Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Answer:
The volume is 40.96 cubic feet
Step-by-step explanation:
Given
[tex]V\ \alpha\ h * d^2[/tex]
Where
[tex]V = Volume\\ h = height\\ d = distance[/tex]
[tex]V = 15.84ft^3; h =22ft; d = 3ft[/tex]
Required
The volume when h = 32 and d = 4
[tex]V\ \alpha\ h * d^2[/tex]
Express as an equation
[tex]V = khd^2[/tex]
Where k is the constant of variation.
Make k the subject
[tex]k = \frac{V}{hd^2}[/tex]
Substitute [tex]V = 15.84ft^3; h =22ft; d = 3ft[/tex]
[tex]k = \frac{15.84}{22 * 3^2}[/tex]
[tex]k = \frac{15.84}{22 * 9}[/tex]
[tex]k = \frac{15.84}{198}[/tex]
[tex]k = 0.08[/tex]
To solve for V when h = 32 and d = 4, we have:
[tex]V = khd^2[/tex]
[tex]V = 0.08 * 32 * 4^2[/tex]
[tex]V = 0.08 * 32 * 16[/tex]
[tex]V = 40.96[/tex]
The volume is 40.96 cubic feet
The volume of the wood obtained from a tree that is 32 feet tall having a measurement of 4 feet around the trunk is [tex]40.96 \: \rm ft^3[/tex]
What is directly proportional and inversely proportional relationship?
Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
[tex]p = kq[/tex]
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n are two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
For this case, we have:
V = volume of the wood varying jointly as height of the tree and square of the distance around the trunk.
Let we take:
- r = distance of the wood around the trunk (in feet)
- h = height of the tree ( in feet)
V will of course increase as r or h increases, and as it varies jointly, thus:
[tex]V \propto h r^2[/tex]
Let the constant of proportionality be 'k', then:
[tex]V = kr^2h[/tex] (in cubic foot)
For case 1, it was specified that V = 15.84 cubic foot when r = 3 ft and h = 22 ft,
Putting these values gives us:
[tex]15.84 = k(3)^2(22)\\\\k = \dfrac{15.84}{198} = 0.08[/tex]
Thus, we have:
[tex]\rm V = 0.08r^2 h \: \rm ft^3[/tex]
Assuming second wood was also obtained from same kind of tree, we get the volume of the wood for h = 32 and r = 4 feet as:
[tex]V = 0.08 (4)^2 (32) = 40.96 \: \rm ft^3[/tex]
Thus, the volume of the wood obtained from a tree that is 32 feet tall having a measurement of 4 feet around the trunk is [tex]40.96 \: \rm ft^3[/tex]
Learn more about proportionality here:
https://brainly.com/question/13082482
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
