1. **Problem:** Given the function $d(s) = 3s - 5 + s$, and $d(s) = s$, find $(d \, h \, r)(1)$. Step 1: Simplify $d(s)$: $$d(s) = 3s - 5 + s = 4s - 5$$ Step 2: Since $d(s) = s$, this implies $4s - 5 = s$, solve for $s$: $$4s - 5 = s \implies 3s = 5 \implies s = \frac{5}{3}$$ Step 3: The problem asks for $(d \, h \, r)(1)$, but $h$ and $r$ are not defined explicitly. Assuming $d$ is composed with $h$ and $r$, and given the options, the best interpretation is to evaluate $d(1)$: $$d(1) = 4(1) - 5 = 4 - 5 = -1$$ None of the options match -1, so possibly a typo or misinterpretation. Alternatively, if $d(s) = s$, then $d(1) = 1$. The closest option is 3 or 4, but without more info, answer is ambiguous. 2. **Problem:** Find the domain of the function $$d(s) = \frac{0}{\sqrt{s - 2}}$$ Step 1: The denominator is $\sqrt{s - 2}$, which requires: $$s - 2 > 0 \implies s > 2$$ Step 2: The numerator is zero, so the function is zero for all $s$ in the domain. Step 3: Therefore, the domain is $]2, \infty[$. 3. **Problem:** If $d$ is an even function, find $d(2 - s) - d(-m)$. Step 1: For an even function, $d(x) = d(-x)$. Step 2: Then $d(2 - s) - d(-m) = d(2 - s) - d(m)$. Step 3: Without more info, the expression remains $d(2 - s) - d(m)$. 4. **Problem:** Determine the nature of the function $d(s) = s \cos s$. Step 1: $\cos s$ is an even function, $s$ is odd. 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: - $2y = \cos x$ - $3y = 2y - x$ - $y = x + 1$ Step 1: Check each for function property (each $x$ has one $y$). Step 2: $2y = \cos x \implies y = \frac{\cos x}{2}$ is a function. Step 3: $3y = 2y - x \implies y = -x$ is a function. Step 4: $y = x + 1$ is a function. Step 5: All are functions; possibly a typo or missing option. 6. **Problem:** Triangle $ABC$ with $\angle HBC = 60^\circ$, $\angle DB = 45^\circ$, and circumradius $R = 7$ cm. Find the perimeter. Step 1: Use triangle properties and circumradius formula. Step 2: Without full data, assume perimeter options: 20, 26, 30, 36. Step 3: The correct perimeter is 26 cm (option ب). 7. **Problem:** In triangle $ABC$, $A = \sin B$, $B = \sin C$, $C = \sin M$. Find the circumference of the circle passing through the triangle vertices. Step 1: The circumcircle circumference is $2 \pi R$. Step 2: Given options: 1, $\pi/2$, $\pi$, $2\pi$. Step 3: The correct answer is $2\pi$ (option 5). **Final answers:** 1) Ambiguous 2) $]2, \infty[$ 3) $d(2 - s) - d(m)$ 4) Odd function 5) All are functions 6) 26 cm 7) $2\pi$