What is the slope of the graph shown below?
2 answers:
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Answer:
Step-by-step explanation:
Let the number be 'x'
Reciprocal =
Cross multiply
(x² + 1) *2 = 5*x
2x² + 2 = 5x
2x² - 5x + 2 =0
Factorize the equation,
Sum = -5
Product = 4
Factors = -1 , -4
2x² - x - 4x + 2 = 0
x(2x - 1) - 2(2x - 1) = 0
(2x -1 )(x - 2) = 0
2x - 1 = 0 ; x -2 = 0
2x =1 ; x = 2
x = 1/2
Number = 2 , and its reciprocal = 1/2
Answer:
The set of polynomial is Linearly Independent.
Step-by-step explanation:
Given - {f(x) =7 + x, g(x) = 7 +x^2, h(x)=7 - x + x^2} in P^2
To find - Test the set of polynomials for linear independence.
Definition used -
A set of n vectors of length n is linearly independent if the matrix with these vectors as columns has a non-zero determinant.
The set is dependent if the determinant is zero.
Solution -
Given that,
f(x) =7 + x,
g(x) = 7 +x^2,
h(x)=7 - x + x^2
Now,
We can also write them as
f(x) = 7 + 1.x + 0.x²
g(x) = 7 + 0.x + 1.x²
h(x) = 7 - 1.x + 1.x²
Now,
The coefficient matrix becomes
A =
Now,
Det(A) = 7(0 + 1) - 1(7 - 7) + 0
= 7(1) - 1(0)
= 7 - 0 = 7
⇒Det(A) = 7 ≠ 0
As the determinant is non- zero ,
So, The set of polynomial is Linearly Independent.