https://file.aiquickdraw.com/mathbot/file/1729489471655wa5jd86r.jpg

Let's solve the three parts of the question one by one:

### Part (a):
The equation is:
\[
s = ut + \frac{1}{2} a t^2
\]
Given:
- \( u = 9 \)
- \( t = 4 \)
- \( a = 7 \)

Substituting the values:
\[
s = 9(4) + \frac{1}{2} (7)(4^2)
\]
\[
s = 36 + \frac{1}{2} (7)(16)
\]
\[
s = 36 + \frac{1}{2} (112)
\]
\[
s = 36 + 56
\]
\[
s = 92
\]

So, the value of \( s \) is **92**.

### Part (b):
The formula is:
\[
F = p + qr
\]
Given:
- \( p = 2.3 \)
- \( q = 3.9 \)
- \( r = 0.9 \)

Substituting the values:
\[
F = 2.3 + (3.9)(0.9)
\]
\[
F = 2.3 + 3.51
\]
\[
F = 5.81
\]

So, the value of \( F \) is **5.81**.

### Part (c):
The formula is:
\[
T = a + (n - 1) d
\]
Given:
- \( a = 9.2 \)
- \( n = 6 \)
- \( d = 1.3 \)

Substituting the values:
\[
T = 9.2 + (6 - 1)(1.3)
\]
\[
T = 9.2 + 5(1.3)
\]
\[
T = 9.2 + 6.5
\]
\[
T = 15.7
\]

So, the value of \( T \) is **15.7**.

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Let me know if you'd like more details or have any further questions!

### Related Questions:
1. How would you modify the formula for \( s \) if the object started with an initial position \( s_0 \)?
2. Can you generalize the equation for \( F \) if \( q \) varies with respect to time?
3. What happens to the value of \( T \) if \( d \) is halved?
4. How can the formula for \( s \) be used to determine the acceleration given the final position?
5. What would the result for \( F \) be if \( r \) were negative?

### Tip:
When solving algebraic equations with multiple terms, always perform operations step by step to avoid mistakes.

a. If s = ut + 1/2 at^2, find s if u = 9, t = 4, and a = 7.
b. Given F = p + qr, find F if p = 2.3, q = 3.9 and r = 0.9.
c. For the formula T = a + (n - 1)d, find T if a = 9.2, n = 6 and d = 1.3.

Learn how to solve kinematic, linear, and arithmetic sequence equations with step-by-step solutions. This problem involves key concepts like kinematic equations, linear equations, and arithmetic sequences. Suitable for students in Grades 9-11.

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