Answer:
The answer is 8:343
Step-by-step explanation:
Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval: f(x) = cot(x), (0,pi)
To show that f(x) = cot(x) is strictly monotonic on the interval (0,pi), we need to show that the derivative of f(x) is either strictly positive or strictly negative on that interval.
Explanation:To show that f(x) = cot(x) is strictly monotonic on the interval (0,pi), we need to show that the derivative of f(x) is either strictly positive or strictly negative on that interval.
The derivative of f(x) can be found using the chain rule as follows:
Find the derivative of cot(x): d(cot(x))/dx = -csc^2(x)Since f(x) = cot(x), the derivative of f(x) is -csc^2(x).Now, let's consider the interval (0,pi). The function f(x) = cot(x) is defined on this interval, and its derivative -csc^2(x) is strictly negative for all x in (0,pi). Therefore, f(x) is strictly decreasing on the interval (0,pi), which means it is strictly monotonic.
Since f(x) is strictly monotonic on the interval (0,pi), it has an inverse function on that interval. The inverse function of f(x) is denoted as f^{-1}(x).
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What is 9/2 as a decimal?
What is 5 3/20 as a decimal?
A rectangular prism has a length of 4.2 cm, a width of 5.8 cm, and a height of 9.6 cm. A similar prism has a length of 14.7 cm, a width of 20.3 cm, and a height of 33.6 cm. The dimensions of the smaller prism are each multiplied by what factor to produce the corresponding dimensions of the larger prism?
Answer:
its (c) 3 1/2
Step-by-step explanation:
HELP PLEASE?! I'm very bad at math and I need help with this question please.
What is the value of y in the equation 6 + y = −3?
A.) −9
B.) −3
C.) 3
D.) 9
A recent poll asked 82 college students 7 questions about their experience at college. When asked their age only 58 responded.
A. Self interest
B. Correlation and casualty
C. Loaded questions
D. Nonresponse
Im stuck between self interest or Nonresponse
Nonresponse. The others might occur, but with this degree of nonresponse inferences to the entire population cannot be made.
A computer virus is eating disk space. during the first day it eats 1/2 of the disk. during the second day, it eats 1/3 the remaining disk space. the third day it eats 1/4 of what still remains and the fourth day it eats 1/5 of what is left. what fraction of the original disk space remains intact?
Which lines are parallel if m4 = m5? Justify your answer.
Answer:
r and s are parellel
Step-by-step explanation:
The correct answer is that lines 4 and 5 are parallel if [tex]\( m_4 = m_5 \).[/tex]
To justify this answer, we must understand the concept of slope in the context of lines in a plane. The slope of a line, denoted by m is a measure of its steepness and is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. Mathematically, if two points on a line have coordinates [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \),[/tex] then the slope m is given by: [tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex] For two lines to be parallel, they must have the same slope. This is because parallel lines have the same steepness and never intersect. Therefore, if the slope of line 4, [tex]\( m_4 \)[/tex], is equal to the slope of line 5, [tex]\( m_5 \)[/tex], then lines 4 and 5 are parallel. In mathematical notation, if [tex]\( m_4 = m_5 \),[/tex] then line 4 and line 5 are parallel, which can be written as: [tex]\[ m_4 = m_5 \Rightarrow \text{Line 4} \parallel \text{Line 5} \][/tex] This conclusion is based on the fundamental properties of slopes and parallel lines in Euclidean geometry. If the slopes of two lines are equal, it means that they rise and run at the same rate, and thus, they will maintain a constant distance from each other, never intersecting, which is the definition of parallel lines.
Which set of ordered pairs represents y as a function of x?
{(5, 4), (2, 3), (1, 1), (2, 4)}
{(-9, 2), (0, 6), (1, -2), (0, 6)}
{(3, 2), (-4, -2), (3, 1), (-4, 1)}
{(-1, 0), (4, 3), (-7, -3), (-1, -8)}
Which power has a value of 1?
Choose all the correct answers.
1^4
2^3
3^2
4^1
5^0
A "bit" is 1/8 of a dollar. How many bits are in a dollar.
There are 8 bits in a dollar.
We have,
If a "bit" is defined as 1/8 of a dollar, we can calculate the number of bits in a dollar by dividing the dollar amount by the value of a bit.
1 dollar / (1/8) bit = 1 dollar * (8/1) bit
Simplifying the equation:
1 dollar * 8 bits = 8 bits
Therefore,
There are 8 bits in a dollar.
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Answer correctly for brainliest and also get a thanks ! Don't answer if you don't know it please !
factor the common factor out of 8x^3+12x
I do not understand how to do this problem please help!
6. Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations.
The first month they made 1200 and the second month they made 1500...
graph a line using the slope-intercept form:
Manipulate the equation into slope-intercept form, y = mx + b.
Identify and plot the y-intercept of the line. Remember, the y-intercept is b. Don't forget: The sign goes with the number.
Identify and use the slope of the line to find a second point. Remember, the slope is m. Don't forget: Starting at the y-intercept, the numerator tells you the rise (count up if positive and down if negative), the denominator tells you the run (count right.)
Draw a straight line through the two points to complete the graph.
Linear Functions:
A linear function is a function that is defined by a linear equation.
To write a linear function with function notation, first write it in slope-intercept form, and then replace y with f(x).
The graph of a linear function is all points (x, f(x)), where x is in the domain of the function.
p² 13p=-30 menentukan nilai p
2. Construct a line that is perpendicular to line m and that passes through point P.
(Apologies since this is extremely late; hopefully this helps future people who need help with this question.)
Answer:
The image below would be the correct construction :)
what are the 12 numbers of pi
Sandra rode her bike 5 times as many miles as Barbara. If b, the distance Barbara rode, equals 3.4 miles, what is the correct expression and distance Sandra rode?
a) b+5; when b=3.4, the distance Sandra rode is 17 miles.
b) 5b; when b=3.4, the distance Sandra rode is 17 miles.
c) 5b; when b=3.4, the distance Sandra rode is 8.4 miles.
d) b+5; when b=3.4, the distance Sandra rode is 8.4 miles.
Answer:
Option b is correct
5b; when b = 3.4 miles , the distance Sandra rode is 17 miles
Step-by-step explanation:
Here, b represents the distance Barbara rode.
As per the statement:
Sandra rode her bike 5 times as many miles as Barbara.
⇒[tex]\text{Distance Sandra rode} = 5b[/tex] miles ....[1]
It is also given that:
the distance Barbara rode, equals 3.4 miles
⇒[tex]b = 3.4[/tex] miles
Substitute in [1] we have;
[tex]\text{Distance Sandra rode} = 5(3.4)=17[/tex] miles
Therefore, the correct expression and distance Sandra rode is
5b ; when b = 3.4 miles , the distance Sandra rode is 17 miles
Given D = 5, E = 10 and F = 4, evaluate
D*E/F
...?
"Sarah is renting a car for her weekend trip to the mountains. The total cost of the rental, y, as it relates to the number of miles driven, x, is shown in the graph below.
Fill in the blanks so that the functions below, written to represent this situation, are correct. If necessary, the answer in terms of a decimal, rounded to the nearest hundredth.
f(x)= ______x+________"
Answer:
[tex]f(x)=\dfrac{1}{4}x+25[/tex]
Step-by-step explanation:
Clearly from the graph we could see that it passes through two points (0,25) and (20,30) and also as the graph is linear so with the help of these two points we can find the relation between f(x) and x.
We know that the equation of a line passing through two points (a,b) and (c,d) is given by:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here we have:
y=f(x) , (a,b)=(0,25) and (c,d)=(20,30).
Hence the equation of this graph is given as:
[tex]f(x)-25=\dfrac{30-25}{20-0}\times (x-0)\\\\f(x)-25=\dfrac{5}{20}\times x\\\\f(x)-25=\dfrac{1}{4}\times x\\\\f(x)=\dfrac{1}{4}x+25[/tex]
Hence,
[tex]f(x)=\dfrac{1}{4}x+25[/tex]
Algebraic terms are separated by ______.
Choose all that apply.
1)=
2)+
3)x
4)÷
5)-
In algebra, terms are separated by addition (+), subtraction (-), multiplication (x), and division (÷) symbols. The equals (=) sign is used to show equality, not to separate terms.
Explanation:In the realm of mathematics, particularly in algebra, algebraic terms are separated by addition (+), subtraction (-), multiplication (x), and division (÷) symbols. These operations are the main components that allow us to manipulate and solve algebraic expressions and equations. For example, in the expression 3x - 2y + 5z, the terms (3x, 2y, 5z) are separated by subtraction (-) and addition (+) symbols. Please note that the equals (=) sign does not separate terms; rather, it is used to show the equality between two mathematical expressions.
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Final answer:
Algebraic terms are separated by plus (+) and minus (-) signs, which denote addition or subtraction between terms in an expression.
Explanation:
Algebraic terms are separated by plus (+) and minus (-) signs.
These signs denote addition or subtraction between terms in an algebraic expression.
While the multiplication sign (x) and division sign (÷) indicate operations between terms, they do not separate independent terms within an expression.
For instance, in the expression 2x + 3y - 5z, the plus and minus signs separate the terms 2x, 3y, and 5z.
Assuming x > 0, which of these expressions is equivalent to 11 times the square root of 245 x to the third plus 9 times the square root of 45 x to the third? ?
5 x times the square root of 104 x
20 times the square root of 290 x to the sixth
20 x times the square root of 290 x
104 x times the square root of 5 x
the lines below are parallel. if the slope of the green line is -3, what is the slope of the red line
What is the probability of getting 3 tails when tossing a coin 4 times?
The probability of getting 3 tails, when tossing a coin 4 times is 25%
To find the probability of getting 3 tails when tossing a coin 4 times, we can use the binomial probability formula:
[tex]\[ P(X = k) = \binom{n}{k} \times p^k \times (1 - p)^{n - k} \][/tex]
Where:
- P(X = k) is the probability of getting exactly k successes (in this case, 3 tails).
- n is the number of trials (coin tosses).
- k is the number of successes we are interested in (in this case, 3 tails).
- p is the probability of success on each trial (in this case, the probability of getting tails).
- [tex]\( (1 - p) \)[/tex] is the probability of failure on each trial (in this case, the probability of getting heads).
Since the coin is fair, the probability of getting tails p is [tex]\( \frac{1}{2} \)[/tex], and the probability of getting heads [tex](\( 1 - p \))[/tex] is also [tex]\( \frac{1}{2} \)[/tex].
Substituting these values into the formula:
[tex]\[ P(X = 3) = \binom{4}{3} \times \left(\frac{1}{2}\right)^3 \times \left(1 - \frac{1}{2}\right)^{4 - 3} \][/tex]
[tex]\[ P(X = 3) = \binom{4}{3} \times \left(\frac{1}{2}\right)^3 \times \left(\frac{1}{2}\right)^1 \][/tex]
[tex]\[ P(X = 3) = 4 \times \left(\frac{1}{8}\right) \times \left(\frac{1}{2}\right) \][/tex]
[tex]\[ P(X = 3) = \frac{4}{16} \][/tex]
[tex]\[ P(X = 3) = \frac{1}{4} \][/tex]
To express the probability as a percentage, we multiply by 100:
[tex]\[ P(X = 3) = \frac{1}{4} \times 100\% = 25\% \][/tex]
Therefore, the probability of getting 3 tails when tossing a coin 4 times is 25%.
Write the area as a product and as a sum.
The area of the square as a product is a multiplication of the two sides.
What is the area of the square?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square.
The square is a quadrilateral having all the sides to be equal and all the angles at 90 degrees. The area of the square will be calculated as,
Area = side x side
Therefore, the area of the square as a product is a multiplication of the two sides.
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What is the factor of 40?
There are $3.90 worth of nickles and quarters in a piggy bank. There are 6 more quarters than nickels.
How many of each coin are in the piggy bank?
Enter your answers in the boxes.
_____ nickels and ____ quarters
For this case, the first thing we must do is define variables.
We have then:
x: number of nickles
y: number of quarters
We now write the system of equations.
We have then:
[tex] 0.05x + 0.25y = 3.90
y = x + 6
[/tex]
Solving the system of equations graphically we have:
[tex] x = 8
y = 14
[/tex]
Answer:
8 nickels and 14 quarters
Note: see attached image for the graphic solution.
Answer: There are 8 nickels and 14 quarters.
Explanation:
Since we have given that
there are $3.90 worth of nickles and quarters in a piggy bank.
Let the number of nickles be x
Let the number of quarters be x+6
As we know that
[tex]1\ nickle=0.05\ dollars\\\\and\\\\\ 1\ quarter=0.25\ dollars[/tex]
According to question,
[tex]0.05x+0.25(x+6)=3.90\\\\0.05x+0.25x+1.5=3.90\\\\0.3x=3.90-1.5\\\\0.3x=2.4\\\\x=\frac{2.4}{0.3}=8\\\\and \\\\x+6=8+6=14[/tex]
Hence, there are 8 nickels and 14 quarters.
What is the absolute value of -5.75 ?
You roll 2 dice. You can use a tree diagram to calculate the probability that the sum of the dice is an even number. true or false? ...?
Round 0.978 to the nearest tenth