R varies jointly as S and the square of T. If R is 32.4 when S=0.2 and T=9, find R when S=0.5 and T=5. I believe the answer is R=25, could someone check this for me?

Solution:

First, find the constant of variation "k",
R = kst^2
Substitute:
(32.4) = k (0.2)(9)^2
(32.4) = k (0.2)(81)
(32.4) = k (16.2)
k = 32.4/16.2
k = 2 - Constant of variation
Then, find R when S=0.5 and T=5
Solution:
R = kst^2
R = (2)(0.5)(5)^2
R = (2)(0.5)(25)
R = 25
Your answer is right bestie <3

Sure, let's check it out using a bit of clown humor!

To solve this problem, we need to set up a proportion. Let's call the constant of variation k:

R = k * S * T^2

Now we can plug in the values we know:
32.4 = k * 0.2 * 9^2

Simplifying, we find k = 32.4 / (0.2 * 81). Good so far?

Now, let's substitute the new values:
R = k * 0.5 * 5^2

Calculating that, we find R ≈ 20.25

Oh no, it seems that your answer of R = 25 is a bit off! It looks like the correct answer is R ≈ 20.25. Keep practicing those math skills, and remember that even Clowns make mistakes sometimes! 🤡

To solve this problem, we need to use the concept of direct variation, or joint variation in this case. In direct variation, one variable is directly proportional to another variable, meaning that as one variable increases or decreases, the other variable changes in the same proportion.

In this case, R varies jointly as S and the square of T, which means that R is directly proportional to the product of S and T^2.

Let's set up the proportion: R = k * S * T^2, where k is a constant of variation.

To find the value of k, we can use the given information when R=32.4, S=0.2, and T=9:

32.4 = k * 0.2 * 9^2
32.4 = k * 0.2 * 81
32.4 = 16.2k
k = 32.4 / 16.2
k = 2

Now that we have the value of k, we can solve for R when S=0.5 and T=5:

R = 2 * 0.5 * 5^2
R = 2 * 0.5 * 25
R = 25

So, your answer is correct. When S = 0.5 and T = 5, R is indeed 25.

Thank you!!

we have

R = k*S*T^2
32.4 = k*.2*9^2 = 16.2k
k=2

R = 2ST^2
R(.5,5) = 2*.5*25 = 25

Good job.