Biquadratic equation - high school - practice problems
Number of problems found: 21
- Combinations 70714
If we increase the number of elements by 1, the number of combinations of the third class without repetitions increases by 10. How many elements do we have? - Members
A geometric sequence with six members has the sum of all six members equal to 63; the sum of the even members (that has an even index) has a value of 42. Find these members. - Given 2
Given g(x)=x²+x+1 where x=t². What is g(t²)? - Polynomial roots
Find the other zeroes of the polynomial 2x4+3x³-3x²-6x-2, if two of them are root2 & -root2
- Truncated pyramid
The truncated regular quadrilateral pyramid has a volume of 74 cm3, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's area. Calculate the area of the upper base. - The cylinder
In a rotating cylinder, it is given: the surface of the shell (without bases) S = 96 cm² and the volume V = 192 cm cubic. Calculate the radius and height of this cylinder. - Rotary cylinder
In the rotary cylinder it is given: surface S = 96 cm² and volume V = 192 cm cubic. Calculate its radius and height. - Land boundary
The land is a right triangle. Its hypotenuse is 30 meters long, and its circumference is 72 meters. What are the sizes of the remaining sides of the land boundary? - Faces diagonals
If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), find the cuboid volume. Solve for x=1.3, y=1, z=1.2
- Geometric progressiob
If the sum of four consecutive terms of a geometric progression is 80 and the arithmetic mean of the second and fourth terms is 30, then find terms. - Three members GP
The sum of three numbers in GP (geometric progression) is 21, and the sum of their squares is 189. Find the numbers. - Eq2 2
Solve the following equation with quadratic members and rational function: (x²+1)/(x-4) + (x²-1)/(x+3) = 23 - Hyperbola equation
Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10] - Rotating 7947
In the rotating cone = 100π S rotating cone = 90π v =? r =?
- Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm² and the side is 13 cm long. - Substitution method
Solve a goniometric equation: sin4 θ - 1/cos² θ=cos² θ - 2 - Diagonals of the rhombus
How long are the diagonals e, and f in the diamond if its side is 5 cm long and its area is 20 cm²? - Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70. - Cuboid
Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm³. Calculate the length of the other edges.
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