What's the equation of the axis of symmetry of g(x)=x^{2}+4 x+3?A) x=0B) x=-2C) x=2D) x=3
Answers
Given a quadratic equation of the form:
[tex]f(x)=ax^2+bx+c[/tex]The equation of the axis of symmetry is obtained using the formula:
[tex]x=-\frac{b}{2a}[/tex]From the given quadratic equation:
[tex]\begin{gathered} g\mleft(x\mright)=x^2+4x+3 \\ a=1 \\ b=4 \end{gathered}[/tex]Therefore, the equation of the axis of symmetry of g(x) is:
[tex]\begin{gathered} x=-\frac{4}{2\times1} \\ x=-2 \end{gathered}[/tex]The correct option is B.
Related Questions
Based on the graph of f(x) shown here what is f^-1(8).
Answers
Answer
2
Explanation:
f⁻¹(8) is equal to the value of x that makes f(x) = 8. So, taking into account the graph, we get:
Therefore, f⁻¹(8) = 2. So the answer is 2
Floyd is an aspiring music artist. He has arecord contract that pays him a base rate of$200 a month and an additional $12 for eachalbum that he sells. Last month he earned atotal of $644.Write an equation to determine the numberof albums (a) Floyd sold last month.Find the number of albums Floyd sold lastmonth.albums
Answers
Explanation:
Equate the given data to solve for x.
$200 + $12x = $644.
To determine the number of albums sold, Let x be the number of album sold by Floyd last month.
200 + 12x = 644
12x =644-200
12x = 444
x = 444/12
x= 37.
Floyd has sold 37 albums last month.
Answer:
The equation to determine the number of albums Floyd sold last month is 200+12x = 644.
and the number of album Floyd sold last month is 37.
For triangle ABC, AB = 3 cm and BC = 5 cm.Which could be the measure of AC?A 2 cmB 4 cmC 8 cmD 15 cm
Answers
ANSWER
2, 4 and 8
EXPLANATION
We have that in a triangle ABC, AB = 3 cm and BC = 5 cm.
To find the possible length of AC, we can apply the triangle inequality theorem.
It states that in any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
This means that:
[tex]\begin{gathered} AB\text{ + AC }\ge\text{ BC} \\ \text{and } \\ AB\text{ + BC }\ge\text{ AC} \\ \text{and} \\ AC\text{ + BC }\ge\text{ AB} \end{gathered}[/tex]So, we have that:
[tex]\begin{gathered} 3\text{ + AC }\ge\text{ 5 }\Rightarrow\text{ AC }\ge\text{ 2} \\ 3\text{ + 5 }\ge\text{ AC }\Rightarrow\text{ AC }\leq\text{ 8} \\ AC\text{ + 5 }\ge3\Rightarrow\text{ AC }\ge\text{ -2} \end{gathered}[/tex]We have to disregard the third line, since the length of a triangle side can only be positive.
So, using the first 2 lines, we see that:
[tex]2\text{ }\leq\text{ AC }\leq\text{ 8}[/tex]This means that from the options, the measure of AC can either be 2, 4 or 8.
A person investigating to employment opportunities. They both have a beginning salary of $42,000 per year. Company A offers an increase of $1000 per year. Company B offers 7% more than during the preceding year. Which company will pay more in the sixth year? what will company A pay? and what will company B pay?
Answers
qANSWER
Company B will pay more
Company A =
EXPLANATION
Both companies start by paying $42,000 per year.
Company A offers an increase of $1000 per year.
This means that after n years, he would have earned:
Earnings = 42000 + 1000n
where n = number of years after the first year
So, after 6 years, he would have worked 5 years after the first, so his earnings would be:
Earnings = 42000 + 1000(5) = 42000 + 5000
Earnings = $47000
Company B offers 7% more than the previous year. That means that his earnings are compounded.
His earnings can then be represented as:
[tex]\text{ Earnings = P(1 + }\frac{r}{100})^t[/tex]where P = initial salary = $42000
r = interest rate = 7%
t = number of years spent = 6 years
Therefore, his earnings after the 6th year will be:
[tex]\begin{gathered} \text{ Earnings = 42000(1 + }\frac{7}{100})^6 \\ \text{ Earnings = 42000(1 + 0.07)}^6=42000(1.07)^6 \\ \text{ Earnings = }42000\cdot\text{ 1.501} \\ \text{Earnings = \$63042} \end{gathered}[/tex]He would have earned $63042.
Therefore, Company B will pay more.
qANSWER
Company B will pay more
Company A =
EXPLANATION
Both companies start by paying $42,000 per year.
Company A offers an increase of $1000 per year.
This means that after n years, he would have earned:
Earnings = 42000 + 1000n
where n = number of years after the first year
So, after 6 years, he would have worked 5 years after the first, so his earnings would be:
Earnings = 42000 + 1000(5) = 42000 + 5000
Earnings = $47000
Company B offers 7% more than the previous year. That means that his earnings are compounded.
His earnings can then be represented as:
[tex]\text{ Earnings = P(1 + }\frac{r}{100})^t[/tex]where P = initial salary = $42000
r = interest rate = 7%
t = number of years spent = 6 years
Therefore, his earnings after the 6th year will be:
[tex]\begin{gathered} \text{ Earnings = 42000(1 + }\frac{7}{100})^6 \\ \text{ Earnings = 42000(1 + 0.07)}^6=42000(1.07)^6 \\ \text{ Earnings = }42000\cdot\text{ 1.501} \\ \text{Earnings = \$63042} \end{gathered}[/tex]He would have earned $63042.
Therefore, Company B will pay more.
Been out of school for health issues trying to catch up work thanks!!
Answers
DEFINITIONS
The union of two sets contains all the elements contained in either set (or both sets). The union is notated A ⋃ B.
The intersection of two sets contains only the elements that are in both sets. The intersection is notated A ⋂ B.
Using a Venn Diagram, the union and intersection of two sets can be seen below:
GIVEN
The sets are given to be:
[tex]\begin{gathered} S=\mleft\lbrace1,2,3,\ldots,18,19,20\mright\rbrace \\ A=\mleft\lbrace3,4,8,9,11,13,14,15,20\mright\rbrace \\ B=\mleft\lbrace4,7,13,14,16,18,19\mright\rbrace \end{gathered}[/tex]QUESTION
1) (A ∪ B): The terms of the two sets contained in either set or the two sets are
[tex](A\cup B)=\mleft\lbrace3,4,7,8,9,11,13,14,15,16,18,19,20\mright\rbrace[/tex]2) (A ∩ B): The elements that are in both sets are
[tex](A\cap B)=\mleft\lbrace4,13,14\mright\rbrace[/tex]Convert 7 liters into gallons using measurement conversion 1 liter= 1.0567 quarts. Round to two decimals
Answers
Convert 7 liters into gallons
We have the measurement conversion 1 liter= 1.0567 quarts
and the gallons = 4 quarts
So, 7 liters = 7 * 1.0567 quarts = 7.3969 quarts
We will convert from the quarts to gallons as follows:
1 gallons = 4 quarts
x gallons = 7.3969 quarts
so, the value of x will be:
[tex]x=\frac{7.3969}{4}=1.849225[/tex]Round to two decimals
so, the answer will be 1.85 gallons
To the right is the graph of f(x) = x^2. The second graph, to the left of f(x) = x^2 is a new function made by stretching f(x) vertically by a factor of 2 and then translating it three units to the left and one unit down. Write the equation of the new function.
Answers
This problem invloves the topic of curved lines in a graph, curved lines or more speccifically curve line which looks like letter C (parabola) all follows a certain standard form of equation, which is;
[tex]y=ax^2+b[/tex]For example you can see that the equation for the black curve line in our picture is y=x² and notice that this equation can also be written as y = (1)x² + 0. Which simillar to the standard form given above where a is just 1 (a=1) and b is just 0 (b=0).
Since our black curve line follows the same standard form of equation as stated above, we can conclude that the RED curve line follows the same form of equation.
To summarize the steps that we must do in order to find the equation of the RED line we will list them as,
1. Sample two(2) points in the graph to be used as reference points.
2. Use the sampled points in our standar eqation in order to find the variables "a" and "b".
3. When we have the variables "a" and "b", we can just directly substitute it into our standard equation to find the equation of our RED line.
Let's start.
1. Sample 2 points to be used as refernce points. (Note that we will find the easiest points
to determine)
Let us use the points (-3, -1) and (-2, 1) as shown in the picture.
2. Use the points (-3, -1) and (-2, 1) in our standard equation.
[tex]\begin{gathered} y=ax^2+b \\ \text{where (x,y)=(-3, -1)} \\ -1=a(-3)^2+b_{} \\ 9a+b=-1 \end{gathered}[/tex]
for our 1st point we have the equation 9a+b = -1, let us now proceed to our next point.
[tex]\begin{gathered} y=ax^2+b \\ \text{where (x,y)=(-2, 1)} \\ 1=a(-2)^2+b_{}_{} \\ 1=4a+b \\ 4a+b=1 \end{gathered}[/tex]and for our 2nd point we have the equation 4a+b = 1, and by the process of subtitution and elimination we can now find "a" and "b", because we have two equations with two unknowns.
[tex]\begin{gathered} 9a+b=-1\text{ and} \\ 4a+b=1 \end{gathered}[/tex]transforming eqatuin number 1 to
[tex]9a+b=-1\text{ is just the same as b = -1 -9a}[/tex]
then substitue b = -1 -9a to the 2nd equation we have.
[tex]\begin{gathered} 4a+b=1\text{ , where b = -1-9a} \\ 4a+(-1-9a)=1 \\ 4a-1-9a=1 \\ -5a=2 \\ a=-\frac{2}{5} \end{gathered}[/tex]
since a = -2/5, we can find b using,
[tex]\begin{gathered} 4a+b=1\text{ , where a=-}\frac{2}{5} \\ 4(-\frac{2}{5})+b=1 \\ b=1+\frac{8}{5} \\ b=\frac{5}{5}+\frac{8}{5} \\ b=\frac{13}{5} \end{gathered}[/tex]therefore our a and b are;
[tex]a=-\frac{2}{5}\text{ and b = }\frac{13}{5}[/tex]3. We can now proceed in substituting it in our standard equation;
[tex]\begin{gathered} y=ax^2+b\text{ , where a = -}\frac{2}{5}\text{ and b = }\frac{13}{5} \\ y=(-\frac{2}{5})x^2+(\frac{13}{5}) \\ y=-\frac{2}{5}x^2+\frac{13}{5} \end{gathered}[/tex]you can also simplify the final equation by multiplying all sides by 5,
[tex]\begin{gathered} 5y=(5)\lbrack-\frac{2}{5}x^2+\frac{13}{5}\rbrack \\ 5y=-2x^2+13 \end{gathered}[/tex]therefore our final answer can be,
[tex]\begin{gathered} f(x)=-\frac{2}{5}x^2+\frac{13}{5} \\ or \\ 5y=-2x^2+13 \end{gathered}[/tex]
OB. 1OC.If X = 24 inches, Y = 45 inches, and Z= 51 inches, what is the tangent of ZA?OA. 19715NOD. 1B
Answers
Given that
We have a right-angled triangle and have to find angle A's tangent.
Explanation -
The triangle is shown as
Here we have,
X = 24 inches
Y = 45 inches
Z = 51 inches
Then, the tangent of angle A will be
[tex]\begin{gathered} The\text{ formula for the tangent is } \\ tan=\frac{Perpendicular}{Base} \\ \\ tan=\frac{P}{B} \\ For\text{ angle A thevalues are, P = 45 and B = 24} \\ Then, \\ tanA=\frac{45}{24} \\ \\ tanA=\frac{15}{8} \end{gathered}[/tex]So the correct option is B.
Final answer -
Therefore the final answer is 15/8A new shopping mall is gaining in popularity. Every day since it opened, the number of shoppers is 20%, percent more than the number of shoppers the day before. The total number of shoppers over the first 4 days is 671.How many shoppers were at the mall on the first day?Round your final answer to the nearest integer.
Answers
if the number of shoppers increases by 20% daily and 671 shoppers had visited over 4 days then let the num ber of shoppers on the first day be x
The numebr of shopperes the next day will be
= x(100 + 20)%
= 1.2x
teh number of shoppers the day after
= 1.2x(100 + 20)%
= 1.44x
the next day, the number
= 1.44x (100 + 20)%
= 1.728x
Given that the total number of people that have shopped after 4 days is 671 then
x + 1.2x + 1.44x + 1.728x = 671
5.368x = 671
x = 671/5.368
= 125
if the number of shoppers increases by 20% daily and 671 shoppers had visited over 4 days then let the num ber of shoppers on the first day be x
The numebr of shopperes the next day will be
= x(100 + 20)%
= 1.2x
teh number of shoppers the day after
= 1.2x(100 + 20)%
= 1.44x
the next day, the number
= 1.44x (100 + 20)%
= 1.728x
Given that the total number of people that have shopped after 4 days is 671 then
x + 1.2x + 1.44x + 1.728x = 671
5.368x = 671
x = 671/5.368
= 125
AMNP ~ AQRP N x + 8 28 M 24 P 3x - 9 R Create a proportion and find the length of side PR*
Answers
Using thales theorem:
[tex]\begin{gathered} \frac{24}{28}=\frac{x+8}{3x-9} \\ 24(3x-9)=28(x+8) \\ 72x-216=28x+224 \\ 44x=440 \\ x=\frac{440}{44} \\ x=10 \\ PR=3(10)-9=21 \end{gathered}[/tex]sean earns $300 in a regular work week. A regular work week for sean consists of 5 work days with 8 hours a day. How much money does sean earn each hour
Answers
Solution:
According to the problem, a regular work week consists of 5 work days with 8 hours a day. This is equivalent to say:
5 x 8 hours every regular work week.
That is:
40 hours every regular work week
then, the money earned per hour is:
[tex]\frac{300\text{ }dollars}{40\text{ hours}}\text{ = 7.5 dollars per hour}[/tex]then we can conclude that the correct answer is:
$7.5
Which is an equivalent expression for 4 times d raised
to the negative third power all over quantity 18 times d
raised to the ninth power end quantity?
Answers
Answer:
2d⁻³/9d⁻⁹
Step-by-step explanation:
4 times d raised to the negative third power = (4 × d)⁻³ = 4d⁻³
18 times d raised to the ninth power = (18 × d)⁻⁹ = 18d⁻⁹
the equation as a quotient:
Expression = 4d⁻³/18d⁻⁹
Expression = 2d⁻³/9d⁻⁹
In the matrix equation below, what are the values of x and y? 1/2 [4 8 x+3 -4] -3 [1 y+1 -1 -2]= [-1 -5 7 4]
Answers
Using the matrix equation, the value of x and y are 5 and 2 respectively.
Consider the 2 by 2 matrix equations,
1/2 [ 4 8 ( x + 3 ) - 4 ] - 3[ 1 y+1 -1 - 2 ] = [ - 1 -5 7 4 ]
[ 2 4 (x+3)/2 -2] + [ - 3 -3y -3 +3 + 6] = [ - 1 - 5 7 4]
[ -1 -3y + 1 (x + 9)/2 + 4] = [ - 1 - 5 7 4]
Therefore,
- 3y + 1 = - 5
Subtracting 1 from each side of the equation,
- 3y + 1 - 1 = - 5 - 1
- 3y = - 6
Dividing each side of the equation by - 3,
y = 2
And;
( x + 9 )/2 = 7
Multiplying each side by 2,
x + 9 = 14
Subtracting 9 from each side of the equation,
x + 9 - 9 = 14 - 9
x = 5
Therefore, the value of x and y is 5 and 2 respectively.
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In a right triangle, one of the acute angles measures of degrees. What is the measure of the other acute angle?
A. 90-d
B. 90 d
C. 180-d
D. 180+d
Answers
The correct answer is A. 90 - d
Since the sum of all the angles in a triangle is 180° and one of the angle is 90° because the triangle is a right triangle. So the sum of the remaining angles is 90°.
And to find the other acute angle we use 90° - d.
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Writing the equation of a quadratic function given its graph
Answers
Answer:
[tex]y=-(x-1)^2+2[/tex]Step-by-step explanation:
A quadratic function in vertex form is represented as:
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the vertex} \end{gathered}[/tex]Given the vertex (1,2) substitute it into the function:
[tex]y=a(x-1)^2+2[/tex]As you can see, we still do not know the value for ''a'', use the point given (4,-7) substitute it (x,y) and solve for ''a'':
[tex]\begin{gathered} -7=a(4-1)^2+2 \\ -7=a(3)^2+2 \\ -7=9a+2 \\ 9a=-7-2 \\ a=-\frac{9}{9} \\ a=-1 \end{gathered}[/tex]Hence, the equation of the function would be:
[tex]y=-(x-1)^2+2[/tex]7-Which beans are the better deal? Kidney Beans $1.18 per lb O Lima Beans $213 for 2 lbs 76-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 or .00, so if answer is 43 cents, its 0.43 or.43, if there is a dollar amount like 1.50, do not add zeros in front).
Answers
Given :
Two kinds of Beans :
1. Kidney Beans $1.18 per lb
The unit price = $1.18
2. O Lima Beans $213 for 2 lbs
The unit price = 2.13/2 = 1.065
Rounding to the nearest hundredth
So,
The unit
Mary estimates the weight of her cat to be 10 pounds.the actual weight of the cat is 13.75 pounds.find the percent error.
Answers
The percentage error is the ratio of the difference between the two readings and the actual
Error = 13.75 - 10
= 3.75
Percent error = 3.75/13.75
= 27.27%
Two airplanes are flying in the air at the same height. Airplane A is flying east at 451 mi/h and airplane B is flying north at 494 mi/h. If they are both heading to the same airport, located 3 miles east of airplane A and 3 miles north of airplane B, at what rate is the distance between the airplanes changing?
Answers
The rate at which the distance between the airplanes is changing is 668.2 mi/h.
In the given question,
Speed of Airplane A:
dA/dt = 451 mi/h
and the Speed of Airplane B:
dB/dt = 494 mi/h
Aircraft A and B will form a right triangle because Aircraft A is flying east and Aircraft B is flying north, and we can use Pythagoras' theorem to calculate their distance from one another.
Let P be the distance.
P² = A² + B²
Differentiating the above equation with respect to t,
2P(dP/dt) = 2A(dA/dt) + 2B(dB/dt)
Dividing each side of the equation by 2,
P( dP/dt ) = A( dA/dt ) + B( dB/dt ) ..........(1)
Where dP/dt is the rate of change in distance between the two aircraft.
Now,
P² = A² + B²
P = √(A² + B²)
Substituting, A = 3 miles and B = 3miles;
P = √(3² + 3²)
P = √( 9+ 9)
P = √18
P = 3√2 miles
Substituting the value in the equation (i)
3√2 (dP/dt) = (3× 451) + (3× 494)
3√2 (dP/dt) = 2835
4.2426 × dP/dt = 2835
dP/dt = 2835/4.2426
dP/dt = 668.2 mi/h
Therefore, the rate at which the distance between the airplanes is changing is 668.2 mi/h
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50% of $277 is $144True or False
Answers
Answer:
FALSE
Explanation:
Given the expression
50% of $277
This can also be written as;
= 50/100 * 277
= 1/2 * 277
= 277/2
= 138.5
Therefore 50% of $277 is $138.5 not $144 rendering the question FALSE
We have a box with a circular base (diameter 20 cm) and height 4 cm.Calculate the volume.
Answers
We can calculate the volume as the product of the area of the base and the height.
The area of the base is function of the square of the diameter, so we can write:
[tex]\begin{gathered} V=A_b\cdot h \\ V=\frac{\pi D^2}{4}\cdot h \\ V\approx\frac{3.14\cdot(20\operatorname{cm})^2}{4}\cdot4\operatorname{cm} \\ V\approx\frac{3.14\cdot400\operatorname{cm}\cdot4\operatorname{cm}}{4} \\ V\approx1256\operatorname{cm}^3 \end{gathered}[/tex]Answer: the volume of the box is 1256 cm^2.
Braden goes to the store to buy earmuffs. The sign says they were originally $13.50 but they are on sale for 15% off. What is the cost of the earmuffs now
Answers
Answer:
$11.48
Step-by-step explanation:
Change 15% to 0.15. then you multiply 13.50 by 0.15
13.50 x 0.15 = 2.025
Then you round 2.025
by rounding 2.025 you should get 2.03
with that you should subtract $13.50 by 2.03
13.50 - 2.03 = 11.48
I hope this helps :)
Evaluate each expression for the given value of the variable. #9 and #10
Answers
Part 9
we have
(c+2)(c-2)^2
If c=8
substitute the value of c in the expression
so
(8+2)(8-2)^2
(10)(6)^2
(10(36)
360
Part 10
we have
7(3x-2)^2
If x=4
substitute the value of x in the expression
7(3(4)-2)^2
7(10)^2
7(100)
700
a sociology Professor assigns letter grades on a test according to the following scheme Scores on the test are normally distributed with the meaning of 67.2 and a standard deviation of 8.5Find the minimum score required for an a grade. Round your answer to the nearest whole number if necessary
Answers
In order to have grade A, the score needs to be in the top 9%.
Since the scores are normally distributed, the top 9% scores correspond to 91% of the area under the normal curve. That means we need to find a value of z in the z-table that corresponds to the value 0.91 (that is, 91%).
Looking at the z-table, the value of z for a probability of 0.91 is z = 1.34.
Now, to find the score that this value of z represents, we can use the formula below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}\\ \\ 1.34=\frac{x-67.2}{8.5}\\ \\ x-67.2=11.39\\ \\ x=11.39+67.2\\ \\ x=78.59 \end{gathered}[/tex]Rounding to the nearest whole number, the minimum score for grade A is 79.
B) Use the quadratic formula to find the roots of each quadratic function.
Answers
Which of these is a simplified form of the equation 8y + 4 = 6 + 2y + 1y? 5y = 25y = 1011y = 211y = 10
Answers
Explanation:
The equation is given below as
[tex]8y+4=6+2y+1y[/tex]Step 1:
Collect similar terms, we will have
[tex]\begin{gathered} 8y+4=6+2y+1y \\ 8y+4=6+3y \\ 8y-3y=6-4 \\ 5y=2 \end{gathered}[/tex]Hence,
The simplified form of the equation will be
[tex]\Rightarrow5y=2[/tex]Each face of a pyramid is an isosceles triangle with a 70 degree vertex angle. What are the measures of the base angles?
Answers
We are given that each face of a pyramid is an isosceles triangle and that its vertex angle is 70 degrees. This problem can be exemplified in the following diagram:
Since the triangle is isosceles, its base angles are the same, and the sum of the interior angles must be equal to 180 degrees. Therefore, we have the following relationship:
[tex]70+x+x=180[/tex]Adding like terms, we get:
[tex]70+2x=180[/tex]Now we solve for "x", first by subtracting 70 on both sides:
[tex]\begin{gathered} 70-70+2x=180-70 \\ 2x=110 \end{gathered}[/tex]Now we divide both sides by 2
[tex]x=\frac{110}{2}=55[/tex]Therefore, the base angles of the pyramid are 55 degrees.
Look at this set of ordered pairs: (-8, 19) (11, 1) (0, 15. Is this relation a function?
Answers
Answer:
Yes, the set of ordered pairs is a function.
Explanation:
To test whether a given set of ordered pairs represents a function, we have to make sure that it satisfies the definition.
By definition, a function cannot have two outputs for one input. For example, the set of ordered pairs (3, 10 ) and (4, 5) represents a function whereas (3, 10) and (3, 13) does not.
With this in mind, looking at the given set we see that every input gives a unique output; therefore, the set represents a function.
1+1=? Need Help! Asap
Answers
By definition, Addition is a mathematical operation.
In this case, you have the following Addition given in the exercise:
[tex]1+1[/tex]Im in algebra 2 but we are also learning geometry the question asks to find the length of each arc
Answers
The length of the arc = 8π/3 mi
Explanation:The length of an arc is given by the fomula:
[tex]L=\frac{\theta}{360}\times2\pi r[/tex]The radius, r = 8 ml
[tex]\theta=60^0[/tex][tex]\begin{gathered} L=\frac{60}{360}\times2\pi\times8 \\ \\ L=\frac{16\pi}{6} \\ \\ L=\frac{8\pi}{3} \end{gathered}[/tex]The length of the arc = 8π/3 mi
Four plumbers estimated the length of the length of the radius of a cylindrial pipe. The estimates made by the plumbers are listed • 3/5 • 3/11 • 9/100 • 3.14/24 ? : . .
Answers
Different estimates:
The length of the radius of a cylindrical pipe:
Plumber W:
Radius had a length: 3/5 inches.
Plumber X:
Radius had a length: sqrt(3/11) inches.
Plumber Y:
Radius had a length of 9/100 inches.
Plumber Z:
Radius had a length of 3/14/24 inches.
Turn them into decimals:
We can turn each length into decimal:
Plumber W: 3/5 = 0.6.
Plumber X: sqrt(3/11) = 0.522222..
Plumber Y: 9/100 = 0.09
Plumber Z: 3.14/24 = 0.13083
The list from the greatest to least:
We can order this list taking into account the following reasoning: when the number is near to zero, this number is less than the other in the list. Examples: 0.001, 0.0002, 0.00004 are very near to zero.
Additionally, when a number is near 1 (the unit), this number is greater than the other less near to 1.
Examples: 0.69, 0.73, 0.888, 0.99 are near to zero.
The numbers we got in the list are decimals numbers coming from fractions and the square root was taken to the estimation of plumber X. Therefore:
From list 0.6, 0.52222..., 0.09, 0.13083
The number nearest to zero is 0.09. Then, 0.13083 is greater than 0.09 but less than the others. The following number is 0.5222..., and the greatest is 0.6.
The list that shows these lengths in order from the greatest to least is:
{0.6, 0.5222..., 0.13083, 0.09}.
Which is equivalent to:
{3/5, sqrt(3/11), 3.14/24, 9/100}.