like 0/0 or / is the L'Hospital rule. L'Hospital's rule is applied to calculate the limits of indeterminate forms for calculus derivatives. It is possible to use the L Hospital rule many times. This rule is still valid after being applied, and it will take any indefinite form. L'Hospital's Rule cannot be applied if the issue is not of the indeterminate types.
The given function is:
[tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex]
Substituting the value of limit we can see that the function is of the indeterminate form 0/0.
Using the L'Hospital rule we have:
[tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}\\\\\lim_{x \to 5} \frac{2x - 5}{2x}\\[/tex]
Substitute the value of limits:
[tex]=\frac{2(5) - 5}{2(5)}\\ \\=\frac{1}{2}[/tex]
Hence, the value of the limit for the given function [tex]\lim_{x \to 5} \frac{x^2 - 5x}{x^2 - 25}[/tex] = 1/2.
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What is the extreme value theorem example?
The function is continuous on [−2,2], and its derivative is f′(x)=4 x 3−9 x 2. Because x=9/4 is not in the interval [−2,2], the only critical point occurs at x = 0 which is (0,−1).
What is meant by function ?
Having or performing a utilitarian function; being able to fulfil its intended function: useful furniture; architectural design that serves a purpose.I dropped the flashlight, yet it still worked. The computer network is working properly.Both sorts of access can be granted to a user using the functional usage model.You can grant a user only one kind of access, such as permission to utilise but not modify a specific feature, element, or object.All biological activities, including respiration, excretion, and nourishment, can be performed by a cell. It is therefore referred to as the functional unit of life. The lowest unit of life is the cell, and cells make up every living thing.To the complete questions is;
Find the maximum and minimum values of f(x)= x 4−3 x 3−1 on [−2,2].
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5/8-5/12x2 3/4+2/3
Pls answer ASAP
The numeric value of the expression 5/8 - 5/12 x 3/4 + 2/3 is given as follows:
47/48.
How to obtain the numeric value of the expression?The expression for this problem is defined as follows:
5/8 - 5/12 x 3/4 + 2/3
The multiplication operation has a higher precedence over the addition/subtraction operation, hence it must be solved first.
5/12 x 3/4 = 15/48.
Then the expression is given as follows:
5/8 - 15/48 + 2/3.
Using a common denominator, we have that:
5/8 - 15/48 + 2/3 = 30/48 - 15/48 + 32/48.
Adding the numerators, the result of the expression is given as follows:
(30 - 15 + 32)/48 = 47/48.
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Suppose consumer incomes increase. How will this affect the demand, supply, price, and quantity of potatoes (an inferior good) in the market?
An increase in consumer incomes would lead to a decrease in the demand and price of potatoes, and an increase in supply and quantity.
When consumer incomes increase, the demand for inferior goods such as potatoes usually decreases. This is because as people's incomes rise, they tend to switch to buying more superior goods, which are generally more expensive than inferior goods.
At the same time, the supply of potatoes may also increase as farmers respond to the potential for higher prices by growing more potatoes.
With both a decrease in demand and an increase in supply, the market price for potatoes is likely to fall. The quantity of potatoes supplied will likely increase as well, as the lower price attracts both consumers and producers.
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Please use R.
Write a function called by_type() that takes an atomic vector as input and an optional argument ‘sort’ with default value FALSE. The function looks at each element in the atomic vector and sees if it can coerce them into integer or floating-point values. The function outputs a list that has separated the values into a list with integers, doubles, and character values. If the optional argument sort is TRUE, then it will sort the results of each vector.
Atomic vectors typically come in four different types: logical, integer, double, and character. Complex and raw are the two less common varieties.
An atomic vector can have any properties, with the exception of a dimension attribute, and is either logical, integer, numeric, complex, character, or raw (like matrices). For example, a matrix or NULL are not atomic vectors, but a factor is. This is, in essence, the same as is. atomic. Using the built-in int function, one can transform texts in Python into integers. Any Python data type can be sent to the int() function to be transformed into an integer.
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two less than a number times four
Answer:
is equal to the number minus six.
3¼% of $500 is?....?
Answer:
16.25
Step-by-step explanation:
1% = 5
times 1 by 3.15 so,
5x3.15=16.25
You are trying to raise money for college. You have $1000 right now to invest into an account. You have two options for accounts:
Option 1: An account that pays 12% interest compounded quarterly.
Option 2: An account that pays 6% interest compounded continuously.
Which option will give you the most money after 2 years? Use numerical calculations and words to justify your answer.
The option that will give you the most money after 2 years is option (a)
Which option will give you the most money after 2 yearsOption (a)
Here, we have
Principal, P = $1000
Rate, r = 12% = 0.12
Number of times, n = 4
Time, t = 2
The formula of amount is
A = P * (1 + r/n)^(nt)
So, we have
A = 1000 * (1 + (0.12/4))^(4 *2)
A = 1266.77
Option (b)
Here, we have
Principal, P = $1000
Rate, r = 6% = 0.06
Time, t = 2
The formula of amount is
A = P * e^(rt)
So, we have
A = 1000 * e^(0.06 * 2)
A = 1127.50
1266.77 is greater than 1127.50
Hence, the option is option (a)
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The sum of two numbers is 25 the difference between three times the larger one and two times the smaller one is 55
Answer:
(21, 4)
Step-by-step explanation:
x+y=25
3x-2y=55
3x+3y=75
3x-2y=55
5y=20
y=4
x+4=25
x=21
What is (56z+5)+(−13z−4) ? Explain how you found your answer. Include in your explanation any properties that you used to simplify the expression
The simplified form after simplifying we get 43z+1
What is an Algebraic Expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Given here: The expression (56z+5)+(−13z−4)
simplifying the expression we get
(56z+5)+(−13z−4)
56z+5-13z-4
Arranging the like terms and combining we get
56z-13z+5-4
43z+1
Hence, The simplified form after simplifying we get 43z+1
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Molly uses 9.3 pints of blue paint and white paint to paint her bedroom walls.
2
5
of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
The white paint did she use to paint her bedroom walls will be 6.975 pints.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Molly uses 9.3 pints of blue paint and white paint to paint her bedroom walls 25% of this amount is blue paint.
The amount of white paint will be calculated as:-
Amount = [ 9.3 x ( 100 - 25 )%]
Amount = [ ( 9.3 x 0.75 ) ]
Amount = 6.975 pints.
Hence, the amount of white paint used for painting is 6.975 pints.
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Can someone PLEASE help? I will give brainliest if possible
Match the angle in the left column with its supplementary angle in the right column
Click on the image to see the answers
Answer:
Step-by-step explanation:
Supplementary angles add up to 180.
49 + 131 = 180 b
114 + 66 = 180 d
71 + 109 = 180 c
87 + 93 = 180 a
for what value of k is y-x^k a solution to the differential equation x^2y'y''
For k =3, y = [tex]x^k[/tex] is a solution to the differential equation [tex]x^2[/tex]y'y'' - 4yy' = 6[tex]x^5[/tex].
The differential equation is [tex]x^2[/tex]y'y'' - 4yy' = 6[tex]x^5[/tex].
Let y = [tex]x^k[/tex] is a solution to the differential equation [tex]x^2[/tex]y'y'' - 4yy' = 6[tex]x^5[/tex].
So y' = k[tex]x^{k-1}[/tex]
y'' = k(k-1)[tex]x^{k-2}[/tex]
Now putting the value of y, y' and y'' in the differential equation.
[tex]x^2[/tex](k[tex]x^{k-1}[/tex])(k(k-1)[tex]x^{k-2}[/tex]) - 4[tex]x^k[/tex](k[tex]x^{k-1}[/tex]) = 6[tex]x^5[/tex]
Now simplifying the equation.
[tex]k^2(k-1)x^2x^{k-1}x^{k-2} - 4kx^kx^{k-1}[/tex] = 6[tex]x^5[/tex]
As we know that the power gets add in the multiplication so
[tex]k^2(k-1)x^{(2+k-1+k-2)} - 4kx^{(k+k-1)}[/tex] = 6[tex]x^5[/tex]
[tex](k^3-k^2)x^{2k-1} - 4kx^{2k-1}[/tex] = 6[tex]x^5[/tex]
[tex]k^3x^{2k-1}-k^2x^{2k-1} - 4kx^{2k-1}[/tex] = 6[tex]x^5[/tex]
Taking common [tex]kx^{2k-1}[/tex]
[tex]kx^{2k-1}(k^2-k - 4)[/tex] = 6[tex]x^5[/tex]
On comparing
2k-1 = 5
Add 1 on both side, we get
2k = 6
Divide by 2 on both side, we get
k = 3
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The complete question is:
For what value of k is y = [tex]x^k[/tex] a solution to the differential equation [tex]x^2[/tex]y'y'' - 4yy' = 6[tex]x^5[/tex]?
Find the ratio of the areas in the following sets or similar triangles with corresponding sides labeled.
The ratios of the areas in the following sets or similar triangles are:
1. 9:1, 2. 4:1, 3. 25:9,
4. 46:9, 5. 9:4, 6. 4:1,
7. 25:4, 8.9:4, 9. 9:1.
What are triangles?Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
Given a set of triangles is similar,
for similar triangles the ratio of their corresponding sides is equal,
so A/a = B/b = C/c
where A, B, and C are sides of larger triangles and a, b, and c are sides of small triangles.
area of small triangle = 1/2*b*h
here b =base and h = height
area of large triangle = 1/2*B*H
here B =base and H = height
the ratio of areas = area of the large triangle/area of the small triangle
the ratio of areas = [1/2*B*H]/[1/2*b*h]
the ratio of areas = BH/bh
since the triangles are similar, B/b = H/h
the ratio of areas = B²/b²
or the ratio of areas = (SIDE)²/(side)²
1. given side of large triangle = 3
side of small triangle = 1
ratio of areas = 3²/1²
ratio of areas = 9/1 = 9:1
2. given side of large triangle = 4
side of small triangle = 2
ratio of areas = 4²/2²
ratio of areas = 16/4 = 4:1
3. given side of large triangle = 5
side of small triangle = 3
ratio of areas = 5²/3²
ratio of areas = 25/9 = 25:9
similarly for other questions,
4.ratio of areas = 16/9 = 16:9
5. ratio of areas = 9/4 = 9:4
6. ratio of areas = 64/16 = 4:1
7. ratio of areas = 25/4 = 25:4
8. ratio of areas = 36/16 = 9:4
9. ratio of areas = 4/1 = 4:1
Hence the ratios are as possible.
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enter the complete name for dl
Deep Learning (DL) is a type of Artificial Intelligence (AI) that uses a set of algorithms to simulate the functioning of the human brain.
It is a form of machine learning that is based on the concept of neural networks. DL uses a set of algorithms to process large volumes of data and identify patterns in the data. DL can be used to identify patterns and relationships in data that are not easily visible to the human eye.
DL works by using a series of layers of neurons, each of which is connected to the next layer by a set of weights and biases. During the training process, these weights and biases are adjusted so that the output of the neural network is adjusted to match the desired output. This is done by using an optimization algorithm such as gradient descent. At each step, the weights and biases are adjusted until the output of the neural network matches the desired output.
Once the DL model has been trained, it can be used to make predictions from new data. It does this by taking inputs and passing them through the layers of neurons to generate an output. This output is then compared to the desired output and an error is calculated. This error is then used to adjust the weights and biases in order to minimize the error. This process of adjusting the weights and biases is repeated until the error is minimized and the model can make accurate predictions from new data.
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Complete question .
What is Deep Learning (DL)?
In this figure, h = 3, and r = 4.
What is the exact surface area of the cone?
Enter your answer in the box.
units²
The exact surface area of the cone having height 3 unit and radius 4 unit, 113.09734 unit²
What is the area?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
Given that,
A Cone having,
Radius r = 4 unit
Height h = 3 unit
Surface Area = ?
Formula for the Cone,
Surface Area of Cone = πrl + πr²
where, l = [tex]\sqrt{h^{2}+r^{2} }[/tex]
Surface Area of Cone = πr([tex]\sqrt{h^{2}+r^{2} }[/tex]) + πr²
= πr([tex]\sqrt{h^{2}+r^{2} }[/tex] + r)
= 4π([tex]\sqrt{3^{2}+4^{2} }[/tex] + 4)
= 4π(5 + 4)
= 20π
≈ 113.09734
Thus, the surface area of cone is 113.09734 unit²
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If f(x) = x5 + x3 + x, find f−1(3) and f(f−1(2)).
For f(x) = x5 + x3 + x, the value of f1(3) is 1. Because of the inverse function feature, the value of f(f1(2)) is 2.
What is function?A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.
Here,
f(x)=x^5 + x^3 + x
f(1)=3
f^-1(3)=1
f[f −1 (x)]=f −1 [f(x)]=x
f(f^(-1)2)=2
The value of f−1(3) is 1 for f(x) = x^5 + x^3 + x. The value of f(f−1(2)) is 2 by property of inverse function.
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Which equation represents the relationship shown in the graph?
Hello, your answer should be B. I hope this helps. Have a great day! ~Ray
is the conditional statement ¬(p → q)→ ¬q tautology?
After solving the statement we get ¬(p → q)→ ¬q = T. So, the conditional statement ¬(p → q)→ ¬q is a tautology.
The conditional statement is ¬(p → q)→ ¬q.
We construct table:
p q p → q ¬q ¬(p → q) ¬(p → q)→ ¬q
T T T F F T
T F F T T T
F T T F F T
F F T T F T
As we know that the conditional statement is a tautology. So
¬(p → q)→ ¬q
As p → q = ¬p ∨ q and ¬(¬p) = p. So
¬(¬(p → q)) ∨ ¬q
(p → q) ∨ ¬q
As we know that q ∨ ¬q = T and q ∨ T = T. So
¬p ∨ (q ∨ ¬q)
¬p ∨ T
T
Hence, ¬(p → q)→ ¬q is Tautology.
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The sum of 11 and three-fourths of a number is less than 112. What are all the possible values of the number? Write an inequality that could be used to solve this problem. Use the letter x as the variable, and write the inequality so that the x term comes first. Where necessary, write numbers as fractions (rather than decimals).
The required inequality that shows the possible value of x is x < 404/3
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Let's call the number we're trying to find "x". Then, the inequality can be written as:
11 + (3/4)x < 112
To solve for x, we'll isolate x on one side of the inequality. First, we'll subtract 11 from both sides.
(3/4)x < 101
Next, we'll divide both sides by (3/4).
x < (4/3) * 101 = 404/3
So, all values of x that are less than 404/3 satisfy the inequality. The possible values of x are all numbers less than 404/3.
x < 404/3
or written as an interval:
x ∈ (-∞, 404/3)
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