The value of derivative dx/dt = 12t³ and dy/dt = 4-2t.
To find the derivatives of x and y as functions of t, we'll calculate dx/dt and dy/dt.
For x=3t⁴, the derivative dx/dt is 12t³. For y=4t-t², the derivative dy/dt is 4-2t.
Now, let's break down the steps in the explanation:
1. Identify the functions x and y: x=3t⁴, y=4t-t².
2. Calculate the derivative of x with respect to t:
dx/dt = d(3t⁴)/dt = 3 * d(t⁴)/dt = 3 * (4t³) = 12t³.
3. Calculate the derivative of y with respect to t:
dy/dt = d(4t-t²)/dt = d(4t)/dt - d(t²)/dt = 4 - 2t.
4. Write the final derivatives: dx/dt = 12t³, dy/dt = 4-2t.
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Write the rule for the linear function
When f(x) = ax + b, where a and b are real values, the function is said to be linear. Here, a denotes the line's gradient and b the y-axis intercept (which is sometimes called the vertical intercept).
What does write a rule for linear function mean?The following expression describes a linear function. Y equals f(x) = a + bx. Both the independent and dependent variables of a linear function are one. X is an independent variable, whereas Y is a dependent variable. The y intercept or constant term is called a.
Any function that depicts a straight line on the coordinate plane is said to be linear. For instance, the equation y = 3x – 2 indicates a straight line on a coordinate plane, indicating that it is a linear function. This function can be expressed as f(x) = 3x - 2 since f(x) can take the place of y in the equation.
If the graph of an equation is a straight line, the equation is linear. This will occur when x has a highest power of 1, which is.
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Eli needs to order some new supplies for the restaurant where he works. The restaurant needs at least 546 knives. There are currently 312 knives. If each set on sale contains 10 knives, write and solve an inequality which can be used to determine xx, the number of sets of knives Eli could buy for the restaurant to have enough knives.
Answer:
The restaurant needs 546 knives and there is 312 knives
The amount remaining is 546-312=234
if each set contains 10 knives
The amount of set remaining is 234/10=23.4 sets
A ceiling fan has 19-inch blades(so the radius of the circular fan is 19 inches). Suppose the dan turns at a rate of 69 revolutions per minute.
a) Find angular speed of the fan in radians per minute
b) Find the linear speed of the tip of a blade in inches per minute
The angular speed of the fan 138π radians/minute or 433.54 radians/minute.
The linear speed of the tip of a blade is 8237.26 inches/minute
How to find angular speed of the fan?a) The angular speed of a fan is the number of revolutions per minute (RPM) multiplied by 2π radians per revolution.
So the angular speed of the fan in radians per minute is:
69 RPM × 2π radians/revolution = 138π radians/minute
b) The linear speed of the tip of a blade is found by multiplying the angular speed in radians per minute by the radius of the fan.
So the linear speed of the tip of a blade in inches per minute is:
138π radians/minute × 19 inches = 8237.26 inches/minute
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Solve 3x + 11 = kfor x.
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve for x ~
[tex]\qquad \sf \dashrightarrow \: 3x + 11 = k[/tex]
[tex]\qquad \sf \dashrightarrow \: 3x + 11 - 11 = k - 11[/tex]
[tex]\qquad \sf \dashrightarrow \: 3x = k - 11[/tex]
[tex]\qquad \sf \dashrightarrow \: x = \dfrac{k - 11}{3} [/tex]
Determine the next three terms
-1 1/2, -1/4, 1/8
The next three terms of the alternating series are - 1 / 16, 1 / 32 and 1 / 64, respectively.
How to predict the next three terms of a series
Herein we find an alternating series of the form:
sₙ = (- 1)ⁿ · rⁿ⁻¹, for n = {1, 2, 3, ..., n}
Where:
n - Index of the n-th element of the series.r - Common ratio.By direct inspection, we find that r = 1 / 2 and the next three terms are: n = {5, 6, 7}
n = 5
s₅ = (- 1)⁵ · (1 / 2)⁵⁻¹
s₅ = - 1 · (1 / 16)
s₅ = - 1 / 16
n = 6
s₆ = (- 1)⁶ · (1 / 2)⁶⁻¹
s₆ = 1 · (1 / 32)
s₆ = 1 / 32
n = 7
s₇ = (- 1)⁷ · (1 / 2)⁷⁻¹
s₇ = 1 · (1 / 64)
s₇ = 1 / 64
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which expression has a product greater than (2 1/6)
The expression has a product greater than (2 1/6) is 2 [tex]\frac{1}{6}[/tex] x 2 [tex]\frac{1}{6}[/tex] .
How to calculate the expression has a product greater than given number?The first step to calculate an expression with a product greater than a given number is to identify the expression. To do this, you need to identify any variables and constants that are present in the expression. Once you have identified these, you can then begin to calculate the expression.The next step is to determine the order of operations of the expression. This determines the order in which the operations should be performed in order to calculate the expression. Generally, the order of operations follows the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.Once the order of operations has been determined, you can begin to calculate the expression. When calculating an expression with a product greater than a given number, it is important to remember to multiply the terms in the expression first before adding or subtracting them. This is because multiplication has a higher order of operations than addition and subtraction.Once all the terms in the expression have been calculated, the final step is to compare the product of the expression with the given number. If the product of the expression is greater than the given number, then the expression is valid and can be used. If the product of the expression is less than the given number, then the expression needs to be modified. This can be done by adding constants or adjusting the coefficients of the variables in the expression.By following these steps, you can calculate any expression with a product greater than a given number. This is a useful skill to have when solving equations and can help you get the correct answer quickly.To learn more about product expression refer to:
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At her ranch, Georgia starts an animal shelter to save cats. After the first three days, she has 34 male cats and 13 female cats. She decides to only accept cats in male-female pairs from then on. In this problem, we find the largest number of pairs of cats she can accept to her shelter and still have at least 60% of her dogs be male.
(a) Let d be the number of pairs of cats she accepts. How many male cats will she have total? Female cats? Total cats?
(b) Write an inequality that means that the percentage of cats at her shelter that are male is at least 60%.
(c)Solve the inequality and determine the largest number of pairs of animal she can accept to her shelter and still have at least 60% of her dogs be male.
Step-by-step explanation:
I know that both sides of the cats, males and females, receive the same # of new cats.
I write an equation, (not an inequality though):
3((34+2x)/5)=2((13+2x)/5)
From here on, I solve for x. I get x = -38. I know we can't have negative pairs and we're only bringing in more cats, and not taking any away. I add 38, and try to see what percentage of cats are male, and I get fairly close, getting to about 62.5% I think. Then, I divide 38 by 2, getting 19, and see what else I can get. I try to find a value between the 38 and lesser 19 so as to find a value which will give me a male cat percentage of 60%. I get about 57.5% with 19 plugged in, which is when I see that hey, the differences are the same. What I then do is find the average of 19 + 38, which is 57.5. I round that to 58, and I get the right answer.
I see that perhaps my solution wasn't really orthodox or anything, but with a little bit of trial and error and a bit of my creative thinking, I guess I managed to solve the problem. What worries me though is this is the first problem in the "questions" section of the inequalities section of AoPS, so I'm definitely struggling to deal with the concepts.
The functions f(x)=−34x+2 and g(x)=(14)x+1 are shown in the graph. What are the solutions to −34x+2=(14)x+1? Select each correct answer. Responses −1 negative 1 0 0 1 1 2 2 3
The solution to both function f(x) and g(x) is (0.02, 1.29)
What is an equation?An equation is an expression relating two or more numbers and variables.
The standard form of an equation is:
Ax + By = C
A, B, and C are constants
The slope intercept of an equation is:
y = mx + b
Where m is the rate of change(slope) and b is the y intercept.
The first function:
f(x) = -34x + 2
while, The second function:
g(x) = 14x + 1
The solution of -34x + 2 = 14x + 1 is the point of intersection of both functions in the graph.
The solution is (0.02, 1.29)
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Describe the transformation that is needed to obtain the graph of g(x)=3x−5 from the graph of g(x)=3x
Answer:
The graph of g(x) = 3x−5 is obtained from the graph of g(x) = 3x by applying the transformation (f(x) = f(x) + b) where b = -5. This transformation is a vertical shift of the graph of g(x) = 3x downward by 5 units.
The graph of g(x) = 3x is a line with a slope of 3 and y-intercept of 0. By subtracting 5 from each y-coordinate, the y-intercept of the graph is shifted downward by 5 units, resulting in a y-intercept of -5. The slope of the graph remains the same as the original function, 3. So the graph of g(x)=3x−5 is the same line as g(x)=3x, but shifted downward 5 units.
Step-by-step explanation:
The following table represents the highest educational attainment of all adult residents in a certain town. If a resident who is 40 or older is chosen at random, what is the probability that they have completed a bachelor's or master's degree? Round your answer to the nearest thousandth.
If a resident who is 40 or older is chosen at random, the probability that they have completed a bachelor's or master's degree is given as follows:
0.436 = 43.6%.
How to obtain a probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The desired and total outcomes for the conditional probability in this problem are given as follows:
Desired outcomes: Bachelor's or master's degree and age 40 or older.Total outcomes: Age 40 or older.Hence the number of total outcomes is given as follows:
3827 + 7106 = 10933.
(40-49 + 50 and over).
The number of desired outcomes is given as follows:
726 + 655 + 2160 + 1226 = 4767.
(either master's or bachelor's degree's for both age intervals).
Hence the probability is calculated as follows:
p = 4767/10933
p = 0.436.
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Using compatible numbers, which is the best estimate of (28.5)(7.1)?
Note that the area of Triangle CDE will be 4 square units.
What is a triangle?
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.
The area of a ΔCDE is derived as follows:
Given that:
C = (4,1)
D = (4, -5) and
E = (2, -3)
A = 1/2 [x1 (y2 - y3_ + x2(y3-y1) + x3 (y1-y2)]
Inputting the given values, we have:
A = 1/2 [ 4(-5+3) + 4(-3+1) + 2(-1+5)]
A = 1/2 [4(-2) + 4 (-2) + 2(4) ]
A = 1/2 [-8-8+8]
A = 1/2(-8)
A = -4
| A | = 4
Thus, the area of ΔCDE is 4 units.
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The function f is continuous on the interval (0,16) and f is twice differential except at x=5 where the derivatives are undefined. Information about the first and second derivatives
Using it's definition, it is found that the function f(x) has a point of inflection at:
A. x = 8 only.
What are the points of inflection of a function?Inflection points are points where the function changes concavity.
The critical points of a function are the values of x for which:
f" (x) =0
Additionally, there has to be a change in the sign of f" (x)
Researching the problem on the internet, it is found that:
For 0 < x < 5, f"(X) > 0
For x = 5, f" (x) is undefined.
For 5 < x < 8, f (x) < 0
For x = 8, f"(x) = 0
For 8 < x < 12,f" (x) > 0
For x = 12, f (x) = 0
For 12 < x < 16, f"(x) > 0
The two conditions, f"(x) = 0 and a change in the signal of f" (x) are only respected at x = 8, which is the lone inflection point.
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Complete option
of f for values of x in the interval (0,16) is given in the table above. At what values of x in the interval (0,16) does the graph of f have a point of inflection?.
A couple pays £1200 for a holiday in Portugal. Unfortunately, due to the pandemic the holiday
company cancels the holiday and gives the customers this option:
Rebook another holiday and get a 20% incentive*
We have a range of alternative holidays available for you to choose from and would love to take
you are
away on holiday. Plus, if the holiday you book is more expensive than your original holiday,
you’ll automatically receive an incentive worth up to 20% of the value of the holiday*.
Given that the customers had already paid the holiday company £1200 for the holiday in Portugal, and are paying an equal share towards this holiday, how much extra will it cost them each?
Answer:
impossible
Step-by-step explanation:
If the customers choose to rebook a holiday that is more expensive than the original holiday in Portugal, and the holiday company is offering an incentive worth up to 20% of the value of the holiday, the customers will have to pay the difference between the original holiday and the new holiday, minus the 20% incentive.
Without more information on the cost of the new holiday, it is impossible to determine how much extra it will cost the customers each
Which expression is equivalent to (m6)−4m−26 for all values of m where the expression is defined?
Responses
1m24
1 over m superscript 24 end superscript
Which expression is equivalent to (m6)−4m−26 for all values of m where the expression is defined?
Responses
1m24
1 over m superscript 24 end superscript
m²
m, ²
m28
m to the power of 28
1m50
m²
m, ²
m28
m to the power of 28
1m50
An expression which is equivalent to (m⁶)⁻⁴/m⁻²⁶ for all values of m where the expression is defined include the following: C. m².
What is an exponent?In Mathematics, an exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.
By applying the law of indices for powers, we have the following:
Expression = (m⁶)⁻⁴/m⁻²⁶
Expression = m⁻²⁴/m⁻²⁶
By applying the law of indices for division, we have the following:
Expression = (m⁶)⁻⁴/m⁻²⁶
Expression = m⁽⁻²⁴ - ⁽⁻²⁶⁾⁾
Expression = m⁽⁻²⁴ ⁺ ²⁶⁾
Expression = m²
In conclusion, we can reasonably infer and logically deduce that the given mathematical expression (m⁶)⁻⁴/m⁻²⁶ for all values of m, is defined at m².
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What number does π represent?
We can conclude that (π) represents a irrational & transcendental number.
What are irrational numbers?An irrational number is a number that cannot be expressed as a fraction p/q for any integers {p} and {q}.
Given is a mathematical constant as {π}.
The number π is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as 22/7 are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an equation involving only sums, products, powers, and integers.The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of π appear to be randomly distributed, but no proof of this conjecture has been found.Therefore, we can conclude that (π) represents a irrational & transcendental number.
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what is the value of the expression below?
64^2/6
Answer:
682 2/3
you could do this on a calculator or you could do this by hand, but i kinda used a calculator
PLSSS HELPPP
What is the domain of the function?
The domain and range of the the function are given below -
Domain → [-5, 10)
Range → [-3, 3)
What is a function?A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes.Given is a graph of the function.
The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes. So, we can write the domain as -
Domain → [-5, 10)
Range → [-3, 3)
Therefore, the domain and range of the the function are given below -
Domain → [-5, 10)
Range → [-3, 3)
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How do you dilate a right triangle?
Dilation is a transformation that can be used to resize an item. Dilation can cause the items to grow or shrink.
What does dilation mean?Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.
You have most likely started labour when your cervix is 3 cm dilated. Your cervix slowly widens to around 6 cm during this phase. It can take anywhere from a few hours to a few days to complete this stage of labour, however it typically takes between 8 and 12 hours. An average woman can dilate between 0.5 and 0.7 cm per hour during the active stage of labour. Whether this is your first child or not will also influence how quickly your cervix dilates. Experienced mothers typically progress through labour more quickly.
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Easy EZ Mark brainliest help meeeee. im
Im at school a desk so hurry
Which ordered pairs lie on the graph of the exponential function f(x)= 5(4)x
Multiple choice*
(2,100)
(1,10)
(3,320)
(0,5)
Answer: The correct answer is (0,5), (1,10), and (3,320). These ordered pairs lie on the graph of the exponential function f(x)= 5(4)x.
At a sale this week, a sofa is being sold for $220.40. This is a 38% discount from the original price. What is the original price? (Don't forget the dollar sign!!)
Answer:
$83.75
$220.40 x 38% =$83.75
Whitch ones are they show pic with the correct ones checkmarked
If each of the aforementioned limits (or both) is a real integer, then y = 1/e, where k is the limit's value.
what is function ?The study of mathematics comprises the study of quantities and their fluctuations, formulae and associated structures, objects and their positions, and locations where they may found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outcomes where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on procedures, each functions, many-to-one functions, within functions, and on functions.
given
f(x) = e^( x-2)
f(x) = 1/e
Step 1: Locate lim x f (x). apply the function's limit as x, etc.
Step 2: Determine lim x - f(x).
Step 3: Write the horizontally asymptote as y = k, where k is the value of the limit, if each (or both) of the aforementioned limits are real integers.
If each of the aforementioned limits (or both) is a real integer, then y = 1/e, where k is the limit's value.
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subtract 3x(x-2) from 6(x^2-xy) and express your answer as a monomial
Answer:
6(x^2-xy) - 3x(x-2) = 6x^2 - 6xy - 3x^2 + 6x
Combining like terms: 3x^2 - 6xy + 6x
To express the result as a monomial it would be 3x^2
So, the final answer is 3x^2
Which point on the graph shows the price of 2 ounces of medicine? Use the formula y=2x to find y when x is 2.
The point on the graph that shows the price of 2 ounces of medicine, given the formula, is 4 currency units.
How to find the price ?The graph shows the relationship between the ounces of medicine and the price of those ounces in the formula y = 2 x. The value of x in this instance, is the number of ounces of medicine to be sold.
The value of y would be the price of those two ounces to be sold. The formula, y = 2 x means that the price of a single ounce of medicine, is 2 currency units.
For 2 ounces therefore, the price is:
y = 2 x
y = 2 x 2
y = $ 4
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Write 40.5 as a fraction
Answer:
40.5=40 1/2
Step-by-step explanation:
Answer: 40.5 as a fraction is 81/2. ✅
Step-by-step explanation:
Sure, here's a step-by-step explanation of how I got the fraction 81/2 for the decimal number 40.5:
Identify the number of decimal places in the decimal representation of 40.5, in this case, it's 1.
Write the decimal number as a fraction by placing the decimal number over a power of 10 that has the same number of zeroes as there are decimal places in the decimal representation. In this case, it's 40.5 / 10^1 (or 40.5/10).
Simplify the fraction if possible by dividing both the numerator and denominator by a common factor if one exists. In this case, the fraction is already in its simplest form.
The fraction representation of 40.5 is 405/10
Simplify the fraction again if possible by dividing both the numerator and denominator by a common factor if one exists. In this case, the fraction can be simplified further by dividing both the numerator and denominator by 5.
So, the fraction representation of 40.5 is 81/2
Hence, the fraction representation of 40.5 is 81/2.
Someone help!! HOW DOES IT DIFFER FROM THE DISTANCE AB
Therefore , the solution of the given problem of distance comes out to be D = 11.66.
Specify the distance.An object's travels are quantified by distance. Simply explained, distance, or t, is the amount of space an object covers within a specific period of time. Displacement is still the shortest distance a moving object can travel. We frequently take into account the concepts of distance et displacement.
Here,
provided parameters
Dimensions of A = (-4,5)
B's coordinate number is (2,-5)
Unknown:
Size of AB =?
Solution:
Use the formula below to calculate the distance between these two places;
D = √(y2-y1)²+(x2-x1)²
x₁ = -4
x₂ = 2
y₁ = 5
y₂ = -5
enter the parameters, then solve;
=> D = √(2-(-4)) ²+(-5-5) ²
=>D = √6² + (-10)² = 11.66
Therefore , the solution of the given problem of distance comes out to be D = 11.66.
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The owner of Nuts2U Snack Shack mixes cashews worth $6.25 a pound with peanuts worth $2.10 a pound to get a half-pound mixed nut bag worth $1.90. How much of each kind of nut is included in the mixed bag?
Answer:
I have solved it and attached in the explanation.
Step-by-step explanation:
The amount of Cashew nuts is 0.205
The amoun of Peanuts is 0.295
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Amount of Cashew nuts = x
Amoun of Peanuts = y
Now,
We can make two equations.
x + y = 1/2 ____(1)
x = 1/2 - y _____(20
Substituting (2) in (3)
6.25x + 2.10y = 1.90 _____(3)
6.25 (1/2 - y) + 2.10y = 1.90
3.125 - 6.25y + 2.10y = 1.90
3.125 - 4.15y = 1.90
3.125 - 1.90 = 4.15y
y = 1.225/4.15
y = 0.295
And,
x = 1/2 - y
x = 1/2 - 0.295
x = 0.205
Thus,
Amount of Cashew nuts = 0.205
Amoun of Peanuts = 0.295
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A chool i arranging a field trip to the zoo. The chool pend 674. 73 dollar on pae for 47 tudent and 2 teacher. The chool alo pend 414. 07 dollar on lunch for jut the tudent. How much money wa pent on a pa and lunch for each tudent?
22.22 was spent on a pass and lunch for each student.
Now, According to the question:
Total money spend on passes = 674.73
Total no. of people = 47 + 2
= 49
Money spend on pass for each person = 674.73/49
= 13.77
Total money spend on lunch = 414.07
Total no. of students = 49
Money spend on lunch for each student = 414.07/49
= 8.45
Total = 13.77 + 8.45
= 22.22
Hence, 22.22 was spent on a pass and lunch for each student.
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A checking account is set up with an initial balance of $6,200, and $350 is removed from the account each month for rent (no other transactions occur on the account). Write an equation whose solution is the number of months, m
, it takes for the account balance to reach $2,700.
An equation, containing variable m that represents the situation described is:
An equation, containing variable m that represents the situation described is 2,700 = 6,200 - 350m.
What is an equation?An equation is a mathematical statement showing the equality or equivalence of two or more mathematical or algebraic expressions.
Equations go with the equal symbol (=) unlike mathematical expressions, which combine variables, numbers, constants, and values with the mathematical operands.
The initial balance in the checking account = $6,200
Monthly withdrawal = $350
The final account balance = $2,700
Let the number of months of withdrawal = m
Equation:2,700 = 6,200 - 350m
Check:
2,700 = 6,200 - 350m
350m = 3,500
m = 10 months
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What is not a function inverse?
A non-function inverse would be a mathematical operation that does not produce a new function.
A function inverse is a new function that can be used to "undo" the effects of an original function. An example of a function inverse would be the inverse sine function of sin(x).
A non-function inverse would be a mathematical operation that does not produce a new function. Examples of non-function inverses include division, subtraction, and multiplication. These operations can be used to undo the effects of an original function, but they do not create a new function. Division can be used to “undo” multiplication, for example. However, the end result is not a new function, but rather a number or set of numbers. Subtraction and multiplication can be used to “undo” addition and division, respectively, but again, the end result is a number or set of numbers, not a new function. Therefore, these operations are not function inverses.
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Choose the correct verb form that completes this sentence: Nosotros _____ la ventana. Select one: a. compartimos b. abro c. escribimos d. abrimos
Answer: abrimos
Step-by-step explanation: That's what it is on my quiz.
In the sentence "Nosotros _____ la ventana", the correct verb form is "abrimos". The best answer is option D.
The verb "abrir" is a Spanish verb that means "to open", and the first person plural form of this verb is "abrimos". So the sentence "Nosotros abrimos la ventana" translates to "We open the window".
The other verb forms in the options ("compartimos", "abro", and "escribimos") do not fit the context of opening the window. "Compartimos" means "we share", "abro" means "I open" (first person singular), and "escribimos" means "we write". So these forms are not the correct form to complete the sentence.
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