The limit of [tex]\lim_{x \to \infty} \frac{lnx}{x}[/tex] using L'Hospital rule is 0.
According to the given question.
We have to find the limit of ln(x)/x when x approaches to infinity.
If we let x = ∞, we get an indeterminate form [tex]\frac{\infty}{\infty}[/tex] ie. [tex]\frac{ln(x)}{x} = \frac{\infty}{\infty}[/tex].
And, we know that whenever we get indeterminate form ∞/∞ we apply L'Hospital rule.
Therefore, defferentiating numerator ln(x) and x with respect to x.
[tex]\implies \frac{d(ln(x))}{dx} = \frac{1}{x}[/tex] and [tex]\frac{d(x)}{dx} =1[/tex]
So,
[tex]\lim_{x\to \infty}\frac{\frac{1}{x} }{1}[/tex]
[tex]= \lim_{x \to \infty} \frac{1}{x}[/tex]
As, x tends to ∞, 1/x tends to 0. Because ∞ is very large number and 1 divided by a very large number always approaches to 0 and it is very close to zero.
Therefore,
[tex]\lim_{x \to \infty} \frac{1}{x} = 0[/tex]
Hence, the limit of [tex]\lim_{x \to \infty} \frac{lnx}{x}[/tex] is 0.
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a
a
¹2-5, find £r(:)
=
En
n=l
n=1
b
Given that Σ
[tex]\sum^{\infty}_{n=1} (a/b)^n=5 \\ \\ =\frac{a/b}{1-\frac{a}{b}}=5 \\ \\ \frac{a}{b-a} =5 \\ \\ \frac{a}{b}=\frac{5}{6}[/tex]
So, we need to find
[tex]\sum^{\infty}_{n=1} n(5/6)^n
[/tex]
Let this sum be S.
Then,
[tex]S=(5/6)+2(5/6)^2 +3(5/6)^3+\cdots \\ \\ \frac{5}{6}S=(5/6)^2 + 2(5/6)^3+\cdots \\ \\ \implies \frac{1}{6}S=(5/6)+(5/6)^2+(5/6)^3+\cdots=5 \\ \\ \implies S=\boxed{30}[/tex]
Solve eight and three fifths minus two and four ninths.
Answer:
6.15555555556
Step-by-step explanation:
the 5 is infinite in 6.15 such as 6.155555555 it does not stop
In the past Reagan got paid 214,350 annually. Since switching to a new career she has been making 347,247 annually. What is the percent of increase in Reagan’s pay
Answer: Reagan's pay was increased by 62%
Step-by-step explanation:
First, lets find the difference between the two pays:
$347,247 - $214,350 = $132,897
Let 214350 = 100%
Dividing 132,897 by 214350 to find the percent increase
[tex]\bold{\frac{132,897}{214,350} }=0.62\times100=62[/tex]
Therefore, Reagan's pay was increased by 62%
for each reasons it gives you the options to choose: commutative property of addition, associative property of addition, distributive property, and combining like terms
The distributive Property States that when a factor exists multiplied by the sum/addition of two terms, it exists critical to multiply each of the two numbers by the factor, and eventually complete the addition operation.
Let the expression be 4+(6+8u)
4 + (6 + 8u) = (4 + 6) + 8u
What is a distributive property?The distributive Property States that when a factor exists multiplied by the sum/addition of two terms, it exists critical to multiply each of the two numbers by the factor, and eventually complete the addition operation.
Adding (distributing) the first numbers of each set, outer numbers of each set, inner numbers of each set, and the last numbers of each set. Combine like terms. Solve the equation and simplify, if needed.
The expression be 4+(6+8u)
4+(6+8u) = (4 + 6)+8u
Therefore, the correct answer is distributive property.
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The population of a country was increased in the past 4 years. The annual presentage increases are 20%,25%,30%,10% respectively.What the overall percentage increase in these 4years?
The answer is 114.5%.
Let the original population be denoted by x.
Now, let's go through the percentage increase per year.
Year 1
x (1 + 20%)x (1.2)1.2xYear 2
1.2x (1 + 25%)1.2x (1.25)1.5xYear 3
1.5x (1 + 30%)1.5x (1.3)1.95xYear 4
1.95x (1 + 10%)1.95x (1.1)2.145xOverall increase : 214.5% - 100% = 114.5%
Hence, the overall percentage increase in these 4 years is 114.5%.
the volume of cylinder is 448 pie cm cube and height 7 cm find its radius
Answer:
[tex]r =\bf 8 \space\ cm[/tex]
Step-by-step explanation:
The formula for volume of a cylinder is as follows:
[tex]\boxed{Volume = \pi r^2 h}[/tex]
where:
• r = radius (? cm)
• h = height (7 cm).
Substituting the values into the formula:
[tex]448 \pi = \pi \times r^2 \times 7[/tex]
Now solve for [tex]r[/tex]:
⇒ [tex]r^2 = \frac{448 \pi }{\pi \times 7}[/tex]
⇒ [tex]r = \sqrt{64}[/tex]
⇒ [tex]r =\bf 8 \space\ cm[/tex]
[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:
[tex]\longrightarrow\bold{Volume= 449 \pi cm^3}[/tex][tex]\longrightarrow\bold{Height= 7cm}[/tex][tex]\longrightarrow\sf{V= \pi r^2 h}[/tex]
[tex]\longrightarrow\sf{448 \pi= \pi r^2 \cdot 7}[/tex]
[tex]\longrightarrow\sf{448=
7r^2}[/tex]
[tex]\longrightarrow\sf{r^2= \dfrac{448}{7} }[/tex]
[tex]\longrightarrow\sf{r^2=64}[/tex]
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
[tex]\longrightarrow\sf{r= 8cm}[/tex]
Circle T is shown. Line segment Q S is a diameters. Point R is opposite of point T. Lines are drawn from points Q and S to point R to form a right triangle. Angle Q R S is a right angle.
The measure of arc QS is (4x – 18)°.
What is the value of x?
40.5
49.5
94.5
180
The value of angle x of the given cyclic segment is; 49.5°
How to find the angle of an arc?We are given the measure of the angle of arc QS as (4x – 18)°
Now, to find the measure of arc QS, this angle is to be equal to 180° and as such;
Thus;
(4x – 18)° = 180°
4x - 18 = 180
4x = 180 + 18
4x = 198
x = 198/4
x = 49.5°
The angle subtended by the arc at the center of a circle with center C is the angle of the arc. It is denoted by. m AB, where A and B are the endpoints of the arc. With the help of the arc length formula, we can find the measure of arc angle.
The formula to measure the length of the arc is;
Arc Length Formula (if angle θ is in degrees); s = 2πr (θ/360°)
Arc Length Formula (if θ is in radians) s = ϴ × r.
Thus, the value of x of the given cyclic segment is; 49.5°
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(a)Find two consecutive odd integers such that the sum of the smallest integer and twice the greater integer is 85.
(b) The sum of three integer is 40.The second integer is three times the first and the third integer exceeds the second by 5.Find the three integers.
Answer:
see explanation
Step-by-step explanation:
(a)
let the two consecutive odd integers ne n and n + 2 , then
n + 2(n + 2) = 85
n + 2n + 4 = 85
3n + 4 = 85 ( subtract 4 from both sides )
3n = 81 ( divide both sides by 3 )
n = 27
n + 2 = 27 + 2 = 29
the 2 consecutive odd integers are 27 and 29
--------------------------------------------------------------------
(b)
let the first integer be n , then 2nd integer is 3n and 3rd is 3n + 5 , so
n + 3n + 3n + 5 = 40
7n + 5 = 40 ( subtract 5 from both sides )
7n = 35 ( divide both sides by 7 )
n = 5
3n = 3 × 5 = 15
3n + 5 = 15 + 5 = 20
the 3 integers are 5, 15, 20
5. The grid shows how many eggs Ms. Benton bought.
The shaded boxes represent the number of eggs she
used to make the cookies. What percent and fraction
of the eggs bought were not used to make the cookies?
Show your work in the space below. Remember to
check your solution.
Answer:
You can count how many boxes that are not shaded to find how many eggs were not used, but that's to find out the fraction
Step-by-step explanation:
Count the boxes total in the grid. then count the number of boxes were not shaded. the number of total boxes is your denominator, and the number of boxes thar aren't shaded is your numerator.
I think...
Find the output, h, when the input, x, is -18.
h = 17+
=
I
6
The value of output, h, when the input, x, is -18 for the given equation is 14
Solving an equationFrom the given question, we are to determine the value of the output, h, when the input x is -18
The given equation written properly is
h = 17 + x/6
Now, to determine the value of output, h, we will put in the value of x into the equation
h= 17 + x/6
The given value of x is -18
Thus, putting the given value of x into the equation, we get
h= 17 + x/6
h= 17 + -18/6
h = 17 + -3
h = 17 - 3
NOTE: + × - = -
h = 14
∴ h is 14 when x is -18
Hence, the value of output, h, when the input, x, is -18 for the given equation is 14
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Jason left a bin outside in his garden to collect rainwater. he notices that 1 over 5 gallon of water fills 2 over 3 of the bin. write and solve an expression to find the amount of water that will fill the entire bin
The amount of water that will serve the entire container exists 3/10 gallons.
What is an expression?An expression exists a sentence with a minimum of two numbers or
variables and at least one math function.
Given: 1 over 5 gallons of water serve 2 over 3 of the container.
(1/5) gallon / (2/3) container = x gallons / 1 container
cross-multiplying the above equation, we get
1/5 = (2/3)x
multiply both sides by the reciprocal of 2/3 = 3/2
(3/2) (1/5) = x = 3/10 gallons serve the total container
Each 1/10 of a gallon serve 1/3 of the container
So 3(1/10) gallons serve 3(1/3)bins
3/10 gallons serve a whole container.
The amount of water that will serve the entire bin container exists 3/10 gallons.
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please help me with questions 1 and 2 (with explanations and calculation) thank you so much
Identify the area of the kite.
Answer: А=480.
Step-by-step explanation:
If two solids are similar and have a linear ratio of 2:5, what is the ratio of the areas?
Answer:
4 : 25
Step-by-step explanation:
given 2 similar figures with linear ratio a : b , then
ratio of areas = a² : b²
here the linear ratio = 2 : 5 , then
area ratio = 2² : 5² = 4 : 25
In order to play at the Mt. Guinea Country Miniature Golf Club, a player has to pay the membership fee and pay for each round played. The total
cost is represented by the function
T-44.09r+12.70, where T the total cost (in dollars) and r= the number of rounds played.
Which of the following statements must be true?
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
PLEASE HELP The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
A graph with two linear functions; f of x passes through 1, 3 and 3, 13, and g of x passes through negative 1, 3 and 1, 13.
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
The transformation of f(x) to g(x) would be 6 units upwards
To transform f(x) to g(x), the equation is; g(x) = f(x) + 6
How to solve transformation problems?We are told that f of x passes through 1, 3 and 3, 13, and g of x passes through negative 1, 3 and 1, 13.
f(x) passes through (1,3) and (3, 13).
Thus;
slope is; m = (13 - 3) / (3 - 1) = 10/2 = 5
y-intercept is; b = y - mx
Thus;
b = 3 - 5*1 = -2
Equation of the line is;
f(x) = 5x - 2
g of x passes through negative 1, 3 and 1, 13. Thus, the slope is;
m = (13 - 3) / (1 + 1) = 10/2 = 5
y-intercept is; b = y - mx
Thus;
b = -1 - (5)(-1)
b = 4
Equation of the line is; g(x) = 5x + 4
part A: The transformation of f(x) to g(x) would be 6 units upwards
part B: k = 6
part C: To transform f(x) to g(x), the equation is;
g(x) = f(x) + k
g(x) = f(x) + 6
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Shaking wants to write 2/6 as a decimal. which method could she use divide 6 by 2. divide 2 by 6. multiply 6 by 2. multiply 2 by 6
she should use 2 by 6
Step-by-step explanation:
2 divided by 6 will give 0.3 in 1d.p
Find the value of x. A. 80 B. 110 C. 100 D. 40
Answer:
110 degrees
Step-by-step explanation:
to find the angle x, we need to use the formula to find the 50 degree angle:
(y - x) / 2 = 50
y is 210
(210 - x) /2 = 50
210-x = 100
x = 110 degrees
Quick algebra 1 assignment for some points!
I LOST MY OLD ACCOUNT I WAS A GENIUS, :((( SO NOW I GOTTA MAKE A NEW ONE !!! :((
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
Oh by the way this is just a section of the real assignment, the assignment calls for you to make an app that people can play to learn inverse variation & direct variation and stuff.
Hope that helps solve this! :)
Inverse variation is the relationship that occurs between two quantities in which one decreases as the other increases.
Inverse variationThe types of variation which exists are;
Inverse variationDirect variationJoint variationFor instance;
The relationship between John's speed and distance is inversely proportional. If John's speed is 5km/h, his distance is 6km. Find John's distance when his speed increases to 6km/h.
s = k / d
where,
k = constant of proportionality
s = k / d
5 = k/6
30 = k
Find d when s = 6km/hs = k / d
6 = 30/d
6d = 30
d = 30/6
d = 5 km
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Some randomly selected high school students were asked to name their favorite sport to watch. The table displays the distribution of results. A 2-column table with 5 rows. Column 1 is labeled sport with entries football, basketball, baseball, soccer, none. Column 2 is labeled probability with entries 0.23, 0.18, 0.26, 0.17, 0.16. What is the probability that a student chose football given that they like watching sports? 0.16 0.23 0.27 0.77
The probability that a student chose football given that they like watching sports is: c. 0.27.
Conditional ProbabilityUsing this formula
P[Like (Football)/Like (Sport)]
Where:
P=Probability
Like (Football)=0.23
Like (Sport)=0.23+0.18+0.26+0.17=0.84
Let plug in the formula
P[Like (Football)/Like (Sport)]=0.23/0.84
P[Like (Football)/Like (Sport)]=0.27
Therefore the probability that a student chose football given that they like watching sports is: c. 0.27.
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Answer:
C.
Step-by-step explanation:
The grocery store where Ms. Maple works pays her $6.50 per hour. Any time she works more than 40 hours per week, she is paid time and a half for the additional hours. Her weekly pay, w, is found using the following equation, where h is the total number of hours worked.
Answer:
$279.25
Step-by-step explanation:
Multiply 6.50x43
[tex]w = 279.50 + (0.5 \times 6.50) \times (43 - 40)[/tex]
Multiply 0.5x6.50
[tex]w = 279.50 + 3.250 \times (43 - 40)[/tex]
Add 43-40
[tex]w = 279.50 + 3.250 \times 3[/tex]
Multiply 3.250x3
[tex]w = 279.50+ 9.750[/tex]
Solution
f(x) = 8x2 – 2x + 3
g(x) = 12x2 + 4x – 3
What is h(x) = f(x) – g(x)?
Answer: [tex]h(\text{x}) = -4\text{x}^2 - 6\text{x} + 6[/tex]
Work Shown:
[tex]h(\text{x}) = f(\text{x}) - g(\text{x})\\\\h(\text{x}) = ( 8\text{x}^2 - 2\text{x} + 3) - ( 12\text{x}^2 + 4\text{x} - 3 )\\\\h(\text{x}) = 8\text{x}^2 - 2\text{x} + 3 - 12\text{x}^2 - 4\text{x} + 3 \\\\h(\text{x}) = (8\text{x}^2-12\text{x}^2) + (- 2\text{x} - 4\text{x}) + (3 + 3) \\\\h(\text{x}) = -4\text{x}^2 - 6\text{x} + 6 \\\\[/tex]
Create one symmetrical (normal) and one asymmetrical set of data, and explain why each fit the definition.
- Knowing the type of distribution and the skewness of the data, is it possible to draw conclusions about the mean and the median?
- Why would it be best to use particular measures of center and spread if the data is symmetrical or asymmetrical?
- What measures would you use in each case?
If the data is symmetrical, then the mean is the best measure of central tendency to use, and the standard deviation is the best spread to use.
If the data is asymmetrical, the median is the best measure of central tendency to use, and the inter-quarterly range is the best spread to use.
What are symmetrical and asymmetrical data?A histogram for symmetrical data will give a symmetrical shape, and the mean, median and mode will all be the same value. Therefore, the best measure of the central tendency to use is the mean. The standard deviation shows how far away the values in a given data set are from the mean, and since the mean is used as the measure of central tendency in this case, the standard deviation should be used as the spread.
A histogram for a an asymmetric data set will give an asymmetric shape, and the mean is not always equal to the median. Therefore, the best measure of central tendency to use is the median. The inter-quarterly range shows the range of the middle 50% of a certain data, which is considered from the median value. Since the median is used as the measure of central tendency in this case, it is wise to use the inter-quarterly range as the measure of spread.
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Ben, Rob, Kelly, Carla and Manu organised a pizza party for their business group, They ordered one vegetarian, one cheese, and one Nutella pizza. After the party, three-fourths of vegetarian pizza, five-eights of cheese pizza, and 11/12 of
Nutella pizza are remaining. Once all guests left, they decided to split the pizza equally among themselves, what
fraction of the whole pizza does each person get?
Answer:
11/24 ths each
Step-by-step explanation:
Add the portions left...then divide by the five of them
3/4 + 5/8 + 11/12 = ? must find common denominator (24) and convert
(18 + 15+22) / 24 = 55/24 now divide by 5 (which is the same as mult by 1/5)
55/24 * 1/5 = 55/120 now simplify to 11/24
When a weed solution is added to a lawn, the number of weeds can be represented by the function W(d)=1650(.85)d where d is the number of days since application. By what percent does the population of weeds decrease each day?
By 15% percent does the population of weeds decrease each day given that the function representing the number of weeds is W(d)=1650(0.85)^d. This can be obtained by using the function representing the exponential decay.
Find percent by which the population of weeds decrease each day:Number of weeds is represented by the function,
W(d)=1650(0.85)^d
⇒ W(d)=1650(1 - 0.15)^d
Here, d = number of days since application
Function representing the exponential decay is,
⇒ A(r) = A(1 - r)^t
where,
A = Initial value
r = Percentage decay
t = duration
By comparing the given function and function representing the exponential decay,
r = 0.15 ≈ 15/100
Or r = 15%
Therefore, population of weeds will decrease 15% each day.
Hence by 15% percent does the population of weeds decrease each day given that the function representing the number of weeds is W(d)=1650(0.85)^d.
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Which of the following represents a function?
The image on the left represents a function. The image on the right does not as a function cannot have multiple variables for a single X quantity.
Answer: A
Step-by-step explanation:
a function is the relation between the independent variable (x) and the dependent variable (y)the defining characteristics which differentiates a function from a relation is its input and output valuesa function can only have single input value that corresponds to a single output value, or an x value can only lead to one possible y value Option A Coordinates[tex](-5,3)\\(-3, 1)\\(-1,-1)\\(1, -1)\\(3, 1)\\(5, 3)[/tex]
each x value only leads to one possible y valuetherefore, option A is a functionshow that xcosec^2x = cotx - d/dx xcotx
The given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.
In the question, we are asked to show that x.cosec²x = cot x - d/dx x.cot x.
To prove, we go by the right-hand side of the equation:
cot x - d/dx x.cot x.
We solve the differential d/dx using the product rule, according to which, d/dx uv = u. d/dx(v) + v. d/dx(u), where u and v are functions of x.
cot x - {x. d/dx(cot x) + cot x. d/dx(x)}
= cot x - {x. (-cosec²x) + cot x} {Since, d/dx(cot x) = -cosec²x, and d/dx(x) = 1}
= cot x + x. cosec²x - cot x
= x. cosec²x
= The left-hand side of the equation.
Thus, the given equation, x.cosec²x = cot x - d/dx x.cot x, is proved using the product rule of differentials.
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Identify the 7th term of the geometric sequence in which a2 = 324 and a4 = 36.
Answer:
a7=4/3 or a7=-4/3
Step-by-step explanation:
using the geometric sequences formula
an=ar^n-1
a2=ar
a4=ar³
when a2=324 and a4=36
324=ar...........(1)
36=ar³............(2)
from equation (1) a=324/r substitute in equation (2)
we have :
36=324/r *r³
36=324r²
r²=36/324
r²=1/9
r=±1/3
substitute when r=±1/3 in (1)
324=a(±1/3)
a=±972
so the 7th term is
when r=±1/3
we have
a7=ar^6
a7=±972(±1/3)^6
a7=972/729
a7=4/3 or a7=-4/3
67 is the difference of Gail’s height and 16.
