answer:First, let's find the perimeter of the rectangle. The perimeter of a rectangle is given by the formula: Perimeter = 2 * (length + breadth) For the given rectangle with length 22 cm and breadth 16 cm, the perimeter is: Perimeter = 2 * (22 cm + 16 cm) Perimeter = 2 * (38 cm) Perimeter = 76 cm Since the perimeter of the square is equal to the perimeter of the rectangle, the perimeter of the square is also 76 cm. The perimeter of a square is given by the formula: Perimeter = 4 * side Let's denote the side of the square as 's'. We can set up the equation: 4 * s = 76 cm Now, we can solve for 's': s = 76 cm / 4 s = 19 cm The side of the square is 19 cm, which is also the diameter of the semicircle. The circumference of a circle is given by the formula: Circumference = π * diameter Since we are dealing with a semicircle, we will take half of the circumference of the full circle and add the diameter to account for the straight edge of the semicircle: Circumference of semicircle = (π * diameter) / 2 + diameter Using the value of π as approximately 3.14 and the diameter as 19 cm, we get: Circumference of semicircle = (3.14 * 19 cm) / 2 + 19 cm Circumference of semicircle = (59.66 cm) / 2 + 19 cm Circumference of semicircle = 29.83 cm + 19 cm Circumference of semicircle = 48.83 cm Rounded off to two decimal places, the circumference of the semicircle is boxed{48.83} cm.

answer:Given the problem, Nikita starts with three natural numbers and then follows the rule of summing the last three numbers and appending the result to the end of the sequence. We need to determine if it is possible for Nikita to write 9 consecutive prime numbers using this method. Let's assume the sequence starts with three natural numbers (a_1, a_2, a_3). According to the rule, the next term is given by: [ a_{n+3} = a_n + a_{n+1} + a_{n+2} ] We are tasked with finding a sequence of 9 consecutive prime numbers. The reference solution provides a specific sequence: (5, 3, 3, 11, 17, 31, 59, 107, 197). 1. **Initial Numbers**: Let: [ a_1 = 5, quad a_2 = 3, quad a_3 = 3 ] 2. **Generating the Sequence**: Using the rule: [ a_4 = a_1 + a_2 + a_3 = 5 + 3 + 3 = 11 ] [ a_5 = a_2 + a_3 + a_4 = 3 + 3 + 11 = 17 ] [ a_6 = a_3 + a_4 + a_5 = 3 + 11 + 17 = 31 ] [ a_7 = a_4 + a_5 + a_6 = 11 + 17 + 31 = 59 ] [ a_8 = a_5 + a_6 + a_7 = 17 + 31 + 59 = 107 ] [ a_9 = a_6 + a_7 + a_8 = 31 + 59 + 107 = 197 ] 3. **Verification of Primality**: Check if all the numbers in the sequence are prime: - 5: Prime - 3: Prime - 3: Prime - 11: Prime - 17: Prime - 31: Prime - 59: Prime - 107: Prime - 197: Prime Since all 9 terms of this sequence are prime numbers, it is indeed possible for Nikita to write 9 consecutive prime numbers by following the given rule. (boxed{5, 3, 3, 11, 17, 31, 59, 107, 197})

answer:First, verify if the provided side lengths form a right triangle. Calculate: [ 7^2 + 24^2 = 49 + 576 = 625 ] [ 25^2 = 625 ] Since 7^2 + 24^2 = 25^2, the triangle is indeed a right triangle. To find its area, use the formula for the area of a right triangle: [ text{Area} = frac{1}{2} (text{leg}_1 times text{leg}_2) ] [ text{Area} = frac{1}{2} (7 times 24) = frac{1}{2} (168) = boxed{84} ]

answer:Given y=-x^3+3x^2, then the derivative y'=-3x^2+6x. Therefore, at x=1, y'=-3(1)^2+6(1)=3. Thus, the equation of the tangent line to the curve y=-x^3+3x^2 at the point (1, 2) is y-2=3(x-1), which simplifies to y=3x-1. Hence, the correct option is boxed{A}.