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.
Related Questions
Use the discriminant to describe the roots of each equation. Then select the best description.
7x2 + 3 = 8x
double root
real and rational root
real and irrational root
imaginary root
Answers
Answer:
imaginary root
Step-by-step explanation:
7x^2 + 3 = 8x
Subtract 8x from each side
7x^2 -8x+ 3 = 8x-8x
7x^2 -8x+3 =0
This is in the form ax^2 +bx+c
The discriminant is b^2 -4ac
a=7 b=-8 c=3
b^2-4ac = (-8)^2 -4(7)(3) = 64 - 84 = -20
Since this is negative, we have imaginary roots
A sequence is defined recursively by the formula f(n + 1) = f(n) + 3 . The first term of the sequence is –4. What is the next term in the sequence?
–7
–1
1
7
Answers
Answer:
-1Step-by-step explanation:
[tex]f(1)=-4\\\\f(n+1)=f(n)+3-\text{the next term is 3 bigger than the previous one}\\\\f(2)=-4+3=-1[/tex]
The slope of the line below is 4. Which of the following is the point-slope form
of the line?
(-3,-4)
A. y+ 4 = 4(x+3)
B. Y-4 =-4(x-3)
C. y-4= 4(x-3)
D. Y+4 = -4(X+3)
Answers
Answer:
A: y+4=4(x+3)
Step-by-step explanation:
Point-Slope Formula:
y-y1=m(x-x1)
Substitute:
y-(-4)=4(x-(-3))
-(-)=+
P: y+4=4(x+3)
Y+4 = 4(x+3)
The answer is A
Hope this helps!
Factor the following expression.
27y3 – 343
a. (3y + 7)(9y2 + 2ly + 49)
b. (3y – 7)(9y2 + 2ly + 49)
c. (3y – 7)(932 – 217 + 49)
D. (3y + 7)(92 – 2ly + 49)
Answers
Answer:
b
Step-by-step explanation:
use formula of a^3-b^3
Answer:
D
Step-by-step explanation:
(3y - 7) (9y^2 + 21y + 49)
let me know if it's right
#platolivesmatter
2.314 (14 repeating) as a fraction
Answers
Answer:
Therefore, x = [tex]\frac{2291}{990}[/tex].
Step-by-step explanation:
Given : 2.314 (14 repeating) .
To find : Express as a fraction .
Solution : We have given 2.314 (14 repeating) .
Let x = 2.31414141.......
On multiplying both sides by 100
100x = 100 * 2.31414141....
100x = 231.414141......
We can express 231.414141...... in term of x .
100x = 229 .1 + 2.31414141.......
100x = 229.1 +x
On subtracting both sides by x .
100 x -x = 229 .1
99x = 229.1
On dividing both sides by 99
x= [tex]\frac{229.1}{99}[/tex].
x = [tex]\frac{2291}{990}[/tex].
Therefore, x = [tex]\frac{2291}{990}[/tex].
The repeating decimal 2.3141414... expressed as a fraction is [tex] \frac{2291}{990} [/tex]
The decimal given : 2.3141414
Let :
x = 2.31414 - - - (1)Since only the 14 keeps repeating :
Multiply (1) by 10 in other to keep the repeating digits only to the right of the decimal Point.10x = 23.1414 - - - - (2)Multiply (2) by 100
1000x - 2314.1414 - - - - (3)Subtract (2) from (3)1000x - 10x = 2314.1414 - 23.1414
990x = 2291
Divide both sides by 990x = 2291 / 990Hence, 2.31414...expressed as a decimal is [tex] \frac{2291}{990} [/tex]
Learn more : https://brainly.com/question/15406832?referrer=searchResults
What are possible outcome of a spin of the spinner
Answers
Answer:
Step-by-step explanation:
it would depend on how many numbers are on the spinner like if their is 6 numbers on the spinner and if your trying to get a 4 then it would be 1/6.
Hope my answer has helped you!
Find p(2)
Find p(2 or fewer)
Answers
Answer:
P(2)=0.021942 approximately
P(2 or fewer)=0.02711 approximately
Step-by-step explanation:
[tex] P(x)=(n choose x) *p^x * q^{n-x} [/tex]
x is the number of successes desired
p is probability of getting a success per trial
n is the number of trials
q is 1-p
So n=15 and p=.4 here
And you want to know P(2) which means x is 2
Plug in this information
[tex] P(2)=(15 \text{ choose } 2) *.4^2 * .6^{15-2} [/tex]
Just plug into calculator... P(2)=0.021942 approximately
For p(2 or fewer) you just do P(0)+P(1)+P(2)
I already found P(2)
You need to find P(1)
Once you get P(1), add that result to 0.021942.
Try to do part b and I will tell you if you got it right or not.
So P(2 or less) is P(0)+P(1)+P(2)
So to complete this we need to find P(1) and almost forgot P(0)...
We already have P(2).
P(0)=(15 choose 0) *.4^0*.6^(15-0)=0.00047
P(1)=(15 choose 1) *.4^1 *.6^(15-1)=.004702
Now P(2)=0.021942
--------------------------add these
0.027114 approximately
5,5,5,7,7 mean median mode range
Answers
[tex]\text{Hey there!}[/tex]
[tex]\text{The mean is when you add up ALL your numbers then divide by the number}[/tex] [tex]\text{of numbers in the equation}[/tex]
[tex]\text{5+5+5+7+7=15+14=29}[/tex]
[tex]\text{We have 5 terms in this equation so divided 29 from 5}[/tex]
[tex]\bf{29\div5=5.8}[/tex]
[tex]\boxed{\text{Mean: 5.8}}\checkmark[/tex]
[tex]\text{Median is the middle number of the set of numbers}[/tex]
[tex]\boxed{\text{Median: 5}}\checkmark[/tex]
[tex]\text{Mode is when you see a number MORE THAN ONCE}[/tex]
[tex]\text{You see 5 three times but the 7 twice, so this will make it tricky to answer}[/tex]
[tex]\text{Since, you see 5 three times.. it could be your mode}[/tex]
[tex]\boxed{\text{Mode: 5}}\checkmark[/tex]
[tex]\text{Range is when subtract the HIGHEST NUMBER from the LOWEST NUMBER}[/tex]
[tex]\text{7-5=2}[/tex]
[tex]\boxed{\text{Range: 2}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
30% of what equals 60
Answers
x/60 = 30/100
x = 200
CHECK ANSWER: 200 x .30 = 60
Answer:
30% of 200 equals 60.
Step-by-step explanation:
There is a formula we use to this specific type of problem. It's called the rule of 3.
30% - 60
100% - x
(60 * 100) / 30 =
6000 / 30 =
200
Step-by-step proof:
To prove our answer, what me must do is use another formula:
(200 * 30) / 100 = 60
6000 / 100 = 60
60 = 60
↑ Both numbers are equal (equation is true), therefore, our solution is correct.
Hope it helped,
BiologiaMagister
Factor the polynomial.
3x^4 +6x^3 + 9x^2
Answers
Answer:
3 x^2 (x^2 + 2 x + 3)
Step-by-step explanation:
Factor the following:
3 x^4 + 6 x^3 + 9 x^2
Hint: | Factor common terms out of 3 x^4 + 6 x^3 + 9 x^2.
Factor 3 x^2 out of 3 x^4 + 6 x^3 + 9 x^2:
Answer: 3 x^2 (x^2 + 2 x + 3)
I have this question in Geometry that I need help with, can you help me solve it?
Find the coordinates of the midpoint of a segment having the given endpoints.
Q(1, -3), R(11, 5)
Answers
Answer(6,1)
Step-by-step explanation:
you need to use the midpoint formula
If you wanted to make the graph of y = 7x- 14 steeper, as well as shift the y
intercept of this line up, which equation could you use?
A. y= 5x - 18
B. y = 9x - 10
C. y= 5x – 10
D. y= 9x - 18
Answers
Answer:
Option B: y = 9x - 10.
Step-by-step explanation:
General equation of a straight line in the 2-D plane is given by:
y = mx + c; where m is the slope and c is the y-intercept.
The given equation of the line is y = 7x - 14; where m=7 and c=-14.
To make the line steeper, the gradient has to be increased. Therefore, Options A and C are incorrect because 5 is less than 7. This makes the Options B and D the remaining options because 9 is greater than 7.
To shift the y-intercept of this line up, the y-intercept has to be increased. Since -10 is greater than -14 and -18 is lesser than -14, therefore the latter option (Option D) is the incorrect option. So the correct answer is Option B: y = 9x - 10!!!
Question 10
Jur's car can travel 340 miles on 12 gallons. Jack's car can travel 390 miles on
16 gallons. Which person has the best mileage (miles per gallon) and what is
their mileage?
Answers
Answer:
Jur's car
Step-by-step explanation:
Jur's car's mileage= 340/12=28.3333333333
Jack's car's mileage=390/16=24.375
brainliest if you are satisfied plz
Answer:
Jur 28 1/3 miles per gallon
Step-by-step explanation:
To find the miles per gallon, take the miles driven and divide by the gallons used.
Jur: 340/12 =28.333333 miles per gallon
Jack : 390/16 = 24.375 miles per gallon
Jur has better gas mileage because his number is higher
Lorne subtracted 6x3 – 2x + 3 from –3x3 + 5x2 + 4x – 7. Use the drop-down menus to identify the steps Lorne used to find the difference.
Answers
Final answer:
Lorne subtracted the polynomial 6x³ − 2x + 3 from − 3x³ + 5x² + 4x − 7 by changing the signs of the second polynomial and combining like terms, resulting in the difference − 9x³ + 5x² + 6x − 10.
Explanation:
To find the difference between two polynomials, we subtract the corresponding terms of the second polynomial from the corresponding terms of the first. In the given problem, Lorne subtracted 6x³ − 2x + 3 from − 3x³ + 5x² + 4x − 7. To do this, we change the signs of the polynomial being subtracted and then combine like terms.
First, we write the problem with the second polynomial's signs changed: − 3x³ + 5x² + 4x − 7 - (6x³ − 2x + 3).
Next, we distribute the negative sign: − 3x³ + 5x² + 4x − 7 - 6x³ + 2x - 3.
Finally, we combine like terms: (− 3x³ − 6x³) + (5x²) + (4x + 2x) + (− 7 − 3).
The resulting difference is − 9x³ + 5x² + 6x − 10.
Terrence buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value of the car
after x years, which function represents the car's value?
f(x) = 20,000(0.85)*
f(x) = 20,000(0.15)*
f(x) = 20,000(1.15)
f(x) = 20,000(1.85)
Answers
Answer:
f(x) = 20,000(0.85)*
Step-by-step explanation:
Answer: [tex]f(x)=20,000(0.85)^x[/tex]
Step-by-step explanation:
We know that the exponential decay (depreciation) equation with rate of decay r in time period x is given by :-
[tex]f(x)=A(1-r)^x[/tex], A is the initial value .
Given: The initial value of truck = $20,000
Rate of depreciation= 15% = 0.15
Now, the function represents the car's value after x years is given by ;-
[tex]f(x)=20,000(1-0.15)^x\\\\\Rightarrow\ f(x)=20,000(0.85)^x[/tex]
What is the length of each leg of the triangle?
Answers
Answer:
the answer you selected is correct
Step-by-step explanation:
this is a special right triangle. to find the other sides that will be equal to each other you can divide by square root of two so then you have to put the square root in the numerator and so you multiply by square root of 2 over square root of 2 which equals one technically so then you get 22 square root of 2 over 2 which simplifies to 11 square root over two
A rectangle has a perimeter of 24 inches. If the width is 5 more than twice the length,
what are the dimensions of the rectangle?
Answers
Answer:
Step-by-step explanation:width is 11 length is 13
Suppose a point at (2, 3) is translated to 7, -1). Which rule describes this translation?
O translate right 5, down 4
O translate left 5, up 4
O translate right 9, down 2
translate left 9, up 2
Answers
Answer:
translate right 5, down 4translate right 5, down 4
Step-by-step explanation:
translate right 5, down 4: Note that the x-coordinate 2 becomes 7, and that the y-coordinate 3 becomes -1.
Answer:
From (2,3) translate 5 to the right and 4 down to get (7,-1).
Step-by-step explanation:
(x,y)→(x+5,y−4)
(2,3)→(2+5,3−4)
(2,3)→(7,-1)
Hope this helps :)
*Pls mark my answer Brainliest*
Help me please!!
A watering can dispenses water at the rate of 0.3 gallon per minute. The original volume of water in the can was 7 gallons. Which set of ordered pairs shows the volume of water in the can in gallons (y), as a function of time in minutes (x), from the first minute after the can starts dispensing water?
{(1, 6.7), (2, 6.4), (3, 6.1)}
{(1, 7.0), (2, 6.7), (3, 6.4)}
{(6.7, 1), (6.4, 2), (6.1, 3)}
{(7.0, 1), (6.7, 2), (6.4, 3)}
Answers
Answer:
{(1, 6.7) , (2, 6.4) , (3, 6.1)}
Step-by-step explanation:
A watering can dispenses water at the rate of 0.3 gallon per minute.
The original volume of water in the can was 7 gallons.
If you plot a graph of volume of water in the can (gallons) against time (minutes),
The set of points on the graph will be:
After 1 minute: (1, 7 - 0.3) = (1, 6,7)
After 2 minutes: (2, 7 - 0.6) = (2, 6.4)
After 3 minutes: (3, 7 - 0.9) = (3, 6.1)
i.e the set {(1, 6.7) , (2, 6.4) , (3, 6.1)}
Please help I need it
Answers
Answer:
Yes. It's a right triangle.Step-by-step explanation:
If a ≤ b < c are the length of the sides of a right triangle, then
a² + b² = c².
We have:
a =30 ft, b = 40 ft and c = 50 ft.
Check the equality:
L = 30² + 40² = 900 + 1600 = 2500
R = 50² = 2500
L = R
Find the zeros of the function.
f(x) = 9x^2 + 6x - 8
Answers
Answer:
[tex]\large\boxed{-\dfrac{4}{3}\ and\ \dfrac{2}{3}}[/tex]
Step-by-step explanation:
[tex]f(x)=9x^2+6x-8\\\\\text{The zeros:}\\\\9x^2+6x-8=0\\\\9x^2+12x-6x-8=0\\\\3x(3x+4)-2(3x+4)=0\\\\(3x+4)(3x-2)=0\iff3x+4=0\ \vee\ 3x-2=0\\\\3x+4=0\qquad\text{subtract 4 from both sides}\\3x=-4\qquad\text{divide both sides by 3}\\\boxed{x=-\dfrac{4}{3}}\\\\3x-2=0\qquad\text{add 2 to both sides}\\3x=2\qquad\text{divide both sides by 3}\\\boxed{x=\dfrac{2}{3}}[/tex]
Please help !!! Urgent !!!What is the value of x???
Answers
Answer:
40
Step-by-step explanation:
x + (4x-20) = 180
5x - 20 = 180
5x = 200
x = 40
Answer:
the answer is 40
Step-by-step explanation:
the value of x and 4x -20 will be 180 degrees because it is a line and so you set the sum of those to 180 and solve for x
You are helping with some repairs at home. You drop a hammer and it hits the
floor at a speed of 8 feet per second. If the acceleration due to gravity (g) is
32 feet/second, how far above the ground (h) was the hammer when you
dropped it? Use the formula:
V = 2gh
Answers
Answer:
1 foot.
Step-by-step explanation
That is not the correct formula. Correct is V^2 = 2gh where h = the height
so the equation is:
8^2 = 2*32* h
h = 64/ 64 = 1 foot.
Answer:
[tex]h=\frac{1}{8} feet[/tex]
Step-by-step explanation:
In order to be able to solve this problem you just have to clear the formula for height:
V=2gh
[tex]\frac{V}{2g}=H[/tex]
[tex]\frac{8}{64}=H[/tex]
[tex]\frac{1}{8}=H[/tex]
So the height from which the hammer is dropped is 1/8 feet.
What is the equation, in point-slope form, of the line that is
perpendicular to the given line and passes through the
point (-4, -3)?
Answers
Answer:
Step-by-step explanation:
There is no given equation, so it is impossible to figure this out. I apologize.
Answer: I was told the third option
Step-by-step explanation:
What is C’ T’ if there was a rotation ?
Answers
Answer: The Answer Is 4) Hope it Helps!
Step-by-step explanation:
A hiking trail is 6 miles long. It has 4
exercise stations, spaced evenly along the
trail. What is the distance between each
exercise station?
Answers
Answer:
8800 ft apart
Step-by-step explanation:
1). Convert miles to feet. 6 2/3 x 5280 = 35200
2). Divide by 4. 35200/4 = 8800
Darwin bought 5 boxes of corned beef.a box contains one and a half dozen cans of corned beef.if he sold all the corned beef at 45.00 pesos each, how much did he earn....please answer with solution of AGONSA
Answers
The answer is:
Darwin earned 4050 pesos
Why?To solve the problem, first, we need to calculate the total quantity of corned beef, and then, calculate the total earning amount.
We have a box of corned beef one and half dozen cans, or 1.5 zones.
So, calculating we have:
[tex]TotalBeef=Dozen*1.5=12*1.5=18[/tex]
We have that there are 18 cans of corned beef per box, now, if he sold all the 5 boxes of corned in 45.00 pesos each, we have:
[tex]TotalEarning=Cans*45.00(pesos)=18*5*45.00pesos=4050(pesos)[/tex]
Hence, we have that Darwin earned 4050 pesos.
Have a nice day!
Solve for q; 6n-5q/11t = c
Answers
Answer:
[tex]\large\boxed{q=\dfrac{6n-11ct}{5}}[/tex]
Step-by-step explanation:
[tex]\dfrac{6n-5q}{11t}=c\qquad\text{multiply both sides by}\ 11t\neq0\\\\6n-5q=11ct\qquad\text{subtract}\ 6n\ \text{from both sides}\\\\-5q=11ct-6n\qquad\text{change the signs}\\\\5q=6n-11ct\qquad\text{divide both sides by 5}\\\\q=\dfrac{6n-11ct}{5}[/tex]
If f(x) = 3х -2 and g(x) = 2х+4 , find (f - g)(x).
ОА. Эх? - 2х - в
ов. 2x – 3х -2
Ос. х2 +2
OD. зх. -2x+2
Answers
Answer:
(f - g)(x) = x - 6Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
We have f(x) =3x - 2 and g(x) = 2x + 4. Substitute:
(f - g)(x) = (3x - 2) - (2x + 4)
(f - g)(x) = 3x - 2 - 2x - 4 combine like terms
(f - g)(x) = (3x - 2x) + (-2 -4)
(f - g)(x) = x - 6
In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x2 + y2 = r2. If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle? (h + x)2 + (k + y)2 = r2 (x – h)2 + (y – k)2 = r2 (k + x)2 + (h + y)2 = r2 (x – k)2 + (y – h)2 = r2
Answers
Answer:
(x – h)2 + (y – k)2 = r2
Step-by-step explanation:
If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle the equation of the new circle
(x – h)2 + (y – k)2 = r2
Based on Pythagorean theorem, and the location of the center of the
circle, (h, k), the equation of the circle is represented by the option;
(x - h)² + (y - k)² = r²How can the equation of the circle be found?
The general form of the equation of the circle is (x - h)² + (y - k)² = r²
Where;
(h, k) = The center of the circle
r = The radius of the circle
A description of the equation of the circle is as follows;
With regard to a location on the edge (circumference), of the circle, (x, y),
where, the center of the circle is (h, k), by Pythagorean the sum of the
square of the length of the horizontal side, (x - h), and the square of the
vertical side (y - k), of the right triangle formed gives the square of the
radius of the circle.
Therefore, the equation of the new circle can be represented by the equation;
(x - h)² + (y - k)² = r²The above equation is the general form of the equation of a circle.
Learn more about the equation of a circle here:
https://brainly.com/question/20863621