t varies directly as the square of v and inversely as the aquare root of g. T = 20 when V = 5 and g = 16. find:
1. the formular connecting T, V and g
2. T when V = 15 and g = 25
3. g when T = 40 and V = 10
1. T = V^2 / g
plug in given values for solutions to 2. and 3.
UPDATE
1. T = k (V^2 / g) ... 20 = k (5^2 / √16) ... solve for k
plug in given values for solutions to 2. and 3.
"t varies directly as the square of v and inversely as the square root of g"
----> t = k (v^2/√g)
when T = 20 , V = 5 and g = 16
20 = k(25/4
k = 80/25
t = (80/25) v^2/√g
#2
find T when V = 15 and g = 25
t = (80/25)(225/5) = 144
#3. you try it
2.048
To find the formula connecting T, V, and g, we can start by using the given information: T varies directly as the square of v and inversely as the square root of g.
Let's write this information in terms of equations:
1. t = k * v^2 / sqrt(g), where k is the constant of variation.
To find the value of k, we can substitute the given values for T, V, and g in equation 1:
20 = k * 5^2 / sqrt(16)
20 = k * 25 / 4
20 * 4 = k * 25
k = 80 / 25
k = 3.2
Now we have the formula connecting T, V, and g:
t = 3.2 * v^2 / sqrt(g)
Using this formula, we can find the respective values of T for the given values of V and g:
2. T when V = 15 and g = 25:
t = 3.2 * 15^2 / sqrt(25)
t = 3.2 * 225 / 5
t = 720 / 5
t = 144
Therefore, when V = 15 and g = 25, T is equal to 144.
3. g when T = 40 and V = 10:
Substituting the given values in the formula, we can solve for g:
40 = 3.2 * 10^2 / sqrt(g)
40 = 3.2 * 100 / sqrt(g)
40 = 320 / sqrt(g)
To isolate g, we can cross-multiply and square both sides:
40 * sqrt(g) = 320
sqrt(g) = 320 / 40
sqrt(g) = 8
To solve for g, we square both sides of the equation:
g = 8^2
g = 64
Thus, when T = 40 and V = 10, g is equal to 64.