Answer :

Brainlysahab

Step-by-step explanation:

To find the value of s when u = 6 and t = 3, we can use the direct variation and inverse variation concepts.

Given that s varies directly with u and inversely with t, we can write the equation as:

s = k * (u / t)

where k is the constant of variation.

To find the value of k, we can substitute the given values u = -1, t = -5, and s = -2 into the equation:

-2 = k * (-1 / -5)

Simplifying the equation, we have:

-2 = k * (1/5)

Multiplying both sides by 5, we get:

-2 * 5 = k

-10 = k

Now we can substitute the value of k into the equation to find s when u = 6 and t = 3:

s = -10 * (6 / 3)

s = -10 * 2

s = -20

Therefore, when u = 6 and t = 3, the value of s is -20.

msm555

Answer:

s = -20

Step-by-step explanation:

Inversely Proportional:

If s is inversely proportional to t, we can write it as:

[tex]\sf s \propto \dfrac{1}{t} [/tex]

In this case, s is directly proportional to u and inversely proportional to t, so we can write:

[tex]\sf s \propto \dfrac{u}{t} [/tex]

Direct Variation:

If s is directly proportional to u, we can write it as:

[tex]\sf s \propto u [/tex]

In this case, we've already combined direct and inverse variations, so our expression is:

[tex]\sf s \propto \dfrac{u}{t} [/tex]

Given the initial conditions, when u = -1, t = -5, and s = -2, we can find the constant of proportionality k.

[tex]\sf -2 = k \cdot \dfrac{-1}{-5} [/tex]

[tex]\sf -2 = k \cdot \dfrac{1}{5} [/tex]

[tex]\sf k = -10 [/tex]

Now that we've found k = -10, we can find s when u = 6 and t = 3.

Substitute the value and simplify:

[tex]\sf s = -10 \cdot \dfrac{6}{3} [/tex]

[tex]\sf s = -10 \cdot 2 [/tex]

[tex]\sf s = -20 [/tex]

So, when u = 6 and t = 3, s = -20.