Frequently Asked Questions
Write the coefficients of x^2 in each of the following
(i) 2 + x^2 + x
(ii) 2 - x^2 + x^3
(iii) pi/2x^2 + x
(iv) √(2)x - 1
Solution:
Explanation:
A coefficient is a number or quantity that is associated with a variable. It's commonly an integer multiplied by the variable immediately adjacent to it.
(i) 2+x^{2}+x
The x^{2} coefficient is 1.
(ii) 2-x^{2}+x^{3}
The x^{2 }coefficient is -1.
(iii) (π/2)x^{2}+x
The x^{2} coefficient is π /2.
(iv)√2x-1
In the provided formulation, there is no x2 term. It can be rewritten as 0x^{2} +√ 2x - 1
The coefficient of x^{2} equals 0 because x^{2} does not exist.
Final Answer:
(i) 2+x^{2}+x , the coefficient of x^{2} is 1.
(ii) 2-x^{2}+x^{3}, the coefficient of x^{2} is -1.
(iii) (π/2)x^{2}+x, here the coefficient of x^{2} is π/2.
(iv) √2x-1, the coefficient of x^{2 } is 0.
Which of the following is are correct
A:6 ÷ 3 =2
B:3 ÷ 6 =1/2
C:6 ÷ 3 ≠ 3 ÷ 6
D: None of the above
Solution:
Explanation
How many faces and edges does a triangular prism have
Solution:
Explanation:
- The triangular prism's sides and bases are either congruent or oblique.
- The prism's edges connect to the appropriate sides.
- The two bases of this prism are equilateral triangles, and their edges are parallel to one another.
- To grasp the structure, look at the diagram below.
- It contains 9 edges, 5 faces, and 6 vertices in total (which are joined by the rectangular faces).
- It features three rectangular sides and two triangular bases.
- The triangular prism is considered to be semiregular if the triangular bases are equilateral and the other faces are squares rather than rectangles.
Final Answer:
5 faces and 9 edges.
Find the cube root of 125
Solution:
Explanation:
- A number's cube root is a number that, when multiplied three times, returns the original number 125.
- The cube root of 125 is represented as ∛125 using the 3rd root sign.
- Let P be an integer such that its cube is 125, P^{3} = 125 or .
- Assume that P = 1,2,3... and that its cube equals 125.
1 x 1 x 1 = 1
2 x 2 x 2 = 8
3 x 3 x 3 = 27
4 x 4 x 4 = 64
5 x 5 x 5 = 125
- As a result, ∛125 = ∛5x5x5=5 .
Final Answer:
Hence, the cube root of 125 is 5 .
Find the square root of 5
Solution:
From the question, we have to find the square of .
So,
Final Answer:
Square root is .