Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region bounded by y 1 3 ex2 /3 , y 0, x 0, and x 3 about the y-axis. Round your answer to three decimal places.
Answers
Answer:
Step-by-step explanation:
[tex]y = f(x) =\frac{1}{\sqrt{3 \pi} } e^{-x^{2/3}}[/tex]
y = 0, x = 0 and x = 3
Consider an element of thickness dx at a distance x from the origin. By Cylindirical Shell Method, the volume of the element is given by
[tex]dV=(2\pi rdr)h=(2\pi xdx)f(x) => dV=(2\pi xdx) \frac{1}{\sqrt{3\pi}}e^{-x^{\frac{2}{3}}}[/tex]
[tex]dV=2\sqrt{\frac{\pi}{3}}xe^{-x^{\frac{2}{3}}}dx[/tex]
Integrate the above integral over the limits x=0 to x=3 which implies
[tex]\int_{0}^{V}dV=2\sqrt{\frac{\pi}{3}}\int_{0}^{3}xe^{-x^{\frac{2}{3}}}dx[/tex]
Solve by subsititution
[tex]Let,\\ -x^{\frac{2}{3}}=y => \frac{-2}{3}x^{\frac{-1}{3}}dx=dy => x^{\frac{-1}{3}}dx=\frac{-3}{2}dy[/tex]
Also, apply the new limits
[tex]At,\\\\ x=0, y=0 \ and \ At, x=3, y=-\sqrt[3]{9}[/tex]
This implies,
[tex]\int_{0}^{V}dV=2\sqrt{\frac{\pi}{3}}\int_{0}^{3}x^{\frac{4}{3}}e^{-x^{\frac{2}{3}}}x^{\frac{-1}{3}}dx=2\sqrt{\frac{\pi}{3}}\int_{0}^{-\sqrt[3]{9}}y^{2}e^{y}(\frac{-3}{2})dy[/tex]
[tex]V=-\sqrt{3\pi}\int_{0}^{-\sqrt[3]{9}}y^{2}e^{y}dy[/tex]
Let,
[tex]I=\int_{0}^{-\sqrt[3]{9}}y^{2}e^{y}dy[/tex]
Integrate by parts the above integral
[tex]u=y^2 \ and \ dv=e^ydy => du=2y \ and \ v=e^y[/tex]
Integrate by parts formula
[tex]\int udv=uv-\int vdu => y^2e^y-\int 2ye^ydy[/tex]
Again integrate by parts
[tex]u=y \ and \ dv=e^ydy => du=1 \ and \ v=e^y[/tex]
Integrate by parts formula
[tex]\int udv=uv-\int vdu => y^2e^y-2[ye^y-e^y]=e^y[y^2-2y+2][/tex]
Therefore,
[tex]I=[e^y(y^2-2y+2)]_{0}^{-\sqrt[3]{9}}\\\\=e^{-2.0802}[(2.0802)^2+2(2.0802)+2]-e^{0}[0-0+2]\\\\\frac{(4.3272+4.1604+2)}{8.0061}-2\\\\=\frac{10.4876}{8.0061}-2\\\\=1.3099-2\\\\=-0.6901[/tex]
This implies, the volume is
[tex]V=-\sqrt{3\pi}I\\\\=-\sqrt{3\times 3.142} \times (-0.6901)\\\\=3.0701 \times 0.6901\\\\=2.1186[/tex]
That is, up to three decimal places
[tex]V\approx 2.118[/tex]
Related Questions
Which of the following functions is graphed below
Answers
Answer:
B
Step-by-step explanation:
help ,, I need help with this one ,, i’m soo confused
Answers
As the x values go up, the y values go down which means the line is higher on the left side than it is on the right side.
The 4th graph would be the correct one
Grandmother bought enough cat food for her four cats to last for 12 days. On her way home she brought back two stray cats. If she gives each cat the same amount of food every day, how many days will the cat food last
Answers
Answer:
The number of days the cat food will last is 8 days.
Step-by-step explanation:
In this case, it it provided that Grandmother bought enough cat food for her four cats to last for 12 days.
Assume that each cat consumes x portions of food each day.
Then the four cats will consume, 4x portions of food each day.
Then in 12 days the amount of food consumed by the 4 cats will be:
Total amount of cat food = 12 × 4x
= 48x.
Now, it is provided that she on her way home she brought back two stray cats.
Then the six cats will consume, 6x portions of food each day.
Compute the number of days the cat food will last as follows:
[tex]\text{Number of days the cat food will last}=\frac{\text{Total amount of cat food}}{\text{Amount of food consumed each day}}[/tex]
[tex]=\frac{48x}{6x}\\\\=\frac{48}{6}\\\\=8[/tex]
Thus, the number of days the cat food will last is 8 days.
[tex]x = \frac{b + - \sqrt{{b}^{2} - 4ac } }{2a} [/tex]
O True
O False
Answers
If it is asking if that equation is the quadratic formula, then the answer is false. The reason why is that the first 'b' should be negative
The quadratic formula is
[tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
if r is the radius of a circle and d is its diameter which of the following is an equivalent formula for the circumference c = 2 pie r
a C = pie d2
b C = pie rd
c C = pie d
d C = 2 pie d
Answers
Answer:
C
Step-by-step explanation:
C=2pier or pied
Answer:
a. C = 2πr
c. C= πd
both are correct
someone answer this
Answers
Answer:
16
Step-by-step explanation:
The right triangle shown is a 30:60:90 triangle.
30:60:90 right triangles have a 1:sqrt(3):2 ratio between their sides.
Since the side opposite from the 30 degree is 8, and x is opposite from the 90 degree angle, 8 and x have a 1:2 ratio, or 8:16.
A random sample of 18 graduates of a certain secretarial school typed an average of 80.6 words per minute with a standard deviation of 7.2 words per minute. Assuming a normal distribution for the number of words typed per minute, compute the 95% prediction interval for the next observed number of words per minute typed by a graduate of the secretarial school.
Answers
Answer: ( 77.27 , 83.93)
Therefore at 95% confidence/prediction interval is
= ( 77.27 , 83.93)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 80.6 words per minute
Standard deviation r = 7.2
Number of samples n = 18
Confidence interval = 95%
z(at 95% confidence) = 1.96
Substituting the values we have;
80.6+/-1.96(7.2/√18)
80.6+/-1.96(1.697056274847)
80.6 +/- 3.33
= ( 77.27 , 83.93)
Therefore at 95% confidence/prediction interval is
= ( 77.27 , 83.93)
Among fatal plane crashes that occurred during the past 55 years, 415 were due to pilot error, 96 were due to other human error, 169 were due to weather, 622 were due to mechanical problems, and 68 were due to sabotage. Construct the relative frequency distribution. What is the most serious threat to aviation safety, and can anything be done about it?
Answers
Answer:
Relative frequency:
[tex]\text{Pilot error}=415/1370=0.30\\\\\text{Other human error}=96/1370=0.07\\\\\text{Weather}=169/1370=0.12\\\\\text{Mechanical problems}=622/1370=0.45\\\\\text{Sabotage}=68/1370=0.05\\\\[/tex]
The most serious threat to aviation safety is, according to this data, "mechanical failures". It can be improved by more rigorous inspection and better maintenance policies and execution.
Step-by-step explanation:
We have the data for fatal plane crashes. The sum of plane crashes is
We can calculate the relative frequency as:
[tex]\text{Pilot error}=415/1370=0.30\\\\\text{Other human error}=96/1370=0.07\\\\\text{Weather}=169/1370=0.12\\\\\text{Mechanical problems}=622/1370=0.45\\\\\text{Sabotage}=68/1370=0.05\\\\[/tex]
We can see that the most frequent cause is "mechanical problems", with a relative frequency of 0.45.
Solve 3(a + 3) – 6 = 21.
Answers
Answer:
a=6
Step-by-step explanation:
to find the value of a you need to simplify the equation first. so...
3(a+3)-6=21 (you remove the bracket first)
3a+9-6=21
3a+3=21 (you collect the like terms then)
3a=21-3
3a=18 (then you both divide both sides by 3 to find the value of a)
a=18/3
a=6
to check your answer substitute 3 instead of a
3(a+3)-6=21
3(6+3)-6=21
3(9)-6=21 (according to BODMAS since multiplication comes first you multiply 3 with 9 before subtracting it from 6.)
29-6=21
21=21
Answer:6
Step-by-step explanation:
3(a + 3) - 6 = 21
3(a + 3) = 21 + 6
3(a + 3) =27
a + 3. = 27 ÷ 3
a + 3. = 9
a. = 9 - 3
a. = 6
Please answer this correctly
Answers
So if we know the perimeter of the circle we can find it's radius using the formula for perimeter:
[tex]p = 2\pi(r)[/tex]
So we can solve for radius:
[tex]r = \frac{10.71}{2\pi} [/tex]
Then we can plug this radius into the formula for the area of a circle:
[tex]a = \pi {r}^{2} [/tex]
[tex]a = \pi( \frac{10.71}{2\pi} ) ^{2} [/tex]
Then it only wants a quarter of that area so we divide that value by 4 which upon simplification becomes the answer:
[tex]2.28 {ft}^{2} [/tex]
Answer:
[tex] \boxed{Area \: of \: quarter \: circle = 7.065 \: square \: feet} [/tex]
Given:
Perimeter of quarter circle = 10.71 feet
To find:
Area of quarter circle
Step-by-step explanation:
First we need to calculate the radius of quarter circle:
Let the radius of quarter circle be 'r'
[tex]Perimeter \: of \: quarter \: circle = \frac{\pi r}{2} + 2r[/tex]
[tex] \implies 10.71 = \frac{\pi r}{2} + 2r \\ \\ \implies 10.71 = \frac{\pi r}{2} +2r \frac{2}{2} \\ \\ \implies 10.71 = \frac{\pi r}{2} + \frac{4r}{2} \\ \\ \implies 10.71 = \frac{\pi r + 4r}{2} \\ \\ \implies 10.71 \times 2 = \pi r + 4r \\ \\ \implies 21.42 = \pi r + 4r \\ \\ \implies 21.42 = (\pi + 4)r \\ \\ \implies 21.42 = (3.14 + 4)r \\ \\ \implies 21.42 = 7.14r \\ \\ \implies 7.14r = 21.42 \\ \\ \implies r = \frac{21.42}{7.14} \\ \\ \implies r = 3 \: ft[/tex]
[tex] Area \: of \: quarter \: circle = \frac{\pi {r}^{2} }{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{\pi \times {(3)}^{2} }{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{\pi \times 9}{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{3.14 \times 9}{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{28.26}{4} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =7.065 \: {ft}^{2} [/tex]
What’s the correct answer for this question?
Answers
Answer:
A.
Step-by-step explanation:
Density = Mass / Volume
D = 3/0.2
D = 15 kg/m³
Answer:
density=mass/volume
d=3kg/0.2m3
=15kgm-3
Karissa begins to solve the equation StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis.. Her work is correct and is shown below. Three lines of math. The first line, StartFraction one-half EndFraction left-parenthesis x minus 14 right-parenthesis plus 11 equals StartFraction one-half EndFraction x minus left-parenthesis x minus 4 right-parenthesis. The second line, StartFraction one-half EndFraction x minus 7 plus 11 equals StartFraction one-half EndFraction x minus x plus 4. The third line StartFraction one-half EndFraction x plus 4 equals negative StartFraction one-half EndFraction x plus 4. StartFraction one-half EndFraction x minus 7 plus 11 equals StartFraction one-half Endfraction x minus x plus 4. StartFraction one-half EndFraction x plus 4 equals negative StartFraction one-half Endfraction x plus 4. When she subtracts 4 from both sides, Startfraction one-half EndFraction x equals negative StartFraction one-half EndFraction x. results. What is the value of ? –1 –negative StartFraction one-half EndFraction 0 StartFraction one-half EndFraction.
Answers
Answer:
x = 0
Step-by-step explanation:
Given
Karissa begins to solve the equation ...
[tex]\dfrac{1}{2}(x-14)+11=\dfrac{1}{2}x-(x-4)[/tex]
Her work is correct and is shown below. Three lines of math.
[tex]\dfrac{1}{2}(x-14)+11=\dfrac{1}{2}x-(x-4)\qquad\text{given}\\\\\dfrac{1}{2}x-7+11=\dfrac{1}{2}x-x+4\qquad\text{eliminate parentheses}\\\\\dfrac{1}{2}x+4=-\dfrac{1}{2}x+4\qquad\text{collect terms}[/tex]
When she subtracts 4 from both sides, the result is ...
[tex]\dfrac{1}{2}x=-\dfrac{1}{2}x[/tex]
Find
What is the value of x?
Solution
Karissa can determine the value of x by adding 1/2x to both sides:
[tex]x=0[/tex]
Answer:
Option C (0)
Step-by-step explanation:
A foundry has been commissioned to make souvenir coins. The coins are to be made from an alloy that is 40% silver. The foundry has on hand two alloys, one with 50% silver content and one with a 25% silver content. How many kilograms of each alloy should be used to make 10 kilograms of the 40% silver alloy?
Answers
Answer:
the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.
Step-by-step explanation:
Suppose, the weight of the alloy with 50% silver content is x kilograms.
As, the weight of the mixed alloy should be 10 kilograms, so the weight of the alloy with 25% silver content will be: kilograms
The percentage of silver content in the mixed alloy is 40%. So the equation will be calculated as
[tex]0.5x+0.25(10-x)=0.4\times10\\0.5x+2.5-0.25x=4\\0.25x=1.5\\\Rightarrow x=\frac{1.5}{0.25} = 6[/tex]
So, the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.
What is the average rate of change for this function for the interval from x= 1
to x = 3?
Answers
Answer:
The average rate of change is 12x=12.0x.
Description:
Function: x= 1x = 3 convert to short form: x 1x 3
Interval: x= 1 , x 3
Steps:
Input: Find the average rate of change of f(x)=3x2 on the interval [x,3x].
We have that a=x, b=3x, f(x)=3x2
Thus, f(b)−f(a)b−a=3((3x))2−(3(x)2)3x−(x)=12x.
Answer: the average rate of change is 12x=12.0x.
Please mark brainliest
Hope this helps.
Answer:
3
Step-by-step explanation:
A P E X
Which graph represents the function f(x) = |x| – 4? On a coordinate plane, an absolute value graph has a vertex at (0, 4). On a coordinate plane, an absolute value graph has a vertex at (negative 4, 0). On a coordinate plane, an absolute value graph has a vertex at (0, negative 4). On a coordinate plane, an absolute value graph has a vertex at (4, 0).
Answers
Answer:
(0, -4)
Step-by-step explanation:
The graph that represents the function is (c) on a coordinate plane, an absolute value graph has a vertex at (0, -4)
The equation of the function is given as:
[tex]f(x) = |x| - 4[/tex]
The above function is an absolute value function shifted down by 4 units
Hence, the graph that represents the function is a graph that has its vertex at (0,-4)
Read more about absolute value graphs at:
https://brainly.com/question/2166748
if the base of a right angled triangle is 4cm and its area is 20cm^2, find its height
Answers
answer will be 10cm² as i calculate it
Identify the domain of a radical function with an odd index.
Answers
Answer:When n is an odd number, [tex]\sqrt[n]{a}[/tex] is a real number for all values of a. Then, the domain is the real domain.
A large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. Twenty-five job applicants are randomly selected from a large university and they produce a mean score of 183 with a standard deviation of 12. Use a 0.05 level of significance to test whether the mean score for students from this university is greater than 160. use the P-value method of testing hypotheses.
Answers
Answer:
[tex]t=\frac{183-160}{\frac{12}{\sqrt{25}}}=9.58[/tex]
The degrees of freedom are given by:
[tex]df=n-1=25-1=24[/tex]
And the p value would be:
[tex]p_v =P(t_{(24)}>9.58)\approx 0[/tex]
Since the p value is very low at any significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 160
Step-by-step explanation:
Information provided
[tex]\bar X=183[/tex] represent the sample mean
[tex]s=12[/tex] represent the sample standard deviation
[tex]n=25[/tex] sample size
[tex]\mu_o =160[/tex] represent the value to test
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true mean is greater than 160, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 160[/tex]
Alternative hypothesis:[tex]\mu > 160[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{183-160}{\frac{12}{\sqrt{25}}}=9.58[/tex]
The degrees of freedom are given by:
[tex]df=n-1=25-1=24[/tex]
And the p value would be:
[tex]p_v =P(t_{(24)}>9.58)\approx 0[/tex]
Since the p value is very low at any significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 160
M5-3/2x less than or equal to 1/3
Answers
Answer: choice A
Step-by-step explanation:
by rearranging the initial inequality you’ll get
[tex]\frac{3}{2} x\leq 5-\frac{1}{3}[/tex]
which equals
[tex]\frac{3}{2} x\leq\frac{14}{3}[/tex]
then multiply both sides by 2/3
[tex]x\leq \frac{28}{9}[/tex]
01:30:4
Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is the
solution set of this problem?
Answers
Answer:
x<_ 21
Step-by-step explanation:
5(x+27)>_ =6(x+26)
5x +135 >_ 6x +156
5x >_6x +21
-x>_21
x<_21
Find the values of x in the figure below. Express your answer in simplest radical form.
Answers
Answer:
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me...
Type answer as integer proper fraction or mixed number
Answers
Answer:
[tex]9\dfrac{5}{6}[/tex]
Step-by-step explanation:
[tex]5\dfrac{1}{6}+4\dfrac{2}{3}=\\\\5\dfrac{1}{6}+4\dfrac{4}{6}=\\\\9\dfrac{5}{6}[/tex]
Hope this helps!
Solve for the value of x
Answers
Answer:
x = 8
Step-by-step explanation:
The angle with the expression in it is complementary to the 30° angle, so is 60°. Then we have ...
4 +7x = 60
7x = 56 . . . . . . subtact 4
x = 8 . . . . . . . . .divide by 7
find the arc length of the particle circle
Answers
Answer:
Is there a picture or graph or..
Step-by-step explanation:
Step-by-step explanation:
arc length = (radians * radians) . 90° is π/2 radians. Arc length is (π/2×4). So the answer is 2π.
Some have argued that throwing darts at the stock pages to decide which companies to invest in could be a successful stock-picking strategy. Suppose a researcher decides to test this theory and randomly chooses 250 companies to invest in. After 1 year, 135 of the companies were considered winners; that is, they outperformed other companies in the same investment class. To assess whether the dart-picking strategy resulted in a majority of winners, the researcher tested Upper H 0: pequals0.5 versus Upper H 1: pgreater than0.5 and obtained a P-value of 0.1030. Explain what this P-value means and write a conclusion for the researcher.
Answers
Answer:
The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance
Null hypothesis is accepted at 0.05 level of significance
The population proportion is equal to 0.5
Step-by-step explanation:
Step (i):-
Given random sample size ' n' = 250
Sample proportion 'p'
[tex]p= \frac{x}{n} = \frac{135}{250} = 0.54[/tex]
Given Population proportion P = 0.5
Q = 1-P = 1-0.5 =0.5
Null Hypothesis : H₀ : P = 0.5
Alternative Hypothesis : H₁ : P≥ 0.5
Step(ii):-
Test statistic
[tex]Z = \frac{p - P}{\sqrt{\frac{PQ}{n} } }[/tex]
[tex]Z = \frac{0.54-0.5}{\sqrt{\frac{0.5 X 0.5}{250} } }[/tex]
Z = 1.2903
Level of significance α = 0.05
Z₀.₀₅ = 1.96
The calculated value Z = 1.2903 < 1.96 at 0.05 level of significance
Null hypothesis is accepted at 0.05 level of significance
Step(iii):-
P- value
The probability of test statistic
P(Z > 1.2903) = 0.5 - A ( 1.2903)
= 0.5 - 0.4015
= 0.0985≅ 0.10
i) P- value =0.10 > α = 0.05
null hypothesis is accepted
Conclusion:-
The population proportion is equal to 0.5
g(-4)
Please help!!
Answers
Answer:
1
Step-by-step explanation:
g(-4) means what is the y value when x is -4.
Find x=-4, and when x=-4. y=1
Answer:
1
Step-by-step explanation:
what is X:
|4x−1|=3
|x|=−4
Answers
Answer:
1
Step-by-step explanation:
A box plot is shown below:
What is the median and Q1 of the data set represented on the plot?
Median = 31; Q1 = 26
Median = 30; Q1 = 26
Median = 31; Q1 = 20
Median = 30; Q1 = 20
Answers
Answer:
Step-by-step explanation:
Hello!
I didn't find the exact box plot for this exercise but I've found one that'll help you identify the required values
When constructing a box plot the box lower and upper limits are defined by the first and third quartiles and the line separating it in two represents the median.
In this case, the box is lying on the side, the first quartile is represented by the left side of the box. If you see the graphic this one corresponds to 25.
The median, as said, is represented by the line drawn inside the box, it is not necessarily in its middle but it will always be inside it.
Watching the example, the median is 33
I hope this helps!
Answer: D
Step-by-step explanation:
For all the people that have to do algebra and dont want to do it yourself there is a website or you can download it on your phone its called*** MATH PAPA*** ****IT SHOWS YOU STEP BY STEP AND GIVES YOU THE ANSWER*** Just input the equation
Answers
what is the solution set for the equation (x-2)(x-8)=0
Answers
Answer:
x=2 x =8
Step-by-step explanation:
(x-2)(x-8)=0
Using the zero product property
x-2 = 0 x-8 = 0
x=2 x =8
Answer:x = 2 and x = 8
Step-by-step explanation:
( 2 - 2)( 8 - 8)
(0)(0)
=0
