Square (second power, quadratic) - practice problems
Squaring a number means multiplying it by itself, raising it to the second power, denoted as n² or n×n. The result is always non-negative for real numbers, creating a parabolic relationship when graphed. Perfect squares are integers that result from squaring whole numbers (1, 4, 9, 16, 25, etc.). Squaring is fundamental to the Pythagorean theorem, area calculations for squares and circles, and the quadratic formula. The inverse operation is taking the square root. Understanding squares is essential for algebra, geometry, and physics, particularly in formulas involving area, distance, and energy.Number of problems found: 2996
- ABCD rhombus
ABCD is a rhombus with sides 10.5cm. If the length of the diagonal AC=15.8cm, using cosine formula. a. calculate the length of the diagonal BD correct to the nearest cm b. the angles of the rhombus to the nearest degree. - Spherical sector - parameters
Find the volume and surface area of spherical sector whose base has an altitude of 8cm. Drawn on a sphere whose diameter is 36 cm. - Insert two > GP
If 4, 36, 324 are in the geometric progression (GP) insert two more numbers in this progression so that it again forms a GP. - The perimeter 13
The perimeter of a rectangle is 22cm. What are its dimensions if it has a maximum area? - Isosceles right triangle
If I have a triangle with a right angle 24 inches long on each side of the right angle what is the length of the third side? - Equilateral RT
On a right triangle, side a is 12, and side b is 12. What is side c? - Four plates
Four equal maximum sized circular plates are cut off from a square paper sheet of area 784 sq cm. Calculate the circumference of each plates. - Square park
Amyra goes for a walk in a square park . The perimeter of the park is 1235 m. Find side of the park. - Area + perimeter TR2
Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm. - GP - negative term
The first term of a GP is -3 and the square of the second term is equal to its 4th term. Find the 7th term of the GP. - Eva wraps
Eva wraps a gift box in the shape of a right rectangular prism. The figure shows a net for the gift box. How much wrapping paper did she use, in square meters? - The surface 5
The surface area of a cylinder is 6140 cm², and the radius is 25 cm. What is the height? - A rope for cow
Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 154 sq m . - Parallel lines - dist
Find the distance between the parallel lines 3x – 4y +7 = 0 and 3x – 4y + 5 = 0 - A person 2
A person has 2 parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own. - Angle of inclination
Find the angle of inclination of a ramp that rise for 80 cm and is 200 cm long. - A rectangle 15
A rectangle is 5 cm longer its width. It areas is 6 cm square. What are the dimensions of the rectangle. - Rhombus = area, diagonal
The area of a rhombus is 144 sq cm. One of its diagonals is twice the other. How long is the shorter diagonal? - The rhombus (a,d)
Find the area of a rhombus, one side of which measures 20 cm, and one diagonal 24 cm. - A tree 3
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.
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