Take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.
What is a domain?The collection of all potential inputs for a function is its domain.
For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
The set of numbers x for which a function is defined in a valid manner is known as the domain of the function.
A function's domain is referred to as a closed interval if it is specified across the interval a ≤ x ≤ b.
So, to find the domain of a, consider the function y = f(x), which has the independent variable x and the dependent variable y.
A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
Therefore, take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.
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Find The Curvature At The Point (2, 8, -1). X = 2t, Y = 8t^3/2, Z = -T² K=
The curvature at the point (2,8,-1) X = 2t, Y = 8[tex]t^{3/2}[/tex], Z = -t² is √2/152 when the formula is k = | r'(t)×r''(t) |/||r''(t)||³.
Given that,
We have to find the curvature at the point (2,8,-1) X = 2t, Y = 8[tex]t^{3/2}[/tex], Z = -t².
We know that,
The curve is x = 2t, y = 8[tex]t^{3/2}[/tex], z = -t².
Putting 2t=2
t=1
So,
t=1 at the point (2,8,-1)
Also r(t) = <2t, 8[tex]t^{3/2}[/tex], -t²>
r'(t) = <2, 8(3/2)√t, -2t>
r''(t) = <0,6/√t,-2>
||r''(t)|| = √(2²+(12√t)²+(-2t)
||r''(t)|| = √(4+144t+4t²)
Cross product = r'(t) × r''(t) = [tex]\left[\begin{array}{ccc}i&j&k\\2&12\sqrt{t} &-2t\\0&6/\sqrt{t} &-2\end{array}\right][/tex]
=i(-24√t+12√t)-j(-4-0)+k(12/√t-0)
=-12√ti+4j+12/√tk
| r'(t)×r''(t) |= √(-12√t)²+4²+(12/√t)² = √(144t+16+144/t)
The curvature at the point t=1 is k = | r'(t)×r''(t) |/||r''(t)||³
k = √(144t+16+144/t) /√(4+144t+4t²)³
k = √(144(1)+16+144/(1)) /√(4+144(1)+4(1)²)³
k = √304/ (152)³
k = √2/152
Therefore, the curvature at the point (2,8,-1) X = 2t, Y = 8[tex]t^{3/2}[/tex], Z = -t² is √2/152 when the formula is k = | r'(t)×r''(t) |/||r''(t)||³.
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3x − 2y = 8
slope
y -intercept
x -intercept
How did you determine each characteristic?
Answer:
Slope: 3/2
Y-intercept: (0,-4)
X-intercept: (8/3 , 0)
Step-by-step explanation:
To find the y-intercept, I just put in 0 for x.
3(0) - 2y = 8
-2y = 8
y = -4
So, the y-intercept is at (0,-4)
To find the x-intercept, I just put in 0 for y.
3x - 2(0) = 8
3x = 8
x = 8/3
So, the x-intercept is at (8/3, 0)
The slope is 3/2
If you get four sticks of butter to a pound, and each stick of butter is 1/2 a cup, how many cups of butter is a pound of butter? Explain your answer.
Answer: 2
Step-by-step explanation:
If you have four sticks of butter that equal a pound, and each stick is 1/2 a cup, then a pound of butter is equal to 2 cups. This is because 1/2 x 4 = 2. Each stick of butter is 1/2 a cup, and since there are four sticks in a pound, the total amount of butter in cups is 2 cups.
Questions are on picture
I don't see the picture. Can you send it in the message.
What are the roots of x2 5x − 6?
The roots of polynomial x2 5x − 6 are x = 3 and x = -2.
Factor the polynomial
x2 5x − 6 = (x - 3)(x + 2)
(x - 3) = 0
x - 3 = 0
x = 3
(x + 2) = 0
x + 2 = 0
x = -2
To find the roots of the equation x2 5x - 6, we must first factor the polynomial into two terms. The equation can be factored as (x - 3)(x + 2). We then have to set each factor equal to zero. For the first factor, (x - 3) = 0. With this equation solved, we obtain x = 3. (x + 2) Equals 0 for the second factor. The answer to this problem is x = -2. As a result, x = 3 and x = -2 are the roots of x2 5x - 6.
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How do you solve direct and inverse proportion questions?
Direct Ratios and/or Variations
If the ratio of two values, x and y, is constant, then they are directly proportional to one another (which always remains same). This would imply that x and y would either change in tandem or separately by a fixed amount that doesn't affect the ratio.Indirect proportions, inverse proportions, or variations
When the product of two values, x and y, is a constant, they are inversely proportional to one another (always remains the same).Accordingly, as x rises, y falls, as well as opposite, by a certain quantity such that x and y remain constant.Forming an equation to predict the value of an unidentified variable is also made possible by understanding that the product doesn't quite change.Thus, Inverse proportion is defined as y = k/x, k is the proportionality constant .
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Sunil want to earn a 90% in her Chemitry cla. On the firt 5 tet, he received a 74%, 92%, 83%, 98%, 100%. What mut he core on the 6th tet to get the 90% he want?
Sunil need to score 93% on the 6th test to be able to get 90% as the average in her Chemistry class.
What is the average?In Mathematics, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. In statistics, the mean is the average of the given sample or data set. It is equal to the total of observations divided by the number of observations. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
In this case, let x be the missing value.
Now, we have:
Average = 90%
Total all values = 74% + 92% + 83% + 98% + 100% + x = 447% + x
Number of values = 6
Average = Total all values / Number of values
90% = (447% + x) / 6
447% + x = 540%
x = 540% – 447%
x = 93%
Hence, the missing value is 93%, which means Sunil need to score 93% on the 6th test to be able to get 90% as the average in her Chemistry class.
Although part of your question is missing, you might be referring to this full question: Sunil wants to earn a 90% in her Chemistry class. On the first 5 test, she received a 74%, 92%, 83%, 98%, 100%. What must she score on the 6th test to get the 90% she wants?
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Use graphing to find the x-coordinate of the solution to each system.
y = 2/9 x +3
y =- 10/9 x -9
A) -9
B) 9
C) 3
D) -4
Answer:
A) -9
Step-by-step explanation:
You want a graphical solution to the system of equations ...
y = 2/9x +3y = -10/9x -9GraphThe graph is attached. It shows the solution is (-9, 1).
The x-coordinate of the solution is -9.
[tex]−20x+40=−20x+20[/tex]
The solution to the equation for x is that the equation −20x + 40 = −20x + 20 has no solution
How to determine the solution to the equation?From the question, we have the following parameters that can be used in our computation:
[tex]−20x+40=−20x+20[/tex]
Rewrite the above equation properly
So, we have the following representation
−20x + 40 = −20x + 20
Collect the like terms in the above equation
This gives
20x - 20x = 20 - 40
Evaluate the like terms in the above equation
So, we have the following representation
0 = -20
The above equation is false
Hence, the equation has no solution
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What makes a set of numbers closed?
The natural numbers are “closed” under addition and multiplication.
A set is closed (under an operation) if and only if the operation on any two elements of the set produces another element of the same set. The set of whole numbers is “closed” under addition and multiplication.
A set of number with a defined operation (e.g. addition, multiplication etc.), such that the outcome of the operation between any two numbers is also a member ot the set.
A Closed Set Math has a way of explaining a lot of things, and one of those explanations is called a closed set.This closed set includes the limit or boundary of 3.
When a set has closure, it means that when you perform an operation on the set, then you'll always get an answer from within the set. This doesn't mean that the set is closed though. Open sets can have closure. Mathematical examples of closed sets include closed intervals, closed paths, and closed balls.
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What is the radius of X² y² 16?
The radius of X² y² 16 is 4.
X² y² 16 is a circle equation. To solve for the radius, we need to divide both sides by 4, then take the square root of both sides. So, 16/4 = 4 and √16 = 4. Therefore, the radius of X² y² 16 is 4. As a reminder, the equation for the radius of a circle is r = √(x² + y²). Therefore, when solving for the radius of a circle, the first step should be to divide both sides of the equation by 4 and then take the square root of both sides.
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What are the types of linear inequality?
Slack and strict are the two types of linear inequalities we deal with our daily examples in mathematics.
What are the operators for linear inequalities?Addition, subtraction, multiplication, and division are the four types of operations that can be performed on linear inequalities. Equivalent inequality refers to linear inequalities with the same solution. Both equality and inequality are subject to laws.
What are the operations that can be used on linear inequality?An inequality is comparable if both sides are multiplied by a positive value. An inequality's direction can be changed by multiplying both sides by a negative amount.
There are two types of linear inequalities
Slack: inequalities containing sign ≤ or ≥ between LHS and RHS.
Strict: inequalities containing < or > between LHS and RHS.
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You have blank when you divid both sides of equation 3n=12by 3
Answer:
n = 4
Step-by-step explanation:
You have ____ when you divide both sides of equation 3n = 12 by 3:
3n = 12
3n/3 = 12/3
n = 4
Consider the degree of each polynomial in the problem. The first factor has a degree of . The second factor has a degree of . The third factor has a degree of . The product has a degree of
The first factor of the expression has a degree of 2.
The second factor has a degree of 3.
The third factor has a degree of 2.
The product has a degree of 7.
[tex](a^{2} ) (2a^{3} )(a^{2}-8a+9)[/tex]
The given expression of this problem is:
The degree of an expression is deduct by the exponent of each power.
So, the first factor of the expression has a degree of 2, because that's the exponent.
The second factor has a degree of 3.
The third factor has a degree of 2.
Now, to know the degree of the product, we have to solve the expression, and see what is the degree of the resulting polynomial expression:
[tex](a^{2})(2a^{3})(a^{2} -8a+9)[/tex]
[tex]2a^{5} (a^{2} -8a+9)[/tex][tex]\\2a^{7} -16a^{6}+18a^{5}[/tex]
so, as you can see, the product has a degree of 7.
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If f(x) has a y-intercept at 3 and x-intercepts at 2 and −4, and if
g(x) = −2f(−2x), what are the intercepts of g(x)?
Answer:
Step-by-step explanation:
The y-intercept of g(x) is 3 * -2 = -6.
To find the x-intercepts of g(x), we need to find the values of x that make g(x) equal to 0. Since g(x) = -2f(-2x), this means we need to find the values of x that make f(-2x) equal to 0. Therefore, we can find the x-intercepts of g(x) by solving the equation f(-2x) = 0 for x.
Since the x-intercepts of f(x) are at 2 and -4, this means that the equation f(x) = 0 has solutions at x = 2 and x = -4. Substituting these values into the equation f(-2x) = 0, we get:
f(-2(2)) = 0
f(-4) = 0
and
f(-2(-4)) = 0
f(8) = 0
Therefore, the x-intercepts of g(x) are at x = -2 and x = 4. These are the only intercepts of g(x) that we can determine for certain.
Statements and Reasons
1) Given information
2) [tex]\overline{RT} \cong \overline{RT}[/tex] (reflexive property)
3) [tex]\triangle RST \cong \triangle RQT[/tex] (SSS)
4) [tex]\angle STP \cong \angle QTP[/tex] (CPCTC)
5) [tex]\overline{PT} \cong \overline{PT}[/tex] (reflexive property)
6) [tex]\triangle SPT \cong \triangle QPT[/tex] (SAS)
7) [tex]\angle SPT \cong \angle QPT[/tex] (CPCTC)
Two sentences from the daily weather report in Seattle are given below. It talks about snowfall levels over a 10-hour period during a snowstorm.
For the first 5 hours, 2 inches of snow fell every hour. There was no additional snow accumulation for the next 5 hours.
Which graph models the piecewise function for the given situation?
The graph of the models the piecewise function for the given situation is attached below.
What is piecewise function?
A piecewise-defined function in mathematics is one that is composed of several smaller functions, each of which has a certain interval of the domain it applies to. Instead of being a property of the function itself, piecewise definition is a means to express the function.
Given that for the first 5 hours, 2 inches of snow fell every hour.
The height of the snow can represent by y = 2x, 0 ≤ x ≤ 5
Where x represents the time and y is the height of the snow.
The height of the snow is (5 × 2) = 10 inches after 5 hours.
After 5 hour, there is no snowfall.
The level of snow is y = 10 when 5 ≤ x ≤ 10.
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A 95-kilogram student climbs 4. 0 meters up a rope in 3. 0 seconds. What is the power output of the student?.
The power output of student is P = 1241.34W
Let the mass of the student be m, length of the rope be l and the time taken by the student to climb the rope be t seconds.
Therefore, it is given that
m = 95kg
l = 4m
t = 3 seconds
Now we know that the formula of work done against the gravity (W) is given by
W = m x g x h
where m is the mass of the object,
g is the gravitational constant with g = 9.8 [tex]m/s^{2}[/tex]
and h is the height of the object from refernce, which in this case is l = 4m
Now, putting these values in work done formula we get,
W = 95 x 9.8 x 4
W = 3724 J
Now to find the power output, we know that
Power = (Work done)/(time taken)
Power = 3724/3
Therefore, power output of the student is equal to 1241.34W
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Calculate the perimeter:
7cm
17cm
Rectangle
Answer:
48
Step-by-step explanation:
2*(L+W)
=2*(7+17)
********
Find the slope of the line graphed below.
Answer:
Step-by-step explanation:
slope equals rise over run
count over from one dot to the other , starting on the left
down 3 , over 6
down means negative, so
- 3/6
or -1/2
100 + 2x = 140 + 6x
Answer:
-10 =x
Step-by-step explanation:
100 + 2x = 140 + 6x
Solve for x
Subtract 2x from each side
100 + 2x-2x = 140 + 6x-2x
100 = 140 +4x
Subtract 140 from each side
100-140 = 140+4x-140
-40 = 4x
Divide each side by 4
-40/4 = 4x/4
-10 =x
Write the logarithmic equation log8 64 = 2 in exponential form
Answer: 64 = 8^2.
Step-by-step explanation:
The logarithmic equation log8 64 = 2 can be rewritten in exponential form as follows:
log8 64 = 2
64 = 8^2
Therefore, the exponential form of the given logarithmic equation is 64 = 8^2.
The function h = 3d models the height, in centimeters, of a corn plant as a function of days after sprouting, for
0 ≤ d ≤ 7 .
The slope of the function represents:
A. The average height of the plant over 7 days.
B. The average number of days.
C. The change in height per day.
D. The height after 7 days.
I will give brainiest to whoever is correct!
The slope of the function represents the change in height per day. In the given function, h = 3d, the slope is 3. This means that for every 1 unit increase in the number of days, the height of the corn plant increases by 3 units (in this case, centimeters).
Therefore, the correct answer is (C) The change in height per day.
Slope of Function represents the change in height per day.(Option C)
What is Slope of a Function?A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.
Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is
[tex]m=\frac{dy}{dx}[/tex] = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line can be shown as
tan θ = Δy/Δx
So, the slope of a line is tanΘ.
So as slope represents change in y per change in x, in the given question as y is height and x is days, slope is change in height per day.
Slope of Function represents the change in height per day.(Option C)
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3. The graph of a linear function is shown.
The following points lie on the line: (0,50) and (11, 90).
What is the equation of the function?
Answer:
preem
100
80
60
40
20
0 2 4 6
Answer:
y = [tex]\frac{40}{11}[/tex] x + 50
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 50 ) and (x₂, y₂ ) = (11, 90 )
m = [tex]\frac{90-50}{11-0}[/tex] = [tex]\frac{40}{11}[/tex]
the line crosses the y- axis at (0, 50 ) ⇒ c = 50
y = [tex]\frac{40}{11}[/tex] x + 50 ← equation of line
How do you find the value of k in a function?
To find the value of k in a function, you need to know the equation of the function and the input values for which you want to find the output, and then substitute these values into the equation and solve for k.
What is a function?A function is a relationship between each element of a non-empty set A and at least one element of another non-empty set B. Functions are the central idea of calculus in mathematics. The functions are special types of relations. A function is a rule that generates a unique outcome for each input x in mathematics.
What is domain of a function?The collection of all input values that you can use in a function without running into problems or producing undefined results is generally referred to as the domain of the function. When dealing with functions, it is crucial to keep in mind the function's domain because utilizing input values outside of the domain might provide erroneous or undefinable outputs.
To find the value of k in a function, you need to know the equation of the function and the input values for which you want to find the output.
For example, if the function is defined as f(x) = kx + b, and you want to find the value of k for a particular value of x, you can substitute the value of x into the equation and solve for k.
For example, if the function is f(x) = kx + b and you want to find the value of k when x = 2, you can substitute 2 for x in the equation to get:
f(2) = k(2) + b
Solving this equation for k gives:
k = (f(2) - b)/2
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name the image point when the object point (4,4) is mapped by the following translations. (x,y)-->(x-4,y+2)
Answer:
(0, 6 )
Step-by-step explanation:
(x, y ) → (x - 4, y + 2 )
mans subtract 4 from the original x- coordinate and add 2 to the original y- coordinate, that is
(4, 4 ) → (4 - 4, 4 + 2 ) → (0, 6 )
How do you know if the limit is positive or negative infinity?
Limit base x to a f(x) is equal to infinity if we can say f(x) arbitrarily large for all x sufficiently x=a, from both sides, without actually letting x=a.
Given that,
We have to find how do we know if the limit is positive infinity or a negative infinity.
We know that,
What is infinity?On a number line, numbers move closer to positive infinity as they advance to the left and negative infinity as they move to the right. Positive infinity is always larger than any number, while negative infinity is always smaller.
Now,
We say
Limit base x to a f(x) is equal to infinity if we can say f(x) arbitrarily large for all x sufficiently close to x=a, from both sides, without actually letting x=a.
And
Limit base x to a f(x) is equal to negative infinity if we can say f(x) arbitrarily large and negative for all x sufficiently close to x=a, from both sides, without actually letting x=a.
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What are the SSS SAS and AAS congruence criteria?
The SSS (side-side-side), SAS (side-angle-side) and AAS (angle-angle-side) are basic congruence criteria to prove the congruency of two triangles.
Congruence postulate:Two triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are equal.
The basic terms of the agreement are as follows.
SSS Consensus CriteriaSAS Consensus CriteriaAAS Consensus CriteriaASA Consensus CriteriaAAA Consensus CriteriaRHS Consensus CriteriaNow, let's talk about SSS, SAS, and AAS basic Congruence Criteria.
SSS Congruence Criteria:
SSS Criterion stands for Side-Side-Side Criterion. According to this criterion, two triangles are congruent if three sides of one triangle are equal to the corresponding sides of the other triangle.
SAS Congruence Criteria :
SAS Criterion stands for Side-Angle-Side Criterion. By this criterion, two triangles are congruent if his two sides and included angles of one triangle are equal to the corresponding sides and included angles of the other triangle.
AAS Congruence Criteria:
AAS Criterion stands for Angle-Angle-Side Criterion. According to the AAS criterion, two triangles are congruent if any two angles and excluded sides of one triangle are equal to the corresponding angles and excluded sides of the other triangle.
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Which equation has an X intercept of 3 and a y intercept of 5?
y = -[tex]\frac{5}{3}[/tex]x+5 equation has an X intercept of 3 and a y intercept of 5 .
The point on a line where it crosses an axis is referred to as the "intercept." The slope of the line passes through a point called an intercept on the y-axis.
The equation for a line, which is written as y = mx+c, which stands for slope and y-intercept, respectively, reflects this.
The two main intercepts are X-intercept and Y-intercept. Where the line crosses the x and y axes, respectively, is where the line's x-intercept and y-intercept are situated.
In this case, you are given both intercepts.
Plot a line from the third x-axis point.
On the y-axis, place the coordinates y = 5.
The necessary line is a straight line that passes through these two places is
y = -[tex]\frac{5}{3}[/tex]x+5
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Which is the solutions of the equations 5x 2y 7 *?
The solution set for the given systems of equations : 5x + 2y = 7 and y = x + 1 is x = 5/7 and y = 12/7
Solving the equations :
5x + 2y = 7 (1)
y = x + 1 (2)
Subtracting x on both sides of equation (2)
y - x = 1
Multiplying the equation by 5 on both sides
5y - 5x = 5 (3)
Adding equation (1) and (3) we get
5x + 2y + 5y - 5x = 7 + 5
7y = 12
y = 12/7
Solving for x by substituting y = 12/7 in (2)
12/7 = x + 1
x = 12/7 - 7/7
x = 5/7
--The question is incomplete, answering to the question below--
"What is the solution set of the given systems? 5x + 2y = 7 and y = x + 1"
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