t varies directly as the square root of l. If l=81, then t=10 what is the constant proportion?
1. a is directly proportional to b. If a = 15, then b = 9
2. M varies directly as n. If n = 2/3, then m = 1/4
3. T varies as the square root of L. If L = 81, then T = 10
4. Z is proportional to the cube of d. If d = 2 then z = 5
5. f varies directly as the square of t. If t = 16, then r = 6
6. p varies directly as the sum of L and W. If L = 4 and W = 3, then P = 14
7. C is directly proportional to r. If r = 5, then c = 10(pi)
8. Y varies directly as the cube root of x. If x = 27, then y = 2z
9. J varies directly as E. If J = 594, then E = 225.
10. X varies as 1/y. If X = 25, y = 10
The constant proportion for the given scenarios can be calculated using the formula:
constant proportion = t / √l
1. a is directly proportional to b. If a = 15, then b = 9
Constant proportion = a / b = 15 / 9 = 5/3
2. M varies directly as n. If n = 2/3, then m = 1/4
Constant proportion = M / N = 1/4 / 2/3 = 3/8
3. T varies as the square root of L. If L = 81, then T = 10
Constant proportion = T / √L = 10 / √81 = 10 / 9
4. Z is proportional to the cube of d. If d = 2 then z = 5
Constant proportion = Z / d³ = 5 / 2³ = 5 / 8
5. F varies directly as the square of t. If t = 16, then r = 6
Constant proportion = F / t² = 6 / 16² = 6 / 256 = 3/128
6. P varies directly as the sum of L and W. If L = 4 and W = 3, then P = 14
Constant proportion = P / (L + W) = 14 / (4 + 3) = 14 / 7 = 2
7. C is directly proportional to r. If r = 5, then c = 10(pi)
Constant proportion = C / r = 10π / 5 = 2π
8. Y varies directly as the cube root of x. If x = 27, then y = 2z
Constant proportion = Y / ∛x = 2z / ∛x = 2
9. J varies directly as E. If J = 594, then E = 225.
Constant proportion = J / E = 594 / 225 = 22/15
10. X varies as 1/y. If X = 25, y = 10
Constant proportion = X / 1/y = 25 / 1/10 = 250
Therefore, the constants proportions for the given scenarios are:
1. 5/3
2. 3/8
3. 10/9
4. 5/8
5. 3/128
6. 2
7. 2π
8. 2
9. 22/15
10. 250
To find the constant of proportionality, we can use the formula for direct variation:
t = k*√l
where t is the dependent variable, l is the independent variable, and k is the constant of proportionality.
Given that when l = 81, t = 10, we can substitute these values into the equation:
10 = k*√81
To solve for k, we need to find the square root of 81:
√81 = 9
Now we can substitute this value back into the equation:
10 = k*9
To isolate k, we divide both sides by 9:
10/9 = k
So the constant of proportionality (k) is equal to 10/9.
Therefore, the answer to the question is: 10/9.
Wow , looks like you want us to do your assignment for you.
I will do one of them, say #8, then you do the rest
#8
Y varies directly as the cube root of x
y = k (x)^(1/3)
given : when x=27, y = 2z
2z = k(27)^(1/3)
2z = k(3)
k = 2z/3
(was this a typo? all the other cases had numbers)