1. **Problem:** Given the function $d(s) = s^2 + 0 = d(s) = s = s$, find $d(1)$. Step 1: Simplify the function: $d(s) = s^2$. Step 2: Substitute $s=1$: $d(1) = 1^2 = 1$. 2. **Problem:** Find the domain of the function $d(s) = s$. Step 1: The function $d(s) = s$ is a linear function defined for all real numbers. Step 2: Therefore, the domain is $(-\infty, \infty)$. 3. **Problem:** If $d$ is an odd function, find $-1 - d(1)$. Step 1: For an odd function, $d(-1) = -d(1)$. Step 2: Calculate $-1 - d(1)$. Since $d(-1) = -d(1)$, then $-1 - d(1) = d(-1) - 1$. Step 3: Without specific values, the expression remains $-1 - d(1)$. 4. **Problem:** Determine the parity of the function $d(s) = s \cos s$. Step 1: $s$ is an odd function, $\cos s$ is an even function. Step 2: The product of an odd and even function is odd. Step 3: Therefore, $d(s)$ is an odd function. 5. **Problem:** Identify which relation is not a function among: - $2y = \cos x$ - $y = x - 1$ - $5y = x + 3 + 1$ Step 1: Solve each for $y$. - $y = \frac{\cos x}{2}$ (function) - $y = x - 1$ (function) - $y = \frac{x + 4}{5}$ (function) Step 2: All are functions since each $x$ corresponds to exactly one $y$. 6. **Problem:** Triangle $ABC$ with $AB=90$, angle $B D = 45$, and circumradius $7$ cm. Find the perimeter. Step 1: Use the formula for perimeter $P = 2R \times \text{sum of sines of angles}$. Step 2: Given data insufficient for exact calculation; assuming right triangle with hypotenuse $2R=14$. Step 3: Perimeter approximately $20$ cm (closest option). 7. **Problem:** In triangle $MBJ$, given $MB = \sin M'$, $\sin B'$, $\sin J' = \sin M$, find the perimeter of the circumcircle. Step 1: The perimeter of the circumcircle is $2\pi R$. Step 2: Given the problem, the answer is $\pi$.