I have a question on my math homework.
The problem is: Suppose r varies jointly as s and t. If s = 20 when r = 140 and t = -5, find s when r = 7 and t = 2.5.
I used r = kst. I plug in and get 140 = k(20)(5). I then multiply and get 140 = k(-100). I then divide each side by -100 and get k = -7/5. I replug and get an equation of 7 = -7/5(2.5)s. I multiple this and get 7 = -3.5s. I divide each side by -3.5 and get s = -2.
My final answer is s = -2, I just want to know if this is correct.
you can get that without worrying about k.
since r = kst, r/st = k and is constant. So, you need s in
140/(-5*20) = 7/(2.5s)
s = -2
as you calculated
Your approach is correct, but there seems to be a minor calculation error in your solution. Let's go through the steps together to find the correct answer:
1. The given variation equation is: r = kst
2. Substitute the values: r = 140, s = 20, t = -5 to find the value of k.
140 = k(20)(-5)
Divide both sides by -100 to isolate k:
k = -7
3. Now we have the value of k, we can use it to find s when r = 7 and t = 2.5.
Substituting the values: r = 7, t = 2.5, and k = -7 into the variation equation:
7 = -7(20)(2.5)s
Simplify:
7 = -7(50)s
Divide both sides by -350:
s = -2
So, the correct answer is s = -2. Well done!
Your approach and calculations so far are correct. However, there is a small mistake in your final calculation. Let's go through the steps together:
1. Start with the equation r = kst, where r varies jointly as s and t.
2. Plug in the given values: s = 20, r = 140, and t = -5. We want to find s when r = 7 and t = 2.5.
3. Solve for the constant of variation k.
- Substitute the given values into the equation: 140 = k(20)(-5).
- Simplify: 140 = -100ks.
- Divide both sides by -100: k = -140/(-100) = 7/5.
4. Now, we have the explicit equation r = (7/5)st.
5. Substitute the given values of r = 7 and t = 2.5 into the equation.
- 7 = (7/5)(20)(2.5)s
- 7 = 70s, because (7/5)(20)(2.5) equals 70.
- Divide both sides by 70: s = 7/70 = 1/10.
6. Simplify the answer: s = 1/10.
Therefore, the correct answer is s = 1/10 or s = 0.1, not s = -2.