1. R varies jointly as S and t. If R=1/6,S=1/8 and T=3, find R when S=2 and T=11.
formula: R=KST
2. U varies jointly as L and H and inversely a S. If U=1.8, L=6.4, H=1.5 and S=-7.2, find U when L=4.3, H=5.1 and S=-2.2.
formula: U=KLH/S
Please Help!!
1.
R=KST, so K = R/ST = (1/6)/[(1/8)(3)] = 4/9
R = 4/9 ST = (4/9)(2)(11) = 88/9
2.
U=KLH/S, so K = US/LH = (1.8)(-7.2)/[(6.4)(1.5)] = -1.35
U = -1.35(4.3)(5.1)/-2.2 = 13.457
thanks! so my answer in number 1 was correct, number 2 is still not answered but ya help me. again, thanks to ur help!!
JezzaD.
1. Given:
R varies jointly as S and T.
R = 1/6, S = 1/8, T = 3.
To find R when S = 2 and T = 11, we need to calculate the constant of variation, K, and use it in the formula.
1/6 = K * (1/8) * 3 (substituting the given values)
1/6 = 3K/8 (simplifying)
To find K, we can cross multiply and solve for K:
8 * 1 = 3 * 6K
8 = 18K
K = 8/18
K = 4/9
Now we can substitute the new values into the formula to find R:
R = (4/9) * (2) * (11)
R = 8 * 11 / 9
R = 88 / 9
R = 9.778
Therefore, R is approximately 9.778 when S = 2 and T = 11.
2. Given:
U varies jointly as L and H, and inversely as S.
U = 1.8, L = 6.4, H = 1.5, S = -7.2.
To find U when L = 4.3, H = 5.1, and S = -2.2, we need to calculate the constant of variation, K, and use it in the formula.
U = K * (L) * (H) / S (substituting the given values)
Substituting the initial values:
1.8 = K * 6.4 * 1.5 / (-7.2)
To find K, we can cross multiply and solve for K:
1.8 * (-7.2) = K * 6.4 * 1.5
-12.96 = 9.6K
K = -12.96 / 9.6
K = -1.35
Now we can substitute the new values into the formula to find U:
U = (-1.35) * (4.3) * (5.1) / (-2.2)
U = -1.35 * 4.3 * 5.1 / -2.2
U ≈ 15.14
Therefore, U is approximately 15.14 when L = 4.3, H = 5.1, and S = -2.2.
Sure! I can help you with these questions. Let's solve them step by step.
1. The given question states that R varies jointly as S and t, and the formula for this variation is R = K * S * t. We need to find the value of R when S is 2 and t is 11, given that R is 1/6 when S is 1/8 and t is 3.
To solve this problem, we need to determine the value of K, which is the constant of variation. We can do this by substituting the known values into the formula and solving for K.
Given that R = 1/6, S = 1/8, and T = 3, we can substitute these values into the formula:
1/6 = K * (1/8) * 3
Simplifying this equation, we get:
1/6 = (3/8) * K
Now, divide both sides by (3/8) to isolate K:
K = (1/6) / (3/8)
K = (1/6) * (8/3)
K = 8/18
Simplifying further, we get:
K = 4/9
Now that we know the value of K, we can use it to find the value of R when S is 2 and T is 11. Substituting these values into the formula:
R = (4/9) * 2 * 11
Simplifying, we get:
R = (4/9) * 22
R = 8/9
Therefore, when S is 2 and T is 11, R is equal to 8/9.
2. The second question states that U varies jointly as L and H and inversely as S, with the formula U = K * L * H / S. We need to find the value of U when L is 4.3, H is 5.1, and S is -2.2, given that U is 1.8 when L is 6.4, H is 1.5, and S is -7.2.
Similarly to the previous question, we need to determine the value of K, which is the constant of variation. We can do this by substituting the known values into the formula and solving for K.
Given that U = 1.8, L = 6.4, H = 1.5, and S = -7.2, we can substitute these values into the formula:
1.8 = K * 6.4 * 1.5 / (-7.2)
Simplifying this equation, we get:
1.8 = (9.6 * K) / (-7.2)
Now, multiply both sides by (-7.2) to isolate K:
(-7.2) * 1.8 = 9.6 * K
-12.96 = 9.6 * K
Now, divide both sides by 9.6 to solve for K:
K = -12.96 / 9.6
K = -1.35
Now that we know the value of K, we can use it to find the value of U when L is 4.3, H is 5.1, and S is -2.2. Substituting these values into the formula:
U = (-1.35) * 4.3 * 5.1 / (-2.2)
Simplifying, we get:
U = 29.2575
Therefore, when L is 4.3, H is 5.1, and S is -2.2, U is approximately equal to 29.2575.