Solved tasks in mathematics, mathematics, math, equation, surface of the pyramid, surfaces of the cube, mathematical tasks, solved tasks, polynomials, binomi, Mathematics for the high school, mathematics for elementary school, fractions
Thursday, April 25, 2013
Thursday, April 18, 2013
Wednesday, April 17, 2013
Quadratic equation solver (High School)
(2x-15)(2x-7)-(x-36)(x-8)+36=0
4x²-14x-30x+105-(x²-8x-36x+288)+36=0
4x²-14x-30x+105-x²+8x+36-288+36=0
3x²-147=0
3x²=147
x²=147/3
x=√49
x1=+7 x2=-7
Division of complex numbers
i2 = −1
3-5 i/7+2 i=3-5 i/7+2 i*7-2 i/7-2 i=21-6 i-35 i+10 i²/7²+2²=21-10-41 i²/49+4=
=11-41 i/53=11/53-41/53 i
Proper quadrilateral prism (primary school)
Calculate the surface proper quadrilateral prism if the base edges 4cm and 8cm high.
Solved:
Solved:
a=6cm M=3a*H P=2B+M
H=8cm M=3*6*8 P=2*9√3+144
B=a²√3/4 M=18*8 P=18√3+144 cm²
B=6²√3/4 M=144cm²
B=36√3/4
B=9√3
Cube surface (primary school)
The sum of the length of the edge of a cube is 48cm. Calculate the surface.
Solved:
Solved:
O=48cm P=6a²
O=12a P=6*4²
48=12a P=6*16
a=48:12 P=96cm²
a=4cm
Surfaces of the cube (primary school)
Calculate the surface of a cube if the diagonal 3√2
Solved:
Solved:
d=a√2 P=6a²
3√2=a√2 P=6*3²
a=3cm P=6*9
P=54cm²
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge,
study, learning") is the abstract study of topics encompassing quantity, structure, space,change, and other properties;it has no generally accepted definition. Mathematicians seek out patterns and formulate new conjectures.
Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical
structures are good models of real phenomena, then mathematical reasoning can
provide insight or predictions about nature.
Through
the use of abstraction and logical reasoning, mathematics
developed from counting, calculation, measurement,
and the systematic study of the shapes and motions of physical objects. Practical
mathematics has been a human activity for as far back as written records exist. The research required to solve
mathematical problems can take years or even centuries of sustained inquiry. Rigorous arguments first appeared in Greek
mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century,
it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions.
Mathematics developed at a relatively slow pace until the Renaissance,
when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of
mathematical discovery that has continued to the present day.
Galileo Galilei (1564–1642) said, "The universe
cannot be read until we have learned the language and become familiar with the
characters in which it is written. It is written in mathematical language, and
the letters are triangles, circles and other geometrical figures, without which
means it is humanly impossible to comprehend a single word. Without these, one
is wandering about in a dark labyrinth. Carl Friedrich Gauss (1777–1855) referred to mathematics as
"the Queen of the Sciences. Benjamin Peirce (1809–1880) called mathematics
"the science that draws necessary conclusions."David Hilbert said of mathematics:
"We are not speaking here of arbitrariness in any sense. Mathematics is
not like a game whose tasks are determined by arbitrarily stipulated rules. Rather,
it is a conceptual system possessing internal necessity that can only be so and
by no means otherwise."Albert Einstein (1879–1955) stated that "as far
as the laws of mathematics refer to reality, they are not certain; and as far
as they are certain, they do not refer to reality."French mathematician Claire Voisin
states "There is creative drive in mathematics, it's all about movement
trying to express itself."
Mathematics
is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of
mathematics concerned with application of mathematical knowledge to other
fields, inspires and makes use of new mathematical discoveries, which has led
to the development of entirely new mathematical disciplines, such as statistics and game theory.
Mathematicians also engage in pure mathematics,
or mathematics for its own sake, without having any application in mind. There
is no clear line separating pure and applied mathematics, and practical
applications for what began as pure mathematics are often discovered.
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