Answer: 36.25p + 7.50r = 185
Step-by-step explanation:
The cost of p gallons of paint is given by;
= 36.25 * p
= 36.25p
Cost of r rollers is given by;
= 7.50 * r
= 7.50r
Total the customer can buy with; $185
Equation is;
36.25p + 7.50r = 185
The polynomials 1, 1-t, and are linear independent and span . So the first four Laguerre polynomials forms a basis of .
We have the first four Laguerre polynomials. Here is the space of all polynomials of degree at most 3.
i.e.,
So the dimension of is 4. Also there are 4 Laguerre polynomials.
Now to show that the first four Laguerre polynomials forms a basis, it remains to show that they are linear independent.
Consider the polynomials 1, 1-t, and . Write them into a matrix with the co-efficient of 1, t, and in each row.
This matrix is already in its echelon form with all its pivots occupied. The pivot of first row is 1. The pivot of 2nd row is -1. The pivot of 3rd row is 1 and the pivot of 4th row is -1.
Hence the polynomials are linearly independent since the columns of the above matrix are linearly independent.
In conclusion, the first four Laguerre polynomials 1, 1-t, and forms a basis for .
Learn more about basis at brainly.com/question/13258990
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Answer:
Step-by-step explanation:
total cost = tickets( c) +50
1400 = 4 (c) + 50
1350 = 4 (c)
337.50 = c
7 and a half hours
Explanation-
8/5=1.6
12/1.6=7.5
Answer:
x = 4
Step-by-step explanation:
The absolute value of 5x is still 5x.
5x - 2 = 18
Add 2 to both sides
5x = 20
Divide both sides by 5
x = 4