Can the triangles be proven similar using the SSS or SAS similarities theorems?
Answers
Answer:
Both!
Step-by-step explanation:
By both!
You have all 3 corresponding sides are proportional so you have SSS. That is
24/8=15/5=18/6
You also have SAS because 15/5=18/6 and you have the angle between the sides that I'm referring to in that proportion.
The SSS (Side-Side-Side) theorem can prove triangle similarity if all sides of two triangles are proportional, whereas the SAS (Side-Angle-Side) can prove similarity if two sides and the included angle of one triangle are proportional to those of another triangle. However, these theorems are only applicable if these conditions are met.
Explanation:In mathematics, particularly in geometry, we often deal with proving the similarity or congruence of shapes, especially triangles. The SSS (Side-Side-Side) and SAS (Side-Angle-Side) theorems are two of those methods used to establish similarity between triangles. However, these theorems need specific conditions to be applicable.
The SSS Similarity theorem states that if the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar. In other words, if you can match up the sides of one triangle to the sides of the other in such a way that every pair of corresponding sides has the same ratio, then the triangles are similar.
On the other hand, the SAS Similarity theorem states that if an angle of one triangle is congruent to an angle of a second triangle, and the sides including these angles are in proportion, then the triangles are similar.
Given the exact measures of the sides and angles of the triangles, it's possible to use either the SSS or SAS theorem to establish similarity. If, however, these specifics are not available or do not meet the conditions required for SSS or SAS, we cannot use these theorems to prove similarity.
Learn more about SSS and SAS Similarity Theorems here:https://brainly.com/question/30104134
#SPJ6
Related Questions
classify the following triangle
Answers
Answer:
Obtuse and Scalene
Step-by-step explanation:
Obtuse means that it is over 90 degrees, in which there is an angle of 102 degrees.
Scalene means that all three side lengths are different.
Answer:
A. Obtuse
C. Scalene
You flip 3 coins 20 times and record the number of heads. The results are listed below. 2, 1, 0, 2, 2, 0, 2, 2, 3, 2, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1 Complete the frequency table. a = ; b = ; c = ; d = Based on these results, which of these statements are true? You would expect to get 0 heads and 3 heads about the same number of times. You would expect to get 1 head and 2 heads about the same number of times. This would be a good experiment to use to find the probability that a family has a dog or a cat. This would be a good experiment to use to find the probability that a family with 3 kids has 1 boy.
Answers
The true statements about the result of the coin toss experiment described are :
You would expect to get 0 heads and 3 heads about the same number of times. You would expect to get 1 head and 2 heads about the same number of timesNumber of heads :__0 __ 1 __ 2 __ 3
Frequency _____ :_ 2___7___9___2
Expected Number of 0 heads = 2 Expected Number of 3 heads = 2Expected Number of 1 head = 7Expected Number of 3 heads = 9Therefore, expected Number of 3 and 0 heads are the same. And the expected number of 1 and 2 heads are almost the same.
The experiment cannot be used to model the events in the options as it only gives the number of occurence of a single event.
Hence, only statements 1 and 2 are true.
Learn more : https://brainly.com/question/18405415
The frequency of 0, 1, 2, and 3 heads in the experiment is 2, 7, 10, and 1 respectively. Statement 2 is the most accurate regarding long-term expectations, while statement 4 can be considered conditionally true. Statements 1 and 3 are not related to the probability outcomes of the experiment.
To complete the frequency table based on the given results, we will count the occurrences of each number of heads (0, 1, 2, or 3) in the 20 trials. The frequencies are:
0 heads (a): 2 times1 head (b): 7 times2 heads (c): 10 times3 heads (d): 1 timeBased on these results, we can discuss the truthfulness of the provided statements:
You would not expect to get 0 heads and 3 heads about the same number of times because the probability of getting 0 or 3 heads is lower than 1 or 2 heads when flipping three coins.You would expect to get 1 head and 2 heads about the same number of times in the long term, according to the law of large numbers, which states that as the number of trials increases, the empirical relative frequency of the outcomes approaches the theoretical probability.This would not be a good experiment to use to find the probability that a family has a dog or a cat, as the outcomes of coin flips do not correlate to pet ownership statistics.This could be a relatively good experiment to use to find the probability that a family with 3 kids has 1 boy, assuming that the gender of each child is independent and that the probability of being born a boy is equal to that of being born a girl (each coin flip can represent the birth of a child, with heads representing boys).2 squares area is 125 yards and 5 yards. how many yards would it take to fence the two squares in separately
Answers
Answer:
[tex]24\sqrt{5}\ yards[/tex]
Step-by-step explanation:
Let A1 be the area of one square and A2 be the area of second square
So,
A1 = s^2
where s is side of square
[tex]s^2=125\\\sqrt{s^2}=\sqrt{125}\\s=\sqrt{25*5}\\ s= \sqrt{5^2 * 5}\\ s= 5\sqrt{5}[/tex]
So side of one square is [tex]5\sqrt{5}[/tex]
To calculate the length of fence we need to find the perimeter of the square
So,
P1 = 4 * s
[tex]=4*5\sqrt{5} \\=20\sqrt{5}[/tex]
For second square:
[tex]A_2=s^2\\5=s^2\\\sqrt{s^2}=5\\{s}=\sqrt{5}[/tex]
The perimeter will be:
[tex]P_2 = 4*s\\=4 * \sqrt{5} \\=4\sqrt{5}[/tex]
So the total fence will be: P1+P2
[tex]= 20\sqrt{5}+4\sqrt{5} \\= 24\sqrt{5}\ yards[/tex]
Akira and tori Chang received a total of $48,000 from an estate. They decided to put $9,600 in a trust and divide the remainder. Tori received 3/8 of the remainder. How much did Akira receive?
Answers
Answer:
$24,000
Step-by-step explanation:
After putting in trust they have left:
48000 - 9600 = $38,400
If Tori gets 3/8, Akira will get the remaining (1 - 3/8 = 5/8). So Akira will get:
[tex]\frac{5}{8}*38,400=24,000[/tex]
Hence akira will get $24,000
-2,10,-50 next two numbers geometric sequence
Answers
Answer:
250, -1250
Step-by-step explanation:
Geometric Sequence is a hint to think multiplication:
What can you multiply to -2 to get 10
or what is 10/-2
I hope you said -5.
So just multiply -5 to a term to get the term right after!
So
-50(-5)=250
250(-5)=-1250
If it takes 45 manage to go to pale city from Heflin then it takes another hour and nine minutes to drive back to Ranburne Alabama how long will it take
Answers
Answer:
1 hour 54 minutes
Step-by-step explanation:
1 hour and 9 minutes + 45 minutes gives your answer. However, since 45+9=54, this is convenient, since now we don't need to carry. Thus, 1 hour and 54 min is your answer.
Hope this helps!
Answer: 114 minutes or 1 hour and 54 minutes.
Step-by-step explanation:
You need to analyse the exercise.
You know that it takes 45 minutes from Helflin to Pale City.
Driving back to Alabama takes 1 hour and 9 minutes. You need to remember that there are 60 minutes in an hour, therefore, this time in minutes is:
[tex]60\ minutes+9\ minutes=69\ minutes[/tex]
To find the total time, you need to add 45 minutes and 69 minutes. Then you get:
[tex]Total=45\ minutes+69\ minutes=114\ minutes[/tex] or 1 hour and 54 minutes.
Given the functions, fx) = x^2-4 and g(x) = x+ 2, perform the indicated operation. When applicable, state the domain
restriction.
F(g(x))
Answers
To perform F(g(x)), substitute g(x) into F(x) by squaring g(x) and subtracting 4. The domain of F(g(x)) is all real numbers.
Explanation:The question asks us to perform the composition of two functions - f(x) and g(x). Composition is denoted by (f ∘ g)(x) and involves substituting the output of the inner function (g(x)) into the input of the outer function (f(x)). In this case, we have f(g(x)), which means we need to substitute g(x) into f(x).
First, substitute g(x) into f(x) to get f(g(x)):
f(g(x)) = (g(x))^2 - 4 = (x+2)^2 -4 = x^2 + 4x + 4 - 4 = x^2 + 4x.
The domain restriction is the set of all values that x can take. Since there are no restrictions mentioned in the question, the domain is all real numbers.
Learn more about Composition of Functions here:https://brainly.com/question/30143914
#SPJ12
Efficient Homemakers Ltd. makes canvas wallets and leather wallets as part of a money-making project. For the canvas wallets, they need two yards of canvas and two yards of leather. For the leather wallets, they need four yards of leather and three yards of canvas. Their production unit has purchased 44 yards of leather and 40 yards of canvas. Let x be the number of leather wallets and y be the number of canvas wallets. If the profit on a canvas wallet is $25 and the profit on a leather wallet is $40, write a function for the total profit for both wallets.
Answers
To find the total profit for both wallets sold by Efficient Homemakers Ltd., use the equation P = 40x + 25y, where x is the number of leather wallets and y is the number of canvas wallets sold.
Explanation:The question involves writing a function for the total profit from selling canvas wallets and leather wallets made by Efficient Homemakers Ltd.
To calculate the total profit, we denote x as the number of leather wallets and y as the number of canvas wallets.
The company makes a profit of $40 for each leather wallet, and $25 for each canvas wallet.
Thus, the total profit P can be represented by the equation:
P = 40x + 25y
This equation represents the total profit as a function of the number of leather wallets (x) and the number of canvas wallets (y) sold.
HELP ASAP
What is the area of the triangle?
A)24 square units
B)32 square units
C)48 square units
D)96 square units
Answers
Answer:
A. 24 square units
Step-by-step explanation:
length is 8 and height is 6
gets you 48 but you need to divide by 2 because its a triangle so you get 24
Answer:
a
Step-by-step explanation:
Brody can fill a bowl with candy in 3 minutes. While Brody fills the bowl, Hudson takes the candy out of the bowl. With Hudson taking candy out of the
bowl, it takes 5 minutes for Brody to fill the bowl.
Which of the following can be used to determine the amount of time it takes for Hudson to empty the bowl if Brody does not add candy?
Answers
Answer:
1/3 - 1/x=1/5
Step-by-step explanation:
Let the total work be "1"
Brody Hudson Brody+Hudson
Time 3 mins x min 5 min
Efficiency 1/3 -1/x 1/5
The efficiency of Hudson is negative as he is taking out the candies out of the bowl, since efficiency of Brody + efficiency of Hudson = efficiency of both, which means,
1/3 - 1/x = 1/5....
Solve for x
(x + 10)(x + 10) = 0
Answers
[tex](x + 10)(x + 10) = 0\\x+10=0\\x=-10[/tex]
ANSWER
[tex]x = - 10[/tex]
EXPLANATION
We have the quadratic equation
[tex](x + 10)(x + 10) = 0[/tex]
This quadratic equation is in the factored form.
According to the zero product principle either the first factor is zero or the second is zero.
We apply the zero product principle to obtain:
[tex](x + 10) = 0 \: \: or \: \: (x + 10) = 0[/tex]
This is a repeated factor therefore,
[tex]x = - 10[/tex]
is the repeated root.
x=4 is a solution to the equation
2
= x - 8
True
O False
Answers
Answer:
False
Step-by-step explanation:
2 = x - 8
Add 8 to each side
2+8 = x-8+8
10 = x
x=4 is not a solution
For this case we have the following equation:
[tex]2 = x-8[/tex]
If we add 8 to both sides of the equation, we have:
[tex]2 + 8 = x-8 + 8\\10 = x[/tex]
Thus, the solution of the equation is [tex]x = 10,[/tex] therefore[tex]x = 4[/tex]is not a solution of the given equation.
Answer:
[tex]x = 4[/tex] is not a solution to the given equation.
False
Which statement is the most appropriate comparison of the spreads
Answers
Answer:
The answer is C
Step-by-step explanation:
Answer: D. The interquartile range (IQR) for Town A , 15° is less than the interquartile range for town B , 20°.
Step-by-step explanation:
The interquartile range is most suitable term to compare the spread of two different data displayed by box-whisker plot.
The formula for interquartile range :-
[tex]IQR=Q_3-Q_1[/tex]
For Town A , First quartile : [tex]Q_1=15[/tex]
Second quartile : [tex]Q_2=30[/tex]
[tex]IQR=30-15=15[/tex]
For Town B , First quartile : [tex]Q_1=20[/tex]
Second quartile : [tex]Q_2=40[/tex]
[tex]IQR=40-20=20[/tex]
Clearly , the interquartile range (IQR) for Town A , 15° is less than the interquartile range for town B , 20°.
A point has coordinates (0, 3). Where is it located in the coordinate plane?
Choose the best answer from the options below:
A x-axis
B y-axis
C quadrant 3
D quadrant 4
Answers
Answer:
A: x-axis
I did a quiz and got it wrong when I choose B: y-axis.
Final answer:
The point with coordinates (0, 3) is on the y-axis, above the origin by 3 units. Therefore, the correct answer is B, the y-axis.
Explanation:
A point with the coordinates (0, 3) is located where the x-coordinate is 0 and the y-coordinate is 3. In the context of a two-dimensional Cartesian coordinate system, this means the point does not move left or right from the origin on the horizontal axis, but it moves up by 3 units on the vertical axis.
Therefore, the correct answer to the question is B, the point is located on the y-axis. It is neither on the x-axis nor in any of the four quadrants since its x-coordinate is zero. Hence, it lies directly above the origin on the y-axis.
Can someone please help
Answers
Check the picture below.
[tex]\bf \stackrel{\textit{triangles' area}}{\cfrac{1}{2}(6)(1)+\cfrac{1}{2}(6)(1)}+\stackrel{\textit{front side}}{(6\cdot 2)}+\stackrel{\textit{left and right sides}}{(4\cdot 2)+(4\cdot 2)}\implies 3+3+12+8+8[/tex]
If g(x) = x2 + 2, find g(3). (2 points) 9 8 11 6
Answers
For this case we have a function of the form [tex]y = g (x)[/tex]
Where:
[tex]g (x) = x ^ 2 + 2[/tex]
We must find the value of the function when x = 3. Then we substitute:
[tex]g (3) = 3 ^ 2 + 2\\g (3) = 9 + 2\\g (3) = 11[/tex]
Thus, the value of the function when [tex]x = 3[/tex] is [tex]y = 11[/tex]
Answer:
[tex]g (3) = 11[/tex]
Option C
Answer: Third Option
[tex]g(3) = 11[/tex]
Step-by-step explanation:
We have the function [tex]g(x) = x^2 + 2[/tex] and we must find the value of g(3).
To find g (3) we must evaluate the function g(x) for x = 3. That is, we must replace x = 3 in the function
Then
[tex]g(x) = x^2 + 2[/tex]
[tex]g(3) = (3)^2 + 2[/tex]
[tex]g(3) = 9 + 2[/tex]
[tex]g(3) = 11[/tex]
Finally the correct answer is the third option
Graph the following piecewise function.
Answers
Step-by-step explanation:
[tex]for\ 2<x\leq4-\text{the horizontal segment}\ y=2\\\\for\ 4<x<8\to y=x+3\\\\\text{put}\ x=4,\ \text{and}\ x=8\ \text{to the equation}\\\\y=4+3=7\to(4,\ 7)\\y=8+3=11\to(8,\ 11)\\\\for\ x\geq8\to y=2x\\\\\text{put}\ x=8,\ and\ x=9\ \text{to the equation}\\\\y=2(8)=16\to(8,\ 16)\\y=2(9)=18\to(9,\ 18)\\\\==========================[/tex]
[tex]<,\ >\ -\ \text{op}\text{en circle}\\\\\leq,\ \geq\ -\ \text{closed circle}[/tex]
What is the value of x in this system of equations? Express the answer as a decimal rounded to the nearest tenth.
-5x - 12y = -8
5x + 2y = 48
Answers
Answer:
x = 11.2
Step-by-step explanation:
-5x - 12y = -8
5x + 2y = 48
you can combine all like terms from both equations together:
0x-10y=40
simplified:
-10y=40
y=-4
now you plug in the value of y into either equation:
5x+2(-4)=48
simplify
5x-8=48
add 8
5x=56
divide by 5
x=56/5=11.2
what is the differences between 2^8 and 8^2?
Answers
Answer:
The answer is 192
Step-by-step explanation:
2^8 = 256
8^2 = 64
256 - 64 = 192
Remember:
2^8 is really 2*2*2*2*2*2*2*2
Remember:
8^2 is really 8*8
To find the difference, you must subtract the smaller product from the larger product.
<Hope this helps!>
Answer:
192
Step-by-step explanation:
Method 1:
2^8 - 8^2 = 2^8 - 2^6 = 2^6(2^2 - 1) = 64(3) = 192
Method 2:
2^8 - 8^2 = 256 - 64 = 192
At a certain electronics company, the daily output Q is related to the number of people A on the assembly line by Q=600+√(A+41). Determine how many people are needed on the assembly line if the daily output is to be 621.
Answers
Answer:
[tex]A=400\ people[/tex]
Step-by-step explanation:
we have
[tex]Q=600+\sqrt{A+41}[/tex]
where
Q -----> is the daily output
A -----> is the number of people
For Q=621
Find the value of A
substitute and solve for A
[tex]621=600+\sqrt{A+41}[/tex]
Subtract 600 both sides
[tex]621-600=\sqrt{A+41}[/tex]
[tex]21=\sqrt{A+41}[/tex]
squared both sides
[tex]21^{2} ={A+41}[/tex]
[tex]441={A+41}[/tex]
Subtract 41 both sides
[tex]441-41=A[/tex]
Rewrite
[tex]A=400\ people[/tex]
Seth bought a T-shirt that costs $21.00. If the tax rate was 8%, what was the total cost of the t-shirt?
Answers
Answer:
$22.68
Step-by-step explanation:
21×.08= 1.68
21+1.68=22.68
Total cost =$22.68
Answer:
22.68
Step-by-step explanation:
The first step is to find the amount of tax
tax = original cost * tax rate
= 21 * 8%
= 21 * .08
=1.68
Then we add the tax to the original cost to find the total cost
total cost = original cost + tax
= 21 + 1.68
=22.68
what is the 17th term in the arithmetic sequence in which a6 is 101 and a9 is 83
Answers
Answer:
The 17th term in arithmetic sequence is 68
Step-by-step explanation:
The general formula of arithmetic sequence is:
aₙ = a₁ + (n – 1)d.
We are given a₆ = 101 and a₉ = 83 and we need to find a₁₇
To find the term a₁₇ we should know a₁ and d. So we would find both
a₆ = a₁ +(6-1)d
101 = a₁ +(5)d
101 = a₁ +5d eq(1)
and
a₉ = a₁ +(9-1)d
83 = a₁ + 8d eq(2)
Subtracting eq(2) from eq(1)
101 = a₁ +5d
83 = a₁ + 8d
- - -
__________
18 = -3d
=> d = 18/-3
=> d = -6
Putting value of d in eq(1)
101 = a₁ + 5d
101 = a₁ + 5(-3)
101 = a₁ -15
=> a₁ = 101+15
=> a₁ = 116
Now finding a₁₇:
aₙ = a₁ + (n – 1)d.
a₁₇ = 116 +(17-1)(-3)
a₁₇ = 116+(16)(-3)
a₁₇ = 116 - 48
a₁₇ = 68
So, the 17th term in arithmetic sequence is 68
One serving of Chad's favorite cereal contains 1 1/4 ounces. How many servings are in a 15 1/3 ounce box
Answers
so namely how many times does 1¼ go into 15⅓?
let's firstly convert the mixed fractions to improper fractions and then divide.
[tex]\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{15\frac{1}{3}}\implies \cfrac{15\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{46}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{46}{3}\div\cfrac{5}{4}\implies \cfrac{46}{3}\cdot \cfrac{4}{5}\implies \cfrac{184}{15}\implies 12\frac{4}{15}[/tex]
What is the radius and diameter of the following circle?
Answers
Answer:
The radius of the circle is already there, 11cm, and the diameter is 2 times the radius, which is 22
Step-by-step explanation:
First, you look at the radius (which is half of the circle) which is 11, then you multiply that times two to get the diameter. :)
Diameter-22cm
Lorena took a survey of the students in her honors science class to determine how many are going to college. She found that 85% of the students plan to go to college.
Can Lorena make the inference that 85% of all the seniors at her school are going to college?
Answers
Answer:
No, Lorena cannot make the inference about all the seniors going to college.
Step-by-step explanation:
We are given that Lorena took a survey of students in her science class to determine how many of them were going to college.
From the survey results, she found that 85% of the students from her science class were going to the college but with these results she cannot infer that 85% of all the seniors at her school were going to college.
This is because the survey was biased as it was not taken from the entire school but only Lorena's science class.
Answer:
No, Lorena’s sample was biased because it was taken only from an honors class.
No, Lorena’s sample was not a random sample of the entire school.
those are the two correct answers, i took the test!
What is 1.2 to the tenth power
Answers
Answer:
Step-by-step explanation:
that would be written as 1.2^10, and the end result would be the same as you'd get if you use 1.2 as a factor 10 times: 1.2*1.2*1.2* .......1.2
You could use a calculator to evaluate 1.2^10:
Typing in 1.2^10, you'll get 6.191736422.
This is not an exact answer; there are more digits following the ones shown.
Another way in which you could do this problem would be to use logs:
Let y = 1.2^10. Then log y = 10*log 1.2, or log y = 10(0.07918) = 0.791812.
Finding the antilog, we get y = 6.19174
The sum of two numbers is 28. The first number, x, is three
times the second number, y.
Answers
Answer:
x=21
y= 7
Step-by-step explanation:
x+y = 28
x = 3y
Substitute the second equation into the first
3y+y = 28
4y = 28
Divide by 4
4y/4 = 28/4
y = 7
Now we need to find x
x = 3*y
x = 3*7
x = 21
What is 692,119 rounded to the nearest thousand
Answers
In order to get the answer to this problem you will have to go to the thousands place value and look at the number next to the place value and if the number is greater then 5 then you round up which will give you your answer.
[tex]692,119[/tex]
[tex]2,119[/tex]
[tex]1<5[/tex]
[tex]= 2000[/tex]
[tex]= 692,000[/tex]
Which means your answer is "692,000."
Hope this helps.
The value 692,119 is rounded to the nearest thousand is 692,000. The nearest thousand for the given number is 2000.
How to round off a number?A number (integer or decimal) is rewritten to the nearest place value (ones, tens, hundreds, thousands, and so on). The rewritten number is said to be the rounded value of the given number. A number is rounded off at any of its place values on the basis of the digit after the digit which is to be rounded.I.e., if the digit after that place is less than 5 (< 5) then round the number down, or if the digit after that place is greater than or equal to 5 ( ≥ 5) then round the number up. If the digit is less than 5, then all the digits after the required place value are rounded as zerosIf the digit is more than 5 or equal to 5, then add 1 to the digit in the required place value and round all the other digits after it as zeros.Rounding the given number to the nearest thousand?The given number is 692,119
The digit in the thousands place of the given number is 2.
The digit after 2 is 1 which is less than 5. So, the digits after the thousand place is rounded as zeros. I.e., 2119 to 2000.
Therefore, the rounded number is 692,000.
Learn more about rounding off here:
https://brainly.com/question/14639222
#SPJ2
solve the equation 53=-6-17x
Answers
Answer:
-59/17 =x
Step-by-step explanation:
53=-6-17x
Add 6 to each side
53+6=-6+6-17x
59 = -17x
Divide each side by -17
59/-17 = -17x/-17
59/-17 = x
-59/17 =x
The density of a American white oak tree is 752 kilograms per cubic meter. If the trunk of an American white oak tree has a circumference of 4.5 meters and a height of 8 meters, what is the approximate number of kilograms of the trunk?
1. 13
2. 9694
3. 13,536
4. 30, 456
Answers
Check the picture below.
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=4.5 \end{cases}\implies 4.5=2\pi r\implies \cfrac{4.5}{2\pi }=r \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} h=8\\ r=\frac{4.5}{2\pi } \end{cases}\implies V=\pi \left( \cfrac{4.5}{2\pi } \right)^2(8)\implies V=\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} \cdot \cfrac{20.25}{\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}\underset{\pi }{\begin{matrix} \pi^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }}(\stackrel{2}{\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}})[/tex]
[tex]\bf V=\cfrac{40.5}{\pi }~cm^3~\hspace{9em} \stackrel{\textit{since density is }752kg~per~cm^3}{density\implies 752\left( \cfrac{40.5}{\pi } \right)}\qquad \approx ~~9694[/tex]
Option 2 is correct. The approximate weight of the trunk of an American white oak tree with a circumference of 4.5 meters and a height of 8 meters is calculated by finding the volume of the trunk and multiplying it by the tree's density, resulting in approximately 9,694 kilograms.
To calculate the approximate weight of the trunk of an American white oak tree, we first need to estimate its volume and then multiply it by the tree's density. Since the tree trunk is cylindrical, we can use the formula for the volume of a cylinder, [tex]V = \(pi \times r^2 \times h\)[/tex], where r is the radius of the base and h is the height of the cylinder. The circumference is given by C = 2 times pi times r, so we can solve for r by rearranging the formula: [tex]\(r = \frac{C}{2 \times \\pi}\)[/tex]. With a circumference of 4.5 meters, the radius is [tex]\(r = \frac{4.5 \text{m}}{2 \times \pi}\approx 0.716m\)[/tex]. Plugging the radius and the height (8 m) into the volume formula gives V approx pi times (0.716m)^2 times 8 m approx 13.07 m^3.
Knowing the volume, we can find the mass of the trunk by multiplying the tree's volume by its density. The density of American white oak is given as 752 kilograms per cubic meter. The mass (m) is then [tex]m = V \times \ext{density} = 13.07 m^3 \times 752 \frac{kg}{m^3} \approx 9,832.64 kg.[/tex] Rounding off gives us approximately 9,694 kilograms, which is option 2 and is the closest answer provided in the question.