![A high-angle forensic photograph depicts an open mathematics textbook or workbook resting on a flat, light-colored surface in an indoor, educational setting. The exact location is Unknown, Unknown. No individuals are visible.
The primary subject is a white page, numbered "21" at the top right, displaying "ВАРИАНТ 3" (Variant 3) at the top. The page contains four distinct mathematics problems written in Russian, along with instructions.
Problem 11 involves a function graph (`f(x) = k/x + b`), a coordinate plane showing a hyperbola passing through (1,1), and asks for `f(-15)`.
Problem 12 asks for the maximum value of a function (`y = 1/3 * sqrt(x) - 3x + 70`) on the interval `[9, 81]`. Both problems have blank "Ответ:" (Answer:) lines.
A grey instructional box below Problem 12, marked with an exclamation point, instructs the user to transfer answers to Answer Sheet #1.
The section "Часть 2" (Part 2) follows, with another grey instructional box detailing the use of Answer Sheet #2 for problems 13-19, requiring full justified solutions.
Problem 13 consists of two parts: a) solving an exponential equation (`8^(1-4x) - 21 * 4^(1.5-3x) + 640 = 0`), and b) finding roots within the interval `[-1; -0.5]`.
Problem 14 is a detailed geometry problem concerning a regular prism and a cutting plane, asking to a) prove a perpendicularity relationship and b) find the volume of a pyramid formed by the intersection.
The bottom of the page includes copyright information dated 2026, indicating publishing entities.
To the right of the textbook page, a portion of a blue-lined notebook or binder page with a blue binding edge is visible. The textbook page shows minor creasing but no handwritten markings on the designated answer lines. Lighting is uniform, suggesting an overhead or ambient light source.](https://firebasestorage.googleapis.com/v0/b/patr-3a75e.appspot.com/o/uploads%2Fimage_picker_4fe37918-24d3-4406-9.jpg?alt=media)
Jan 22, 2026
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A high-angle forensic photograph depicts an open mathematics textbook or workbook resting on a flat, light-colored surface in an indoor, educational setting. The exact location is Unknown, Unknown. No individuals are visible. The primary subject is a white page, numbered "21" at the top right, displaying "ВАРИАНТ 3" (Variant 3) at the top. The page contains four distinct mathematics problems written in Russian, along with instructions. Problem 11 involves a function graph (`f(x) = k/x + b`), a coordinate plane showing a hyperbola passing through (1,1), and asks for `f(-15)`. Problem 12 asks for the maximum value of a function (`y = 1/3 * sqrt(x) - 3x + 70`) on the interval `[9, 81]`. Both problems have blank "Ответ:" (Answer:) lines. A grey instructional box below Problem 12, marked with an exclamation point, instructs the user to transfer answers to Answer Sheet #1. The section "Часть 2" (Part 2) follows, with another grey instructional box detailing the use of Answer Sheet #2 for problems 13-19, requiring full justified solutions. Problem 13 consists of two parts: a) solving an exponential equation (`8^(1-4x) - 21 * 4^(1.5-3x) + 640 = 0`), and b) finding roots within the interval `[-1; -0.5]`. Problem 14 is a detailed geometry problem concerning a regular prism and a cutting plane, asking to a) prove a perpendicularity relationship and b) find the volume of a pyramid formed by the intersection. The bottom of the page includes copyright information dated 2026, indicating publishing entities. To the right of the textbook page, a portion of a blue-lined notebook or binder page with a blue binding edge is visible. The textbook page shows minor creasing but no handwritten markings on the designated answer lines. Lighting is uniform, suggesting an overhead or ambient light source.
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