In calculus, 0^0 is an indeterminate form. It is not equal to infinity. But 0x0 is equal to zero.
Some of the indeterminate forms 0/0, 0×∞,∞/∞, ∞ −∞, ∞/0, [tex]0^{0}[/tex].
An unknown value is referred to as being "indeterminate." Even after inserting the limits, we are still unable to determine the original value, according to the indeterminate form of mathematics. When two functions are considered as a ratio, the indeterminate form frequently appears when both functions go closer to 0 in the limit. The term "indeterminate form 0/0" refers to these circumstances. The indeterminate form can also be created, much as addition, subtraction, multiplication, and exponential operations. If the limiting behavioral of separate components of the provided expression cannot identify the overall limit, a limit is said to be indeterminate.
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why is x!/10^6x diverging
[tex]x!/10^{(6x)}[/tex] diverges as x approaches infinity.
What is expression ?
In mathematics, an expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can be as simple as a single number or variable, or they can be complex combinations of multiple variables and operations.
Examples of expressions include:
3 + 5
x - 2y
(a + b) * (c - d)
2x^2 + 3x - 5
sin(x) / cos(x)
Expressions can be evaluated to obtain a numerical value or simplified to make them easier to work with. For example, the expression 2x^2 + 3x - 5 can be simplified by factoring as (2x - 5)(x + 1) or by completing the square as 2(x + 3/4)^2 - 49/8.
Expressions are an important part of algebra and other branches of mathematics, where they are used to represent mathematical relationships and solve equations. They are also used in computer programming and other areas of science and engineering to represent mathematical models and calculations.
According to given condition :
The expression [tex]x!/10^{(6x)}[/tex] is a mathematical function that represents the factorial of x divided by 10 to the power of 6 times x. This expression diverges as x becomes large because the factorial function grows much faster than the exponential function.
As x increases, the value of x! grows very rapidly because x! is the product of all integers from 1 to x. In contrast, the value of 10^(6x) grows much more slowly because it is an exponential function with a fixed base of 10.
Therefore, as x gets larger, the value of [tex]x!/10^{(6x)}[/tex] grows very rapidly, eventually becoming much larger than any fixed value. This means that the expression diverges to infinity as x approaches infinity.
To see this more formally, we can use Stirling's approximation, which states that n! is approximately equal to [tex](n/e)^n * sqrt(2pin)[/tex] for large values of n. Substituting this into the expression for [tex]x!/10^{(6x)}[/tex], we get:
[tex]x!/10^{(6x)} ≈ [(x/e)^x * sqrt(2pix)] / 10^{(6x)}[/tex]
Taking the logarithm of both sides, we get:
[tex]ln(x!/10^{(6x)}) ≈ x * ln(x/e) + 0.5 * ln(2pix) - 6x * ln(10)[/tex]
As x approaches infinity, the first two terms on the right-hand side dominate, and the expression grows without bound.
Therefore, [tex]x!/10^{(6x)}[/tex]diverges as x approaches infinity.
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Unit 3B Test
PART 1
Need THESE ANSWERS ASAP
Cosine is negative, we know that angle C is obtuse. Therefore, the triangle with sides 9, 15, and 19 is an obtuse triangle.
What is triangle ?
Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
To determine whether a triangle with sides 9, 15, and 19 is acute or obtuse, we can use the Law of Cosines, which relates the sides and angles of a triangle:
c^2 = a^2 + b^2 - 2ab*cos(C)
where a, b, and c are the side lengths, and C is the angle opposite side c.
In this case, we have:
a = 9, b = 15, c = 19
Using the Law of Cosines, we can solve for the cosine of angle C:
cos(C) = (a^2 + b^2 - c^2) / 2ab
cos(C) = (9^2 + 15^2 - 19^2) / (2915)
cos(C) = -0.283
Since, cosine is negative, we know that angle C is obtuse. Therefore, the triangle with sides 9, 15, and 19 is an obtuse triangle.
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Marques made some three point shots and some free throw shots (worth one point each). Marques made a total of 8 shots altogether and scored a total of 12 points. Determine the number of three point shots marques and number the number of free throws he made
By using the method of Normal Distribution, Marques made 4 three point shots and 4 free throws.
Let's denote the number of three point shots that Marques made as x and the number of free throws he made as y.
According to the problem, Marques made a total of 8 shots, so we have:
x + y = 8
And he scored a total of 12 points, which can be expressed as:
3x + y = 12
We now have a system of two equations with two unknowns:
x + y = 8
3x + y = 12
We can solve this system by either substitution or elimination. Here, we'll use the elimination method.
Multiplying the first equation by 3, we get:
3x + 3y = 24
Subtracting the second equation from this, we get:
2y = 12 - 3x
Dividing by 2, we get:
y = 6 - (3/2)x
We can substitute this expression for y into the first equation:
x + (6 - (3/2)x) = 8
Simplifying, we get:
(1/2)x = 2
x = 4
So Marques made 4 three point shots. We can substitute this value into either of the original equations to find y:
4 + y = 8
y = 4
So Marques made 4 free throws.
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Answer:
CFGGFF
Step-by-step explanation:
CGDF
Priya says, “once I know the vertex is (4,10), I can find out, without graphing, wether the vertex is maximum or the minimum of function p. I would just compare the coordinates of the vertex with the coordinates of a point on either side of it.” Complete the table and then explain how Oriya might have reasoned about whether the vertex is the minimum or maximum.
Step-by-step explanation:
Hello, So use the function p, to find the output
[tex]p(3) = - (3 - 4) {}^{2} + 10 = - 39[/tex]
[tex]p(5) = - (5 - 4) {}^{2} + 10 = 9[/tex]
Since p(4)>p(5) and p(3), p(4) is the maximum.
Also p is written in vertex form which is
[tex]a(x - h) {}^{2} + k[/tex]
Since a is negative, we will have a maximum vertex.
The answer is
Oriya has reasoned the vertex is a maximum because p(4) is the highest points compared to points near it such as p(3) and p(5).
AD=9cm
FD=13cm
FHG=49°
Find the x°
In a right angled triangle, the angles are given by the fοrmula:
Angle A + Angle B + Angle C = 180°Therefοre, x° = 131°.
What is angle?Angle is a geοmetrical figure fοrmed by twο rays with a cοmmοn endpοint. It is measured in degrees οr radians and is used tο describe the amοunt οf turn between twο lines. It can alsο be used tο measure the size οf an angle in a triangle, the amοunt οf rοtatiοn οf a 3D οbject, and mοre. Angles are impοrtant in bοth mathematics and science as they're used tο calculate the amοunt οf fοrce needed tο mοve an οbject οr the amοunt οf energy needed tο keep an οbject in mοtiοn.
In a right angled triangle, the angles are given by the fοrmula:
Angle A + Angle B + Angle C = 180°
Given that FHG = 49°, we can calculate the οther angles:
Angle A = 180° - 49° = 131°
Angle B = 180° - 131° - 49° = 0°
Angle C = 180° - 131° - 0° = 49°
Therefοre, x° = 131°.
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3. Quinton started his own tutoring business and is tracking the amount of money he makes using the
function f(m) = 120m - 75, where mrepresents the number of months he has been tutoring.
a. How much money does
Quinton expect to make
from tutoring each
month?
ONL
b. How much money will he
have saved in 4 months?
c. What could the number -75 represent in this context?
a. Quinton expect to make 45 $ from tutoring each month b. he will save 405 $ in 4 month. the number -75 represent the amount deducted.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets,, and grouping can all be represented by mathematical symbol.
We are given that Quinton started his own tutoring business and is tracking the amount of money he makes using the function;
f(m) = 120m - 75,
where m represents the number of months he has been tutoring.
a. for one month
m = 1
f(1) = 120(1) - 75,
f(1) = 120 - 75 = 45
b. for 4 month
m = 4
f(4) = 120(4) - 75,
f(4) = 480 - 75 = 405
c. The number -75 represent the amount deducted in this context.
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i want the answers please
Answer:
Step-by-step explanation:
A
Find the equation of a line perpendicular to -3x + y = -5 that
passes through the point (9,5).
-x-3y = -24
-3x + y = -22
y=x+8
y=-3x -5
Answer:y=-x/-+8
Step-by-step explanation:
If 0° ≤ Θ≤ 360°, then find angle(s) Θ.
cosΘ=-1/2
The angle Θ has these possible values:
Θ = 120º.Θ = 240º.How to obtain the angle measure?The cosine of the angle is given as follows:
cosΘ=-1/2.
The angle on the first quadrant with a cosine of 1/2 is given as follows:
60º.
The cosine is negative on the second and on the third quadrant, hence the equivalent angles are given as follows:
Θ = 180 - 60 = 120º. (to obtain the angle in the second quadrant, we subtract 180 from the angle).Θ = 180 + 60 = 240º. (to obtain the angle in the third quadrant, we add 180 to the angle).More can be learned about angle measures at https://brainly.com/question/30820033
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What is a predictor variable in statistics?
In statistics, a predictor variable is an independent variable that is used to predict or explain the outcome of a dependent variable.
Predictor variables are often used in regression analysis, where the goal is to model the relationship between one or more predictor variables and a response variable. Predictor variables can take on different forms, including categorical (e.g., gender, race) and continuous (e.g., age, income). The choice of predictor variables depends on the research question and the underlying theory or knowledge about the phenomenon being studied. For example, in a study investigating the relationship between physical activity and body weight, physical activity might be the predictor variable and body weight the outcome variable. The study might collect data on physical activity levels (e.g., minutes per day of moderate-to-vigorous physical activity) and body weight (e.g., BMI) from a sample of participants, and then use regression analysis to model the relationship between these variables. In regression analysis, predictor variables are typically entered into the model as explanatory variables or covariates, along with other relevant factors such as demographic or environmental variables. The goal is to identify the predictor variables that are most strongly associated with the outcome variable and to determine the direction and magnitude of the relationship. By understanding the role of predictor variables, we can gain insight into the factors that influence or predict the outcomes of interest in a given study.
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Consider formula a to be v = startfraction 2 pi r over t endfraction and formula b to be v2 = gv = g startfraction m subscript central over r endfraction. Write the letter of the appropriate formula to use in each scenario.
Formula a = (v = 2 * pi * r / t)
Formula b = (v2 = g * m_central / r)
The scenario in context to formula a and formula b is given below:
Formula a = (v = 2 * pi * r / t)
It is used to calculate the velocity (v) of a circular object moving with a constant speed around a circle of radius (r) in time (t).
Example scenario: if you want to find the velocity of a moving object in a circular path, use formula a.
Suppose you want to find the velocity of a car moving in a circular path on a race track. The radius of the track is "r" and the time taken for the car to complete one lap is "t".
Using the equation (v = 2 * pi * r / t), we can calculate the velocity as follows:
Let's say the radius of the track is 100 meters and the time taken for the car to complete one lap is 60 seconds. Then, the velocity can be calculated as follows:
v = 2 * pi * (100 m) / (60 s)
v = 31.42 m/s
So, the velocity of the car moving in a circular path on the race track is 31.42 m/s.
Formula b = (v2 = g * m_central / r)
It is used to calculate the velocity squared (v^2) of an object moving under the influence of a central force (g * m_central) and is related to the radius (r) of its orbit.
Example scenario: If you want to find the velocity squared of an object under the influence of a central force, use formula b.
Suppose you want to find the velocity squared of a planet moving in a circular orbit around a star (a central force). The mass of the star is "m_central" and the distance of the planet from the star is "r".
Using the equation (v² = g * m_central / r), we can calculate the velocity squared as follows:
v² = (6.67 x 10^-11 N m² /kg² ) * (m_central) / (r)
Let's say the mass of the star is 2 x 10^30 kg and the distance of the planet from the star is 1.5 x 10^11 m.
Then, the velocity squared can be calculated as follows:
v² = (6.67 x 10^-11 N m² /kg² ) * (2 x 10^30 kg) / (1.5 x 10^11 m)
v² = 2.22 x 10^20 m² /s²
So, the velocity squared of the planet moving in a circular orbit around the star is 2.22 x 10^20 m² /s² .
At, last we can say if you want to find the velocity of a moving object in a circular path, use formula a. If you want to find the velocity squared of an object under the influence of a central force, use formula b.
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TEXT ANSWER
Question 7
Are the sides proportional?
Set up each ratio of sides and determine if they are equal ratios. Show all of your work.
3.61 cm
R
44°
11.97 cm
9.71 cm
N
T
17.955 cm
14.565 cm
121°
M
44°
5.415 cm
Answer:
Yes.
Step-by-step explanation:
We need to make sure that we match up the right sides before checking for proportionality.
From the picture, we can see that SRT pairs with MLN.
It's easier to see if you draw a diagram of MLN on paper with the same orientation as SRT.
Were you to do this, you would see that as SR lies on the left side of SRT, so does MLN lie on the left side of ML.
Also, both ST of SRT and MN of MLN lie on the right side and RT of SRT and LN of MLN are the base.
Thus, the proportions are
[tex]\frac{SR}{ML}=\frac{ST}{MN}=\frac{RT}{LN} \\\\\\\frac{3.61}{5.415}=\frac{2}{3} \\\\\frac{9.71}{14.564}=\frac{2}{3}\\ \\ \frac{11.97}{17.955}=\frac{2}{3}[/tex]
Since all the ratios simplify to 2/3 and are equal, the sides are proportional.
1 whole and 13/20 as a percentage
Answer: 165%
Step-by-step explanation:
1 whole =100% 13/20=65%
100+65=165
How much iwater do you add to make each concentration?
1% sugar syrup using 12 g sugar
The amount of water required to produce 1% sugar syrup from 12g sugar is 1.2L.
What is volume of water?Volume is the amount of space occupied by an object, whereas capacity is the ability of an object to hold a substance, such as a solid, liquid, or gas.
The amount of water that must be added for a given weight of solution is expressed as weight by volume solution (w/v).
w/v (weight by volume percentage):
The grams of solute in 100 milliliters of solution are defined as the percent weight per volume.
This method determines the concentration of the solution.
The concentration given is 1%.
The sugar weight is 12g.
Solvent volume = weight/concentration
Volume = 12/1 = 12 x 100 mL
Volume = 1.2 L
Hence, 1.2l of water is required to produce 1% sugar syrup from 12g of sugar
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What is the value of 193cm in feet
Answer:
Step-by-step explanation: the value is 633.202 ft
a fraction that is the same as 5
what is 36.6 celsius in fahrenheit
Using the conversion formula of converting temperatures from Celsius to Fahrenheit, we get 36.6°C is 98.68°F.
Temperature is often measured using two different scales: Celsius (°C) and Fahrenheit (°F). To convert a temperature in Celsius to Fahrenheit, we use the formula °F = (°C × 9/5) + 32. In this formula, we first multiply the temperature in Celsius by 9/5 (which is equivalent to multiplying it by 1.8), and then add 32 to the result.
So for example, to convert 36.6 degrees Celsius to Fahrenheit, we plug in 36.6 for °C, and get:
°F = (36.6 × 9/5) + 32
°F = 98.68
Therefore, 36.6 degrees Celsius is equivalent to 98.68 degrees Fahrenheit. This conversion is useful for comparing temperature measurements between different regions, where different temperature scales are commonly used.
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what is 6 divided by 3 fraction form
Answer:
Step-by-step explanation:
[tex]\frac{6}{3}[/tex] = [tex]\frac{2}{1}[/tex]
Answer:
Step-by-step explanation:
The diameter of a hat is 4.7 inches. What is the distance around the hat using π = 3.14? Round to the hundredths place.
1.50 inches
7.38 inches
17.34 inches
14.76 inches
Answer:
14.76
Step-by-step explanation:
Circumference = 2πr
Substitue the values into the formula
2(3.14) (2.35)=
Multiply pi by the radius
2(7.379)= 14.758
Round the answer to the hundreths place
14.76
Select the two values of x that are roots of
this equation.
3x - 5 =-2x2
D A. X=-3
0 B. x=-3
. C. x=2
. D. x= 1
Answer: B is the answer
Step-by-step explanation:
how many if any solutions 17. y = 7x + 13
-21x + 3y = 39
The given system of equation have no solutions.
What is no solution in an equation?A linear equation is one whose variables all have degree 1.
An inconsistent pair of linear equations is a system of linear equations that cannot be solved. By comparing the coefficients of the equations in a system of linear equations, we can determine whether the system of equations has no solution. We can also infer this from the graph.
The given equations are:
y = 7x + 13
-21x + 3y = 39
Substitute the value of y from equation 1 to equation 2:
-21x + 3(7x + 13) = 39
-21x + 21x + 39 = 39
0
Hence, the given system of equation have no solutions.
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A disco ball has a circumference of 16.558 centimeters, and 448 rhinestones on its surface. Approximately how many rhinestones per square centimeter are on the surface of a disco ball ?
The number of rhinestones per square centimeter on the surface of a disco ball is 448/274.167.
How to find the surface area of a sphere?Suppose that radius of the considered sphere is of 'r' units.
Then, its surface area S would be:
[tex]S = 4\pi r^2 \: \rm unit^2[/tex]
Given;
A disco ball has a circumference of 16.558 centimeters
448 rhinestones on its surface.
Now,
2pi*r=16.558
r=8.279/pi
Surface area of sphere=4pi*r^2
=4*68.541841
=274.167
Here, 448/274.167
Therefore, the surface area per square cm will be 448/274.167.
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Help with geometry right triangles word problems.
The height of the ladder is 19.939 feet
How to determine the length of the ladderFirst, we need to know the six trigonometric identities. They are;
secantcotangenttangentcosinesinecosecantFrom the information given, we have that;
The angle, θ = 65 degreesThe opposite side is the height of the ladderThe hypotenuse is 22 footThen
sin θ = opposte/hypotenuse
Substitute the values, we get;
sin 65 = h/22
Find the value
0.9063 = h/22
cross multiply
h = 19.939 feet
Hence, the value is 19.939 feet
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If the area of a rectangle is given by m² + 11m + 28, write an expression to represent the perimeter.
An expression to represent the perimeter is P = 2m + 2(m² + 11m + 28)/m
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
We are given that;
The expression m² + 11m + 28
Now,
Let's assume that the length of the rectangle is "m" and the width is "n".
The formula for the area of a rectangle is A = l × w. We are given that the area of the rectangle is m² + 11m + 28, so we can write:
A = m² + 11m + 28
Substituting the formula for the area, we get:
m² + 11m + 28 = m × n
We can rearrange this equation to solve for n:
n = (m² + 11m + 28) / m
The perimeter of a rectangle is given by the formula P = 2(l + w). Substituting the values of l and w, we get:
P = 2(m + n)
Substituting the value of n, we get:
P = 2(m + (m² + 11m + 28) / m)
P = 2m + 2(m² + 11m + 28) / m
Therefore, by the given area of rectangle perimeter will be 2m + 2(m² + 11m + 28) / m
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Jerold had $20 to spend at the
county fair. Admission was $7
and the rides cost $0.50 each.
How many rides Jerold can go on?
Answer: 26
Step-by-step explanation: if each ride costs $.50 each, and admission costs $7, you multiply .50 by 26 and get 13. After you then add $13 and $7 and that equals $20. $13 dollars Jerold can spend
What does the expression "three less than five" mean? A. 3 – 5
HELP QUICKLY PLEASEE!!!!
Answer:
Step-by-step explanation:
Answer:
(1) A
(2)C
(3)B C
Step-by-step explanation:
(1)B. base=5x17=85
C.(5x4.3)/2+3x(5x17)=10.75+255=265.75
(2) A is wrong
B. surface area=2x(3.5x8)+2x(3.5x16)+2x(8x16)=56+112+256=424[tex]cm^{2}[/tex]
(3) A. base=(15x8)/2=60[tex]mm^{2}[/tex]
B. 17x6+8x6+15x6=240[tex]mm^{2}[/tex]
C. 240+2x60=360[tex]mm^{2}[/tex]
A circular plate has a radius of 6 centimeters. What is the approximate
circumference, in centimeters, of this plate?
O 18.84
O 37.68
O 75.36
O 113.04
Answer: B) 37.68
Step-by-step explanation:
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.
Plugging in the given radius of 6 centimeters, we get:
C = 2πr
C = 2π(6)
C ≈ 37.68
At a local fast food restaurant, a regular drink costs $2.25. A larger drink can be purchased for an additional $0.25 per ounce above the regular size.
If n represents the number of ounces above the regular size, which inequality shows how much can be added to the regular size for a drink that costs under $4.00?
The inequality that shows how much can be added to the regular size for a drink that costs under $4.00 is given as follows:
2.25 + 0.25n < 4.
How to model the inequality?The drink costs $2.25, plus each of the n additionals cost $0.25, hence the total cost is given as follows:
T(n) = 2.25 + 0.25n.
For a cost under $4, the cost must be less than $4, hence the inequality is given as follows:
2.25 + 0.25n < 4.
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help 17-20 algebra 2
The index forms are solved to give:
17. 5x
18. 3x^2
19. 4
20. 2
What are index forms?Index forms are described as mathematical forms of writing numbers that are too small or too large in more convenient ways.
From the information given, we have that;
[tex]\sqrt{\frac{100x^6}{4x^4} }[/tex]
Find the square root
10x³/2x²
Divide the values
5x
[tex]\sqrt{\frac{81x^8}{9x^4} }[/tex]
Find the square root
9x⁴/3x²
Divide the values
3x²
[tex]\sqrt{\frac{64x^9}{4x^7} }[/tex]
Find the square root
8/2√x⁹/x⁷
4
[tex]\sqrt{\frac{24x^5}{6x^3} }[/tex]
√4x²
Find the square root
2
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