I am in 7th Grade and have some holiday homeworks. Please help.
1. Write all the algebraic identities.
2. Write the statement & proof for remainder theorem & factor theorem each.
3.Write all the quadrilaterals and their properties.
4. Write the formulae for finding the area and perimeter of the following plane figures with one example solved by you.. : 1)Square 2)Circle 3)Rectangle 4)Triangle 5)Parallelogram 6)Trapezium
5.Write the formulae for finding the area and perimeter of the following solid figures with one example solved by you : 1) Cube 2) Cuboid 3) Cylinder 4) Cone 5) Sphere 6) Hemisphere..
Thankyou so much for your answer.
It seems like you want us to do your homework for you, which we do not do. Have you searched through your textbook? Try looking at the index in the back of your book for the terms you want.
Also, you might find the information you desire, if you use appropriate key words to do your own Internet search. Also see http://hanlib.sou.edu/searchtools/.
I hope this helps. Thanks for asking.
I'd be happy to help you with your holiday homework! Here are the answers to your questions:
1. Algebraic identities are important in algebra as they help simplify and solve equations. Some common algebraic identities are:
- (a + b)^2 = a^2 + 2ab + b^2
- (a - b)^2 = a^2 - 2ab + b^2
- a^2 - b^2 = (a + b)(a - b)
- (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
- (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
- a^3 + b^3 = (a + b)(a^2 - ab + b^2)
- a^3 - b^3 = (a - b)(a^2 + ab + b^2)
2. The Remainder Theorem states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). The proof involves using polynomial long division, where you divide f(x) by (x - a) and express the result in the form f(x) = (x - a) q(x) + r, where q(x) is the quotient and r is the remainder.
The Factor Theorem states that if f(a) = 0, then (x - a) is a factor of the polynomial f(x). The proof involves substituting a for x in f(x) and showing that the result is 0.
3. Quadrilaterals are four-sided polygons. Here are some common quadrilaterals and their properties:
- Square: All sides are equal, all angles are right angles.
- Rectangle: Opposite sides are equal and parallel, all angles are right angles.
- Parallelogram: Opposite sides are equal and parallel.
- Rhombus: All sides are equal, opposite angles are equal.
- Trapezium (Trapezoid): One pair of opposite sides is parallel.
- Kite: Two pairs of adjacent sides are equal.
4. Formulas for finding the area and perimeter of plane figures:
- Square:
- Area = side^2
- Perimeter = 4 * side
- Circle:
- Area = π * radius^2
- Perimeter (or circumference) = 2 * π * radius
- Rectangle:
- Area = length * width
- Perimeter = 2 * (length + width)
- Triangle:
- Area = 1/2 * base * height
- Perimeter = sum of all three sides
- Parallelogram:
- Area = base * height
- Perimeter = 2 * (sum of adjacent sides)
- Trapezium:
- Area = (sum of parallel sides) * height / 2
- Perimeter = sum of all four sides
Let's take an example for finding the area and perimeter of a square:
Example: Square with side length = 5 units
- Area = side^2 = 5^2 = 25 square units
- Perimeter = 4 * side = 4 * 5 = 20 units
5. Formulas for finding the area and perimeter of solid figures:
- Cube:
- Surface area = 6 * (side^2)
- Volume = side^3
- Cuboid:
- Surface area = 2 * (length * width + width * height + height * length)
- Volume = length * width * height
- Cylinder:
- Surface area = 2 * π * radius * (radius + height)
- Volume = π * radius^2 * height
- Cone:
- Surface area = π * radius * (radius + slant height)
- Volume = 1/3 * π * radius^2 * height
- Sphere:
- Surface area = 4 * π * radius^2
- Volume = 4/3 * π * radius^3
- Hemisphere:
- Surface area = 2 * π * radius^2
- Volume = 2/3 * π * radius^3
Let's take an example for finding the surface area and volume of a cube:
Example: Cube with side length = 3 units
- Surface area = 6 * (side^2) = 6 * (3^2) = 54 square units
- Volume = side^3 = 3^3 = 27 cubic units
I hope these explanations help you with your holiday homework! If you have any further questions, feel free to ask.