Answers
Answer:
x = 1, y = 20
Step-by-step explanation:
The question is asking the length of two wires, so instead of area, we are looking at the perimeter.
For the triangle, the equation looks like this:
(2-x) + 15 + y
For the rectangle, the equation looks like this:
(5-x) + (y-6) × 2
Let's say that x = 2, and y = 12.
The triangles new equation would look like this:
(2-2) + 15 + 12 = 27
The rectangles new equation would look like this:
(5-2) + (12-6) × 2 = 18
The wires are the same length, so these numbers can't be correct.
Let's say that x = 1 and y = 20.
The triangles new equation would look like this:
(2-1) + 15 + 20 = 36
The rectangles new equation would look like this:
(5-1) + (20-6) × 2 = 36
These numbers are the same, so therefore the answer is
x = 1 and y = 20.
Related Questions
the sample space contains 5 as and 7 bs. what is the probability that a randomly selected set of 2 will in- clude 1 a and 1 b?
Answers
the probability that a randomly selected set of 2 will include 1 a and 1 b is 35/66
What is probability?The probability is equal to the variety of possible outcomes. the total number of outcomes that could occur. For instance, there is only one way to get a head and there are a total of two possible outcomes, so the probability of flipping a coin and getting heads is 1 in 2. Writing P(heads) = 12
What are the 4 types of probability?Classical
Empirical
Subjective.
Axiomatic
There are 66 equally likely outcomes, or C(5+7,2) =C(12,2)=66 possible outcomes. Only C(5,1)*C(7,1)=35 of these contain 1A and 1B. thus, the likelihood is 35/66.
The value of the solution is 35/66
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Find the x value of the axis of symmetry for the following function: f(x) = - 3x ^ 2 + 13x + 10
Answers
The axis of symmetry of the equation f(x) = - 3x ^ 2 + 13x + 10 is
x = 13/6How to find the axis of symmetryThe axis of symmetry is calculated
= -b / 2a
The quadratic equation is an equation of the form
ax^2 + bx + c
Comparing the given equation f(x) = - 3x^2 + 13x + 10 with ax^2 + bx + c the values of the axis of symmetry is
x = -b / 2a
x = -13 / 2(-3)
x = -13 / -6
x = 13/6
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need help on 11 and 12! or you can solve one instead of both if u want
Answers
Answer:
11. (-4, 5)
12. (0, 2)
Step-by-step explanation:
The solution from the graph is to determine the point of intersection of the two rays. And find the x and y values corresponding to that point.
In 11, the point of intersection is at x = -4, y =5
In 12, the point of intersection is at x = 0, y = 2
I am not clear on what they want you to do for checking the solution. You could mathematically solve for the set of equations.
I think what they mean is to check if your reading of the point coordinates from the graph is correct.
In which case just plug in the values of x and y into both equations in each problem and find if they are consistent
Let's take Problem 12 which has a solution of x = 0, y = 2
Plug in these values into each of the equations:
For 2x - y = -2, with x = 0, y = 2
2(0) - 2 = 0 - 2 = -2 so consistent
For 2x + 4y = 8
2(0) + 4(2) = 0 + 8 = 8
So both equations are consistent with the values read off the graph.
Use the same technique for the others
Hope that helps
in the past, 75% of the tourists who visited chattanooga went to see rock city. the management of rock city recently undertook an extensive promotional campaign. they are interested in determining whether the promotional campaign actually increased the proportion of tourists visiting rock city. the correct set of hypotheses is
Answers
the alternative hypothesis will state that the proportion is not significantly different than 0.75.
This should be researched with a hypothesis test on the proportion of tourists visiting Rock City.
The claim that want to be tested is if the proportion has increased from the past proportion (π=0.75).
Then, the alternative hypothesis will state that the proportion is significantly higher than 0.75.
On the contrary, the alternative hypothesis will state that the proportion is not significantly different than 0.75.
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an integer from the range 00000 - 99999 is generated uniformly at random. we are interested only in even integers that start with 2 odd digits where all digits are unique. if we randomly generate 8 of these numbers in succession, what is the probability we get exactly 5 numbers that meet our criteria?
Answers
Randomly generating 8 of these numbers in succession, the probability we get exactly 5 numbers that meet our criteria is 0.13875.
Fundamental Principle of Counting, also called the counting rule, is the method to count how many ways multiple independent events can occur.
Thus, by Fundamental Principle of Counting, the number of possible even integers that start with 2 odd digits is 13875.
= (5 x 5 x 5) + (5 x 5 x 10 x 5) + (5 x 5 x 10 x 10 x 5)
= 125 + 1250 + 12500
= 13875
Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.
probability = desired outcome / total outcomes
probability = 13875/100000
probability = 0.13875
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help me please 123456789`10
Answers
Answer:
B is in the 1st quadrant
J is slightly in the 2nd quadrant
T is in the 3rd quadrant
P is in the 4th quadrant
Positions:
B.) 4, 3
J.) 0, 7
T.) -4, -4
P.) 4, -6
Tip:When you are looking at an axis graph, picture a big "C" over it, the tip of the "C" is the 1st quadrant, as you go down the "C" it symbolizes each quadrant. When the point is only on one line or axis (depending on which axis), then it is, for example, (0, 3) or (3, 0).
with 50 gallons of fuel in its tank, the airplane has a weight of 2195 pounds. what is the weight of the plane with 17 gallons of fuel in its tank?
Answers
The airplane with 17 gallons will weight 746.3 pounds.
What is unitary method ?With the unitary method, you first determine the value of a single unit before determining the value of the necessary quantity of units. What can values and units be?
Consider going to the store to buy 6 apples. You are informed by the merchant that 10 apples are available for Rs 100. In this scenario, the units are apples and the value is their cost. It's crucial to understand the units and values while using the unitary technique to solve a problem.
Airplane weight with 50 gallons = 2195 pounds
So, airplane weight with 1 gallons = 2195 / 50
= 43.9 pounds
Hence,
Airplane with 17 gallons = 17 * 43.9 pounds
= 746.3 pounds
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question in a statistics class with 32 students, how many ways can a group of 5 lucky students be selected to sit in the front of the classroom?
Answers
There are 201376 ways can a group of 5 lucky students be selected to sit in the front of the classroom.
What are combinations?
Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in any order.
Permutations and combinations are often mistaken. The chosen components' order is crucial in permutations, though. For instance, whereas permutations treat the arrangements differently, combinations treat the arrangements ab and ba equally (as one arrangement).
Use the combinations formula:
n = 32, r=5
[tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex]
[tex]^{32}C_{5}=\frac{32!}{(32-5)! 5!}[/tex]
= (32*31*30*29*28*27!)/(5!*27!)
= (32*31*30*29*28)/ (5*4*3*2*1)
= 201376
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A line passes through (1, 1) and (-3,5).
What is the equation of the line in slope-intercept form?
Answers
Answer: Y=-x+2
Step-by-step explanation:
[tex]17x+1+15x+7[/tex]
Answers
Answer:
All the best
The answer is fully correct
the probability that a marksman will hit a target each time he shoots is 0.89. if he fires 15 times, what is the probability that he hits the target at most 13 times?
Answers
The probability that the marksman hits the target at most 13 times is 11.57.
Define binomial probability.
The likelihood of precisely x successes on n further trials in an experiment with two possible outcomes is known as a binomial probability (commonly called a binomial experiment). A random variable's binomial probability is indicated by the notation X B(n, p) (where the prefix stands for "has distribution..."). The distribution's parameters are known as n and p.
The binomial probability is nCx⋅px⋅(1−p)n−x when the probability of success on a given trial is p. In this case, nCx denotes the number of various combinations of x objects chosen from a set of n objects.
Solution Explained:
Given,
P(HT) = 0.89
so if we multiply the chances of hitting he target with 13, we get
P(H13) = 0.89 X 13 = 11.57
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Simpliy. 4x+2(2+5)+1
Answers
Answer:
4x + 15
Step-by-step explanation:
1. Add the numbers
4x + 2(2 + 5) + 1
4x + 2(7) + 1
2. Multiply the numbers
4x + 2(7) + 1
4x + 14 + 1
3. Add the numbers
4x + 14 + 1
4x + 15
Solution:
4x + 15
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 6 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
4x + 15
How I got this:
4x+2(2+5)+1
First I started with the brackets because of bedmas
4x+2(7)+1
Then I multiplied 2 by 7 since the 7 is in brackets
4x+14+1
Then I added 14 to 1
4x + 15
We leave it like that because 4x and 15 don't have any common terms so it can't be simplified further
For the weight of the box that she measured, beatriz determined the margin of error as 23. 5 pounds to 24. 5 pounds. What was the greatest possible error for her actual measurement?.
Answers
The greatest possible error for her actual measurement 0.5 pounds
What is a mistake, exactly?
A mistake is an inaccurate or incorrect action (the Latin word error, which means "wandering"). Sometimes the terms "mistake" and "error" are used synonymously. The Latin word "errare," which means "to stray," is the source of the etymology.
Given:
Beatriz calculated the error range to be 23.5 to 24.5 pounds.
How much room did she have for error in her actual measurement?
Solution:
We initially locate the median of the supplied numbers before calculating the margin of error.
23.5 and 24.5 as the median
[tex]M=\frac{23.5+34.5}{2}= \frac{48}{2}=24[/tex]
Therefore, the largest inaccuracy is 24.5-24 = 0.5 pounds.
As a result, 0.5 pounds is accurate.
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Given the equation V/7.9 equals 14.6, solve for v.
Answers
The required value of V for the given equation is 115.34
What is a simple equation?
A simple equation is a mathematical formula that, on both sides of the "equal to" sign, expresses the relationship between two expressions. It primarily consists of a variable, sometimes with a numerical constant in addition. There cannot be a simple equation without a variable. A known, fixed quantity that is used in a straightforward equation is referred to as a constant.
Given an expression, V/7.9 equals 14.6
or, V/7.9 = 14.6
or, V = 14.6*7.9
or, V = 115.34
Hence, the required value of V is 115.34
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7 the cost of a pen and a notebook used to be the same, but recently the cost of the pen was increased by $44, whereas, the cost of notebook became $66 less than 55 times its original value.after the revised cost, if the pen was more expensive than the notebook, what could have been the possible original value of both the products, if the initial price was a natural number?
Answers
x>2 might the original value of both goods have been if the initial price had been a natural number and the pen had been more expensive than the notebook.
Given that,
Pens and notebooks used to cost the same, however recently the price of the pen went up by $4 while the price of the notebook went down by $6 from its previous value of $5.
We have to find what might the original value of both goods have been if the initial price had been a natural number and the pen had been more expensive than the notebook.
We know that,
We get the equation as
x+4>5x-6
By solving the x
The inequality with x<2.5
So, natural number, n=2
x>2
Therefore, x>2 might the original value of both goods have been if the initial price had been a natural number and the pen had been more expensive than the notebook.
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a ladder is leaning against a wall. the ladder touches the wall 15 feet above the ground. how far is the bottom of the ladder from the wall if the length of the ladder is one foot more than twice its distance from the wall
Answers
The bottom of the ladder is at 8 feet from the wall.
The position of the ladder will form a right angled triangle with the wall. The perpendicular is 15 feet. Let the distance between ladder and wall be x. Thus, the length of the ladder will be 2x + 1. Forming a equation according to Pythagoras theorem.
(2x + 1)² = x² + 15²
Expanding the equation
4x² + 1 + 4x = x² + 225
Rewriting the equation
4x² - x² + 4x = 225 - 1
Performing subtraction
3x² + 4x = 224
3x² + 4x - 224 = 0
Factorizing the quadratic equation, we get -
x = -9.3 and 8
The distance can not be negative. Hence, the value of x is 8.
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Given that (-2,3) is on the graph of y=f(x), find a point that must be on the graph of y=f(2x+1)+3. Express your answer as an ordered pair (a,b) where a and b are real numbers.
Answers
The point that must be on the graph of y=f(2x+1)+3 is (-6, 0)
What is ordered pair?An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.
Given that, (-2,3) is on the graph of y=f(x), we need to find a point that must be graphed of y=f(2x+1)+3
3 = f(2X(-3)+1) + 3
0 = f(-6)
Hence, the point on the graph is (-6, 0)
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If a polynomial has one root in the form a-sqrt b it has a second root in the form of a sqrt b.
Answers
The second root is in the form [tex]a+\sqrt{b}[/tex].
Polynomial roots are the solutions to any given polynomial for which the value of the unknown variable must be determined. We can evaluate the value of polynomial to zero if we know the roots. A polynomial of degree 'n' in variable x is an expression of the form [tex]a^nx^n + a^{n-1}x^{n-1} +....+ a^1x^1 + a^0[/tex], where each variable has a constant accompanying it as its coefficient. The term refers to each variable in the expression that is separated by an addition or subtraction symbol. The degree of a polynomial is defined as the maximum power of a polynomial variable.
Given,
one root of polynomial is [tex]a-\sqrt{b}[/tex]
If a given root is complex, its conjugate is the other root. As a result, if a+ib is a root, a-ib is another a root.
If the root given is a surd of the form [tex]a+\sqrt{b}[/tex], then [tex]a-\sqrt{b}[/tex] is another root as well.
If the given root is rational, we can apply the product of the roots rule.
Thus, The polynomial's second root will be [tex]a+\sqrt{b}[/tex].
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a test has a mean of 100 and a standard deviation of 15. a client scores 130 on the test. at what percentile (rounded off) would this client's score place her?
Answers
As per the concept of z - score, the percentile would this client's score is 0.4772
Z - score:
In statistics, z - score is also termed the standard score, is used to determine how much each data point position is away from its mean. Where as in other words, it measures the deviation of x (data point) in terms of the standard deviations. Here the percentage of the population above or below the score can be obtained using z tables.
Given,
A test has a mean of 100 and a standard deviation of 15. a client scores 130 on the test.
Here we need to find at what percentile (rounded off) would this client's score place her.
As per the formula of z score, here we have the values,
mean = 100
standard deviation = 15
Score = 130
Therefore, the z score is calculated as,
=> z score = (130 - 100) / 15
=> z score = 30 / 15
=> z score = 2
According to the z score table the resulting value is 0.4772.
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Solve: 3 2/4 + 5 4/11 = ___
Answers
Answer: 195/22 or 8[tex]\frac{19}{22}[/tex]
Step-by-step explanation:
Calculate the unit rate for each option and determine which one is the BEST buy.
16 pounds for $31.68
28 pounds for $49.56
Answers
The best buy will be;
''28 pounds for $49.56''
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The two options are,
16 pounds for $31.68
28 pounds for $49.56
Now,
Since, The two options are,
16 pounds for $31.68
28 pounds for $49.56
Hence, The unit rate for each are;
Since, The cost of 16 pounds = $31.68
Hence, The cost of 1 pounds = $31.68/16
= $1.98
And, The cost of 28 pounds = $49.56
Hence, The cost of 1 pounds = $49.56/28
= $1.77
Thus, The best buy will be;
''28 pounds for $49.56''
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50% of the tickets sold at a school carnival were early-admission tickets. If the school sold 64
tickets in all, how many early-admission tickets did it sell?
Answers
Answer: 32
Step-by-step explanation:
50% = x/2
50% of 64 = 64/2
50%=32
Answer: The correct answer is 32 tickets were early admission
Step-by-step explanation:
T = Total tickets sold
E = Early admission tickets
If 50% of the total tickets are for early admission, then our equation would be:
E = T * 50% (or .5)
Substitute 64 for the total tickets
E = 64 * .5
E = 32
for a molecule with the formula ab2 the molecular shape is . question 14 options: a) t-shaped b) trigonal planar c) linear or t-shaped d) linear or bent e) linear or trigonal planar
Answers
The shape of the molecule having formula ab2 has been linear or trigonal planar. Hence, the correct option will be e) linear or trigonal planar
What is hybridization?The hybridization is been given as the combining of the valence shells with the formation of the given hybridized shell which have equal energy distribution.
The molecule that has A as a central atom, and B bonded to the fixed central atom. The molecular hybridization of the given molecule will be sp hybridization and that accounts for the linear shape of the molecule according to VSEPR theory.
Hybridization of A having the lone pair, and the shape of the molecule will be trigonal planar.
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How many sides do 2 decagons and 5 hexagons have in all?
Answers
Answer: 50 sides
Step-by-step explanation:
a decagon has 10 sides and 2 decagons have 20 sides total
a hexagon has 6 sides and 5 hexagons have 30 total
20 + 30 = 50
Therefore the answer is 50 sides
Which number did he add?
Answers
x= 7 and x=11 are two solutions of equation x²+7x-11=0
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is x²+7x-11=0
x square plus seven times of x minus eleven
Add 11 on both sides
x²+7x=11
x(x+7)=11
x=11
and x+7=11
Now subtract 7 on both sides
x=7
Hence, x= 7 and x=11 are two solutions of equation x²+7x-11=0.
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Find the Slope please!!
Answers
Answer:
The slope is y=-2x.
If solving the equation for the line it is y=-2x-1
a couple plans to have three children. all arrangements are (approximately) equally likely. let x be the number of girls the couple has. what the probability that x is greater than or equal to 2
Answers
The probability that the couple will have more than 2 girls is 1/2.
Here, we are given that a couple is planning to have 3 children.
Let us list down all the possible combination of outcomes-
GGG, GGB, GBB, BBB
Here G stands for a girl and B for a boy.
Thus, there are a total of 4 outcomes. We need to find the probability that the number of girls is greater than or equal to 2.
Out of the listed outcomes, 2 combinations- GGG and GGB have number of girls ≥ 2.
We know that probability = Number of favorable outcomes/ total number of outcomes
P(x ≥ 2) = 2/4
= 1/2
Thus, the probability that the couple will have more than 2 girls is 1/2.
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n this scenario, what is the test statistic? the digital marketing specialist would like to test the claim that the percent of customers who use online coupons when making an online purchase is different than 75%. sample size
Answers
The test statistic is 3.10
Hypothesis :
In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population. It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.
Complete question:
In this scenario what is the test statistic? • The digital marketing specialist would like to test the claim that the percent of customers who use online coupons when making an online purchase is different than 75% Sample size = 80 online customers • Sample proportion = 0.90 Calculate the test statistic using the formula: P-Po where • p = sample proportion, n sample size, and po - population proportion under the null hypothesis Round your answer to 2 decimal places. Provide your answer below:
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PLS HELP I'M VERY CONFUSED IT"S DUE 2DAY!!!! 100PTS!!!! NO SCAM ANSWERS!!!
In the following activity, match each pair of equivalent expressions.
(IT'S IN THE PICTURE)
Answers
The equivalent expressions of each number are respectively;
1) 2(x - 2) = -7 + 6x - 4x + 3
2) (x + 14) - (8 - 2x) = 9x - 2(3x - 3)
3) 3(x + 5) = -2x + 9 + 5x + 6
4) -4(x + 1) + 5x = (7 - 2x) + (3x - 11)
5) (7 + 5x) + (4x - 1) = -3x + 6 + 4x
How to use algebraic properties?The properties of algebra include associative property, distributive property, Identity property, Inverse property, e.t.c.
Now, let us simplify the terms on the right;
a) (7 - 2x) + (3x - 11)
Expanding the brackets gives us;
7 - 2x + 3x - 11
= x - 4
This can also be expressed as;
-4(x + 1) + 5x
b) -7 + 6x - 4x + 3
Simplifying gives;
2x - 4
= 2(x - 2)
c) 9x - 2(3x - 3)
Simplifying gives;
9x - 6x + 6
3x + 6
It can also be written as;
(x + 14) - (8 - 2x)
d) -3x + 6 + 4x
Simplifying gives;
x + 6
This can also be expressed as;
(7 + 5x) + (4x - 1)
e) -2x + 9 + 5x + 6
This can also be expressed as;
3x + 15
3(x + 5)
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Answer:
[tex]\boxed{4.} \quad (7-2x)+(3x-11)[/tex]
[tex]\boxed{1.} \quad -7+6x-4x+3[/tex]
[tex]\boxed{2.} \quad 9x-2(3x-3)[/tex]
[tex]\boxed{5.} \quad -3x+6+4x[/tex]
[tex]\boxed{3.} \quad -2x+9+5x+6[/tex]
Step-by-step explanation:
Simplify the given expressions numbered 1 through 5:
[tex]\begin{aligned}\textsf{1.} \quad 2(x-2)&=2 \cdot x + 2 \cdot (-2)\\&=2x-4\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{2.} \quad (x+14)-(8-2x)&=x+14-8+2x\\&=x+2x+14-8\\&=3x+6\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{3.} \quad 3(x+5)&=3 \cdot x + 3 \cdot 5\\&=3x+15\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{4.} \quad -4(x+1)+5x&=-4 \cdot x -4 \cdot 1+5x\\&=-4x-4+5x\\&=5x-4x-4\\&=x-4\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{5.} \quad (7+5x)+(-4x-1)&=7+5x-4x-1\\&=5x-4x+7-1\\&=x+6\end{aligned}[/tex]
Simplify the given answer expressions:
[tex]\begin{aligned}(7-2x)+(3x-11)&=7-2x+3x-11\\&=3x-2x+11-11\\&=x-4\end{aligned}[/tex]
[tex]\begin{aligned}-7+6x-4x+3&=6x-4x+3-7\\&=2x-4\end{aligned}[/tex]
[tex]\begin{aligned}9x-2(3x-3)&=9x-2 \cdot 3x-2 \cdot (-3)\\&=9x-6x+6\\&=3x+6\end{aligned}[/tex]
[tex]\begin{aligned}-3x+6+4x&=4x-3x+6\\&=x+6\end{aligned}[/tex]
[tex]\begin{aligned}-2x+9+5x+6&=5x-2x+9+6\\&=3x+15\end{aligned}[/tex]
Therefore, the matching pairs of equivalent expressions are:
[tex]\boxed{4.} \quad (7-2x)+(3x-11)[/tex]
[tex]\boxed{1.} \quad -7+6x-4x+3[/tex]
[tex]\boxed{2.} \quad 9x-2(3x-3)[/tex]
[tex]\boxed{5.} \quad -3x+6+4x[/tex]
[tex]\boxed{3.} \quad -2x+9+5x+6[/tex]
Find the volume v of the described solid s. The base of a solid s is the triangular region with vertices (0, 0), (4, 0), and (0, 4). Cross-sections perpendicular to the y-axis are equilateral triangles.
Answers
The volume of the solid S in the given question is 5.48unit³.
What is volume?A three-dimensional space's occupied volume is measured.
It is frequently expressed numerically in a variety of imperial or US-standard units as well as SI-derived units.
The definition of length and volume are connected.
So, the volume of the solid S:
An equilateral triangle's sides are shown as a cross-section.
An equilateral triangle's height is determined by:
[tex]h = sSin60 = \frac{\sqrt{3} }{2} s[/tex]
Consequently, one triangle's area is:
[tex]A=\frac{1}{2} s h=\frac{1}{2} s \cdot \frac{\sqrt{3}}{2} s=\frac{\sqrt{3}}{4} s^2[/tex]
The line equation that depicts the diagonal is:
[tex]\begin{aligned}& x+y=1 \\& y=-x+1 \\& x=-y+1\end{aligned}[/tex]
This will indicate the s value integrate from 0 to 2 if we integrate along the y-axis.
[tex]\begin{aligned}& V=\int_0^2 \frac{\sqrt{3}}{4} s^2 d x \\& =\frac{\sqrt{3}}{4} \int_0^2(-y+1)^2 d x \\& =\frac{\sqrt{3}}{4} \int_0^2\left(y^2-2 y+1\right) d x \\& =\frac{\sqrt{3}}{4}\left[\frac{1}{3} y^3-y^2+y\right] \\& \left.=\frac{\sqrt{3}}{4}\left[\frac{1}{3}(2)^3-(2)^2+2\right)\right] \\& =5.48\end{aligned}[/tex]
Therefore, the volume of the solid S in the given question is 5.48unit³.
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Correct question:
Find the volume V of the described solid S. The base of S is the triangular region with vertices (0, 0), (2, 0), and (0, 2). Cross-sections perpendicular to the y-axis are equilateral triangles.