1. Suppose that y varies jointly with w and x, inversely with z, and suppose that y = 360 when w = 8 x = 15 and z = 3 Write the equation that models the relationship.
y = 9wx/z
y= z/9wx
y = wx/9z
(1 point)
2. A neighborhood group wants to build a new playground using donations from residents. The amount needed from each donor varies inversely to the number of people donating if 25 people donate, each of them would need to contribute $135. How much would each person need to contribute if 45 people donate? Round your answer to the nearest cent, if necessary.
$75.00
$243.00
$25.00
$58.33
(1 point)
AAAaannndd the bot gets it wrong yet again!
see below
1. None of the provided options correctly represent the relationship between y, w, x, and z. However, the correct equation that models the relationship is:
y = (wx)/(9z)
2. If the amount needed from each donor varies inversely with the number of people donating, we can set up the equation:
Amount needed = k/number of people donating
where k is a constant. We can solve for k using the given information:
135 = k/25
k = 3375
Now, we can find the amount needed if 45 people donate:
Amount needed = 3375/45 = $75.00
Therefore, each person would need to contribute $75.00 if 45 people donate.
1. To determine the equation that models the relationship, we can use the formula for joint and inverse variation.
Joint variation:
y varies jointly with w and x, so we can represent this as y ∝ wx.
Inverse variation:
y varies inversely with z, so we can represent this as y ∝ 1/z.
Combining these variations, we have:
y = k(wx)/(1/z)
Now, we can plug in the given values to find the constant of variation k:
360 = k(8)(15)/(1)(3)
Simplifying the equation:
360 = 120k
Solving for k:
k = 360/120
k = 3
Now that we know the constant of variation, we can rewrite the equation as:
y = 3(wx)/z
Therefore, the equation that models the relationship is y = 3(wx)/z. Answer: y = 3wx/z.
2. The problem states that the amount needed from each donor varies inversely with the number of people donating.
Let's denote the amount needed from each donor as a, and the number of people donating as p.
We can write the equation of inverse variation as:
a ∝ 1/p
Now, we can use the given information to find the constant of variation. When 25 people donate, each of them needs to contribute $135:
a1 = 135
p1 = 25
Using the equation of inverse variation, we can write:
a1 ∝ 1/p1
Substituting the values:
135 ∝ 1/25
Now, we can find the constant of variation k:
135 = k/25
Solving for k:
k = 135 * 25
k = 3375
Now, we can rewrite the equation of inverse variation as:
a = k/p
To find the amount each person needs to contribute when 45 people donate, we can substitute the values into the equation:
a2 = ?
p2 = 45
Using the constant of variation k, we can write:
a2 = 3375/45
Calculating the value:
a2 = 75
Rounding the answer to the nearest cent, we get $75.00.
Therefore, each person would need to contribute $75.00 if 45 people donate. Answer: $75.00.
1. To find the equation that models the relationship, we need to identify the variables and the relationships between them.
In this case, we know that:
- y varies jointly with w and x
- y varies inversely with z
We can write the equation in the form:
y = k * (w^a) * (x^b) / (z^c)
where k is a constant, and a, b, and c are the exponents associated with w, x, and z, respectively.
Given that y = 360 when w = 8, x = 15, and z = 3, we can substitute these values into the equation:
360 = k * (8^a) * (15^b) / (3^c)
To find the values of a, b, and c, we can use the fact that y varies jointly with w and x, inversely with z. This means that when we increase w or x, y increases, and when we increase z, y decreases.
From the given information, we can deduce that when z = 1, y = k * (8^a) * (15^b). So we can substitute these values into the equation:
360 = k * (8^a) * (15^b) / (1^c)
Simplifying, we get:
360 = k * (8^a) * (15^b)
Now, we need to solve for a and b. We can use the given information that y = 360 when w = 8 and x = 15. Therefore:
360 = k * (8^a) * (15^b)
Using these values, we can solve for k, a, and b. Substituting the given values, we get:
360 = k * (8^a) * (15^b)
360 = k * (8^1) * (15^1)
360 = 8k * 15
Simplifying, we find:
k = 360 / (8 * 15)
k = 3
Therefore, the equation that models the relationship is:
y = 3 * (w^a) * (x^b) / (z^c)
2. To find out how much each person needs to contribute if 45 people donate, we can use the inverse variation relationship between the amount needed from each donor and the number of people donating.
According to the problem, if 25 people donate, each person needs to contribute $135. This can be written as the equation:
y = k / x
where y is the amount needed from each donor, x is the number of people donating, and k is a constant.
We can substitute the given values into the equation to solve for k:
135 = k / 25
k = 135 * 25
k = 3375
Now that we have the value of k, we can use it to find out how much each person needs to contribute if 45 people donate:
y = 3375 / 45
y ≈ $75.00 (rounded to the nearest cent)
Therefore, each person would need to contribute approximately $75.00 if 45 people donate.