The given sequence [tex]2^{\frac{1}{n} }[/tex] converges with limit 1.
According to the given question.
We have a sequence,
[tex]a_{n} = 2^{\frac{1}{n} }[/tex]
Since, we know that
The sequence of real numbers [tex]S_{n}[/tex], where n goes from 1 to infinity has a limit L, the the sequence is convergent to L. If the sequence doesn't have limit then it is divergent.
The nth root function is strictly increasing for positive real values.
Therefore,
[tex]1^{\frac{1}{n} } \leq 2^{\frac{1}{n} } \leq n^{\frac{1}{n} }[/tex] [tex]\forall \ n\geq 2[/tex]
Also,
[tex]\lim_{n \to \infty} n^{\frac{1}{n} } = 1[/tex]
[tex]\implies \lim_{n \to \infty} 1^{\frac{1}{n} } =1[/tex] ( by squeeze theorem)
Thereofore,
[tex]\lim_{n \to \infty}2^{\frac{1}{n} } =1[/tex]
So, the given sequecence has a limit i.e. 1. Which means [tex]2^{\frac{1}{n} }[/tex] is a convergent sequence.
Hence, the given sequence [tex]2^{\frac{1}{n} }[/tex] converges with limit 1.
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A clock has a diameter of 16 inches. How far does the hour hand travel during 5 hours? Use 3.14 for pi.
Therefore the hour hand travels 40.192in in 5 hours
A sector is said to be a part of a circle made of the arc of the circle along with its two radii.
The formula for calculating the area of a sector is expressed as;
A = r²β/2
where
r is the radius of the circle
β is the angle subtended
Since the the hour hand travel during 5 hours, the subtended angle by the sector will be;
β = 360/5
β = 72 degrees
Given the following parameters
r = 16/2
r = 8in
Substitute into the formula
A = 8²(72π)/360
A = 40.192in
Therefore the hour hand travels 40.192in in 5 hours
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Find lim f(x) if f(x)
x->5
=
{
-x² -1, x #5
-3, x=5
Given
[tex]f(x) = \begin{cases} -x^2 - 1 & \text{if }x \neq 5 \\ -3 & \text{if }x=5 \end{cases}[/tex]
we have
[tex]\displaystyle \lim_{x\to5} f(x) = \lim_{x\to5} (-x^2-1) = -5^2-1 = \boxed{-26}[/tex]
since we are approaching [tex]x=5[/tex], so effectively [tex]x\neq 5[/tex] and we use the definition of [tex]f(x)[/tex] under that condition.
A population of n = 10 scores has = 50 and = 5. what is the population variance? 5
The value of the Population Variance is 100.
According to the statement
we have given that the A population of N = 10 scores has μ = 50 and σ = 5. And we have to find the population variance.
So, For this purpose,
we know that the population variance can be defined as the average of the distances from each data point in a particular population to the mean squared, and it indicates how data points are spread out in the population.
Population variance = mean /(standard deviation/number of samples)
Population variance = μ / (σ /N )
Substitute the values in it and then
Population variance = 50 / (5 /10 )
Population variance = 50 / (0.5 )
Population variance = 100.
So, The value of the Population Variance is 100.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
A population of N = 10 scores has μ = 50 and σ = 5. What is the population variance?
a. 10
b. the square root of 5
c. the square root of 50
d. 25
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Which graph represents the function f(x)=(x+4)(x+1)(x−3)?
Answer:
your answer will be C .
Step-by-step explanation:
Last week a painter painted 6 houses in 2 days. this week she painted 5 houses in 4 days. in which week was the painter more productive?
Answer:
The painter was more productive in week a.
Step-by-step explanation:
Find the unit rate. How many houses could be painted in 1 day?
6/2 means that she could paint 3 houses per day
5/4 means that she could paint 1.25 houses per day.
The painter was more productive in the last week.
Explanation:In this problem, we need to find in which week did the painter paint the most.
To find the solution to this problem, first, we need to divide 6 by 2 (last week)
which equals 3.
Next, divide 5 by 4 (this week)
which equals 1.25
Now, compare the two quotients and identify the larger number (3 and 1.25).
Basically, we can see that the number 3 is larger.
This means that the painter could paint 3 houses per day in the last week, and 1.25 houses per day in this week.
Therefore, we can say that the painter was more productive in the last week.
I hope this helps :)
.
Find the value of x for which ABCD must be a parallelogram.
The value of x that would make ABCD a parallelogram is x = 5
How to find the interior angle of a parallelograms?A parallelogram, opposite sides are equal and parallel, which means opposite interior angles are equal.
Opposite sides of a parallelogram are congruent and parallel
Therefore,
5x - 3 = 14x - 48
subtract 5x from both sides
5x - 5x - 3 = 14x - 5x - 48
-3 = 9x - 48
add 48 to both sides
-3 + 48 = 9x - 48 + 48
45 = 9x
x = 45 / 9
x = 5
Therefore, the value of x that would make ABCD a parallelogram is x = 5
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The figure below is made of 222 rectangular prisms.
What is the volume of this figure?
A shape made up of two rectangular prisms. The first rectangular prism has a base that measures 9 inches length by 6 inches width, and has a height of 3 inches. The second rectangular prism sits behind the first rectangular prism. It has a base that measures 10 inches length by 7 inches width and has a height of 3 inches.
please help its a khan question and i have a timer :'D
Answer:
372 in^3.
Step-by-step explanation:
The volume of the first prism = 9*6*3
= 162 in^3.
Volume of second prism
= 10*7*3
= 210 in^3.
Total vol = 162 + 210
= 372 in^3.
The required volume of the composite prism is 372 cubic inches,
Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
here,
To determine the volume of the composite prism,
As we can see there is two rectangular prisms,
Calculate the volume of two individual prisms and add their volume to the composite volume of the figure.
The volume of the first prism
= lenght × width × height
= 9 × 6 ×3 = 162 in³
The volume of the second prism
= lenght × width × height
= 10 × 7 ×3 = 210 in³
The total volume of the composite figure = 162 + 210 = 372 in³.
Thus, the required volume of the composite prism is 372 cubic inches,
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The equations of two lines are given below.
3 x minus y equals 5
3 y equals x minus 15
Are these lines parallel, perpendicular, or neither?
The lines are neither parallel nor perpendicular
How to determine the relationship between the lines?The equations of the lines are given as
3 x minus y equals 5
3 y equals x minus 15
Rewrite the equations properly
3x - y = 5
3y = x - 15
Make y the subject in both equations
In 3x - y = 5, we have
y = 3x + 5
In 3y = x - 15, we have
y = 1/3x - 5
The slopes of the two lines are
m1 = 3
m2 = 1/3
The above values are not equal, and they are not opposite reciprocal
This means that the lines are neither parallel nor perpendicular
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A boat traveled 27 miles in 2 hours. at this rate how many miles will the boat travel in 1/2 hour
Answer:
6.75
Step-by-step explanation:
Distance in Miles
MPH -------------------------
Time in Hours
27/2 = 13.5. That is 1 hour. Half that and you get 6.75 MP1/2H
Find the area of the shaded region if the dimensions of the unshaded region are 12ft x 20ft . use 3.14 for π as necessary.
The area of the shaded region = 810.66 ft²
What is rectangle?
A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees. Hence, it is also called an equiangular quadrilateral. Since, the opposite sides are equal and parallel, in rectangle, therefore, it can also be termed as a parallelogram.Area of Shaded region:
(12+2*7)*20 - 12*20 + 3.14*((12+2*7)/2)² =
14*20 + 530.66 =
810.66 ft²
Therefore, the area of the shaded region = 810.66 ft²
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An78swer:
Step-by-step explanation:
If no denominator equals zero , which expression is equivalent to
Answer: Choice D
[tex]\frac{-19}{\text{x}-5}[/tex]
=================================================
Work Shown:
[tex]\frac{\text{x}^2+10\text{x}+25}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}+5)}{\text{x}+5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}+5}{1} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{(\text{x}+5)(\text{x}-5)}{1(\text{x}-5)} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\[/tex]
[tex]\frac{\text{x}^2-25}{\text{x}-5} - \frac{\text{x}^2-6}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-(\text{x}^2-6)}{\text{x}-5}\\\\\\\frac{\text{x}^2-25-\text{x}^2+6}{\text{x}-5}\\\\\\\frac{-19}{\text{x}-5}\\\\\\[/tex]
This matches with choice D as the final answer.
Keep in mind that we can only subtract fractions when the denominator is the same. The rule is [tex]\frac{a}{c}-\frac{b}{c} = \frac{a-b}{c}[/tex]
A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. event a is defined as drawing a black tile from the bag on the first draw, and event b is defined as drawing a white tile on the second draw. if two tiles are drawn from the bag, one after the other without replacement, what is p(a and b) expressed in simplest form?
P(A and B) expressed in the simplest form is (B) 2/21.
What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To express P(A and B) in the simplest form:
P(A and B) means that you need to multiply the two probabilities together since both A and B need to happen. The probability of drawing a black tile on the first draw is 4/15 since there are 15 total tiles and 4 of those are black. On the second draw, the bag is already missing a tile, and there are therefore 14 tiles remaining. For the second one, the probability is 5/14, since there are 14 total tiles and 5 of them are white. Multiplying these two together, we get 4/15 × 5/14 = 20 / 210 = 2/21.Therefore, P(A and B) expressed in the simplest form is (B) 2/21.
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The complete question is given below:
A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. Event A is defined as drawing a black tile from the bag on the first draw, and event B is defined as drawing a white tile on the second draw.
If two tiles are drawn from the bag, one after the other without replacement, what is P(A and B) expressed in the simplest form?
A. 4/45
B. 2/21
C. 4/15
D. 5/14
-6(4x + 5) = -24x - 30 associative property of addition commutative property of multiplication distributive property inverse property of addition
Answer:
distributive property
Step-by-step explanation:
Which number has a repeating decimal form?
A. sqrt{15
B. 11/25
C. 3/20
D. 2/6
Answer:
D It repeats
Step-by-step explanation:
square root of 15 is 3.87298334621
11/25= 0.44
3/20=.6
D = 0.33333333333
please help me if you can
The time, t in seconds that it takes a car to travel a quarter-mile when starting from a full stop can be estimated by using the formula:
[tex]t=5.825\sqrt[3]{w/p\\}[/tex]
Where w = weight of the car
p = power delivered by the engine in horsepower (hp)
If the quarter-mile time for a 3,590-pound car is 13.4 s, how much power does its engine deliver? Round to the nearest pound.
Two students solved this problem. Natasha’s answer was 295 hp and Daniel’s was 679 hp. Why was Daniel wrong? Show each step that led Daniel to the wrong answer
Natasha got the power right. The power is 295 hp.
How to calculate power?t = 5.825∛w / p
where,
w = weight of the carp = power delivered by the engine in horsepowerquarter mile time = tTherefore,
t = 13.4 s
p = 3590
13.4 = 5.825∛ 3590 / p
cube both sides
13.4³ = 5.825³ × 3590 / p
2406.104 = 197.645890625 × 3590 / p
cross multiply
2406.104 p = 709548.747344
p = 709548.747344 / 2406.104
p = 294.895294361
p = 295 hp
Therefore, Natasha got the power right
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Which of the following alternatives are similar monomials?
a) 8x and -7x
b) 5a² and 5a
c) 4 and -17
d) 2ab and 3abc
e) -3ab and 9abc
f) - [tex]\frac{x}{3}[/tex] and 11x
The alternatives that are similar monomials are given as follows:
a) 8x and -7x.
c) 4 and -17.
f) -x/3 and 11x.
What are similar monomials?Similar monomials are monomials in which the part with the letters are equal. For example, 8x and -7x, as x = x, or even 9x²y and -2x²y, as x²y = x²y.
Hence options a, c and f are correct in this problem.
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Last week the value of an investment changed at a rate of -$3.15 each day. After How many days was the total change in value -$12.60?
In four days,the total change in value -$12.60.
According to the statement
we have given that the value of an investment changed at a rate of -$3.15 each day. And we have to find that the after how many days the change in value reaches at the -$12.60.
So, here we use division rule to find the solution.
The given change value is :
-$3.15 each day.
The desired change value is :
-$12.60.
Number of days required = -12.60 / -3.15
Number of days required = 12.60 / 3.15
Number of days required = 4 days.
So, in four days the change in value reaches at the desired value of change.
So, In four days,the total change in value -$12.60.
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A sports teacher divided a class into two groups. Three-fifth of the first group and 80% of the second group play soccer.
What fraction of the class plays soccer?
Answer:
7/5
Step-by-step explanation:
80/100 = 0.8 = 8/10 = 4/5 (to the simplest fraction).(three-fifth) 3/5 + 4/5 = 7/57/5 of the class plays soccer ✅Hope this helpsGood luck ✅In the year 2000, there were 200,000 cell phone subscribers in a city in new york. the number of subscribers increased by 60 percent per year after 2000. which equation can be used to model the number of subscribers, y, in the city t years after 2000?
The equation can be used to model the number of subscribers, y, in the city t years after 2000 is y = 200,000(1+60)t.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
The first step is to calculate the percentage increase for each year.
If the subscribers increase by 60%, it means that the subscribers will be (100+60)% of the previous year.
(100+60)% = (100/100 + 60/100)
= (1 + 0.6)
After 2,000, the subscribers will be 200,000×(1+0.6).
For the following years the 200,000×(1+0.6)t
So, the value of y will be given by,
Y=200,000(1+0.6)t
Hence,The equation Y=200,000(1+0.6)t .
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Suppose 5 different integers are randomly chosen from between 20 and 69, inclusive. What is the probability that they each have a different tens digit?
The probability that they each have a different tens digit is 0.047.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin. The probability of either "heads" or "tails" is half because there are only two possible outcomes (heads or tails), and because the coin is fair, both outcomes (heads and tails) are equally likely.
Solution:- The collection contains 50 integers, hence there are [tex]^{50}C_5[/tex] different ways to select 5 different integers.
Sample space = [tex]^{50}C_5[/tex]
Each of the five numbers must correspond to one of the five available tens-digits, which are 2 through 6. There are a total of 105 ways to choose the five numbers that satisfy these properties because there are 10 ways to choose a number with a particular set of ten digits (such as 30, 31, or 39).
Therefore,
probability that each have a different tens digit = [tex]\frac{10^5}{^{50}C_5}[/tex]
= [tex]\frac{10\times 10\times 10\times 10\times 10}{^{50}C_5}[/tex]
= [tex]\frac{10\times 10\times 10\times 10\times 10}{\frac{50!}{(50-5)!5!} }[/tex]
= [tex]\frac{10\times 10\times 10\times 10\times 10}{\frac{50!}{45!5!} }[/tex]
= 0.047
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Two parallel lines are cut by a transversal. Complete the following statements.
The consecutive interior angles is...
supplementary, complementary, congruent
The alternate interior angles is...
supplementary, complementary,congruent
To complete the statements;
The consecutive interior angles is supplementary
The alternate interior angles is congruent
Properties of parallel lines cut by a transversal
The properties are;
Corresponding Angles are congruentAlternate Exterior Angles are congruentAlternate Interior Angles are congruentConsecutive Interior Angles sum to 180 degrees, that is, they are supplementaryConsecutive interior angles are supplementary
Alternate interior angles are congruent
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The floor of a rectangular room measures 5m by 4m and the ceiling is 3m from the floor. An ant is at the top of a corner of the room and crawls to the opposite bottom corner of the room. Find the shortest distance it can travel. (Cannot do its diagonal distance)
Answer:
12 m
Step-by-step explanation:
Well, imagine you got this nice room. How can it reach the other corner? It has to go along the 3 dimensions. So the shortest path would be: 5 + 4 + 3 12m
Answer:
3 + √(41) = 9.4 m (nearest tenth)
Step-by-step explanation:
The room can be modeled as a rectangular prism with:
width = 4 mlength = 5 mheight = 3 mIf the ant is at the top of a corner of a room and crawls to the opposite bottom corner of the room, the shortest distance will be to travel down one vertical edge of the room then to travel the diagonal of the floor of the room (or to travel the diagonal of the ceiling and then one vertical edge).
Vertical edge = height of room = 3m
The diagonal of the floor (or ceiling) is the hypotenuse of a right triangle with legs of the width and length. Therefore, to find the diagonal, use Pythagoras Theorem.
Pythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right trianglec is the hypotenuse (longest side) of the right triangleGiven:
a = width = 4 mb = length = 5 mc = diagonalSubstitute the given values into the formula and solve for c:
[tex]\implies 4^2+5^2=c^2[/tex]
[tex]\implies c^2=41[/tex]
[tex]\implies c=\sqrt{41}[/tex]
Therefore, the shortest distance the ant can travel is:
⇒ 3 + √(41) = 9.4 m (nearest tenth)
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The measure of angle is 5. The equivalent measurement in degrees is...
Answer:
300 degrees
Step-by-step explanation:
pi should be 180 degrees so 5*180/3 = 5*60=300
Which solution finds the value of x in the triangle below?
A right triangle is shown. The hypotenuse has a length of 8. Another side has a length of x. The angle between the hypotenuse and the other side is 60 degrees.
Secant 60 degrees = StartFraction 8 Over x EndFraction. 2 = StartFraction 8 Over x EndFraction. 2 x = 8. x = 4.
Cosecant 60 degrees = StartFraction 8 Over x EndFraction. StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction = StartFraction 8 Over x EndFraction. x times 2 StartRoot 3 EndRoot = 24. x = StartFraction 24 Over 2 StartRoot 3 EndRoot EndFraction. x = StartFraction 12 Over StartRoot 3 EndRoot EndFraction times StartFraction StartRoot 3 EndRoot Over StartRoot 3 EndRoot EndFraction. x = StartFraction 12 StartRoot 3 EndRoot Over 3 EndFraction. x = 4 StartRoot 3 EndRoot.
Secant 60 degrees = StartFraction 8 Over x EndFraction. One-half = StartFraction 8 Over x Endfraction. x = 16
Cosecant 60 degrees = StartFraction 8 Over x EndFraction. StartFraction StartRoot 3 EndRoot Over 2 EndFraction = StartFraction 8 Over x EndFraction. x times StartRoot 3 EndRoot = 16. x = StartFraction 16 Over StartRoot 3 EndRoot EndFraction. x = StartFraction 16 Over StartRoot 3 EndRoot EndFraction times StartFraction StartRoot 3 EndRoot Over StartRoot 3 EndRoot EndFraction. x = StartFraction 16 StartRoot 3 EndRoot Over 3 EndFraction.
The value of x in the triangle is 4
How to determine the solutions?The complete question is added as an attachment
From the question, the given parameters are as follows:
Hypotenuse = 8
Adjacent = x
Angle = 60
The cosine of the angle is then calculated as:
cos(angle) = Adjacent/Hypotenuse
Substitute the known values in the above equation
cos(60) = x/8
Multiply both sides by 8
x = 8 * cos(60)
Evaluate the product
x = 4
Hence, the value of x in the triangle is 4
So, the complete parameters are:
Hypotenuse = 8
Adjacent = x
Angle = 60
x = 4
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Answer:
Secant 60 degrees = StartFraction 8 Over x EndFraction. 2 = StartFraction 8 Over x EndFraction. 2 x = 8. x = 4.
Step-by-step explanation:
The answer above is correct.
Please Help me its a math question i will give brainlist please !!! the image is attached
Answer:
D
Step-by-step explanation:
When you reflect the point it goes to point (-2,5). From that point, go 4 left and 8 down. That gets you to (-2,-3)
86cm, 132cm,1m 6cm, 1.6m, 1m 20cm, 1.15m Arrange the heights in order of size, starting with the smallest to the Tallest
Answer:
6cm,20cm,80cm,1m,1m,1.15m,132cm
Step-by-step explanation:
Hence,1 m=100 cm
What step would be necessary if you wished to conduct a poll with a margin of error of zero?
The necessary step would be we would have to get every respondent in the population to participate if you wished to conduct a poll with a margin of error of zero.
What is a poll?An opinion poll, often known as a poll or a survey, is a human research survey of public opinion from a specific sample. Opinion polls are often designed to depict a population's opinions by asking a series of questions and then extrapolating generalities in ratio or within confidence intervals. A pollster is somebody who conducts polls.If we were to conduct a poll with a margin of error of zero, we would need to recruit every responder in the population to participate.As it is given in the description itself, if we were to conduct a poll with a margin of error of zero, we would need to recruit every responder in the population to participate.
Therefore, the necessary step would be we would have to get every respondent in the population to participate if you wished to conduct a poll with a margin of error of zero.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each series with the equivalent series written in sigma notation
The series and the sigma notations are[tex]\sum\limits^4_0 3(5)^n = 3 + 15 +75 + 375 +1875[/tex], [tex]\sum\limits^4_0 4(8)^n = 4 + 32 + 256+ 2048 + 16384[/tex], [tex]\sum\limits^4_0 2(3)^n = 2 + 6 + 18 + 54 + 162[/tex] and [tex]\sum\limits^4_0 5(3)^n = 5 + 15 + 45 + 135 + 405[/tex]
How to match each series with the equivalent series written in sigma notation?To do this, we simply expand each sigma notation.
So, we have:
[tex]\sum\limits^4_0 3(5)^n[/tex]
Next, we set n = 0 to 4.
So, we have:
3(5)^0 = 3
3(5)^1 = 15
3(5)^2 = 75
3(5)^3 = 375
3(5)^4 = 1875
So, we have:
[tex]\sum\limits^4_0 3(5)^n = 3 + 15 +75 + 375 +1875[/tex]
[tex]\sum\limits^4_0 4(8)^n[/tex]
Next, we set n = 0 to 4.
So, we have:
4(8)^0 = 4
4(8)^1 = 32
4(8)^2 = 256
4(8)^3 = 2048
4(8)^4 = 16384
So, we have:
[tex]\sum\limits^4_0 4(8)^n = 4 + 32 + 256+ 2048 + 16384[/tex]
[tex]\sum\limits^4_0 2(3)^n[/tex]
Next, we set n = 0 to 4.
So, we have:
2(3)^0 = 2
2(3)^1 = 6
2(3)^2 = 18
2(3)^3 = 54
2(3)^4 = 162
So, we have:
[tex]\sum\limits^4_0 2(3)^n = 2 + 6 + 18 + 54 + 162[/tex]
[tex]\sum\limits^4_0 5(3)^n[/tex]
Next, we set n = 0 to 4.
So, we have:
5(3)^0 = 5
5(3)^1 = 15
5(3)^2 = 45
5(3)^3 = 135
5(3)^4 = 405
[tex]\sum\limits^4_0 5(3)^n = 5 + 15 + 45 + 135 + 405[/tex]
Hence, the series and the sigma notations are[tex]\sum\limits^4_0 3(5)^n = 3 + 15 +75 + 375 +1875[/tex], [tex]\sum\limits^4_0 4(8)^n = 4 + 32 + 256+ 2048 + 16384[/tex], [tex]\sum\limits^4_0 2(3)^n = 2 + 6 + 18 + 54 + 162[/tex] and [tex]\sum\limits^4_0 5(3)^n = 5 + 15 + 45 + 135 + 405[/tex]
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find the domain and range
Answer:
domain should be x=1
range is all real numbers
Step-by-step explanation:
Answer:domain should be x=1
range is all real numbers
Step-by-step explanation:
Evacuate the following using suitable identities (102)^3
The value of [tex](102)^3[/tex] exists 1061208.
How to estimate the value of [tex](102)^3[/tex]?Let us rewrite [tex](102)^3[/tex] as [tex](100+2)^3[/tex]
Now utilizing the identity [tex](a+b)^3=a^3+b^3+3ab(a+b)[/tex], we get
a = 100 and b = 2 then substitute the values of a and b then
[tex](100+2)^3=100^3+2^3+[(3\times100\times2)(100+2)][/tex]
= 1000000 + 8 + (600 × 102)
= 1000000 + 8 + 61200
= 1061208
Hence, [tex](102)^3=1061208[/tex]
Therefore, the value of [tex](102)^3[/tex] exists 1061208.
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