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 = ![\left[\begin{array}{ccc}7&1&0\\7&0&1\\7&-1&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%261%260%5C%5C7%260%261%5C%5C7%26-1%261%5Cend%7Barray%7D%5Cright%5D)
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.
You would do 2x-3+x+3x-15=360
combine like terms which then gives you
5x-18=360 then you would add 18 to both sides giving you
5x=378
and then you divide by 5 on both sides which will then give you your answer x=?
Driving with a dog cause you just have to mixed them to ether that’s it
Answer:
Step-by-step explanation:
area of a cylinder = (area of a circle) times the (height)
area of a cylinder = π radius² × height
radius = 57 cm height = 40 cm
area of a cylinder = π 57² cm² × 40 cm
= π (57² × 40) cm³
= π ( 57 × 57 × 40) cm³ 57x57 = 399 + 2850 = 3249
= π (3249 × 40) cm³
= 129969π cm³ π = 3.14
= 129969 × 3.14 cm³
= 408,074.4 cm³ < ----------------- Final Answer
50%
The very left point on the box of a box plot is the first quartile, the very right. The very left and right points are the minimum and maximum and the middle line is the second quartile. Since quarters each equal 25%, two quartiles, the data between the first and third quartile, would equal 50%. This is also evident by looking at the graph itself in this problem.
