y-y1 = m(x-x1)
where: x1 = 1 y1 = 8 (given point (1,8) and m = -3
y - (8) = -3 (x - (1))
y - 8 = -3 (x-1)
y- 8 = -3x +1
Answer:
3²
Step-by-step explanation:
We have to use BPEMDAS Order of Operations:
B - Brackets
P - Parenthesis
E - Exponents
M - Multiply
D - Divide
A - Addition
S - Subtraction
We use this order left to right. Since we have parenthesis, we look at that first. Inside, we have division and exponents. Since exponents come first, we have to evaluate 3² first.
Answer:
5
Step-by-step explanation:
Remember, the rank of a matrix is the number of pivots or number of rows different of zero in the echelon form of the matrix.
Then, if A is a matrix 
the maximum number of pivots that can have is one by row, that is, 5.
Then the maximum rank that A can have is 5.
Answer:
yp = -x/8
Step-by-step explanation:
Given the differential equation: y′′−8y′=7x+1,
The solution of the DE will be the sum of the complementary solution (yc) and the particular integral (yp)
First we will calculate the complimentary solution by solving the homogenous part of the DE first i.e by equating the DE to zero and solving to have;
y′′−8y′=0
The auxiliary equation will give us;
m²-8m = 0
m(m-8) = 0
m = 0 and m-8 = 0
m1 = 0 and m2 = 8
Since the value of the roots are real and different, the complementary solution (yc) will give us
yc = Ae^m1x + Be^m2x
yc = Ae^0+Be^8x
yc = A+Be^8x
To get yp we will differentiate yc twice and substitute the answers into the original DE
yp = Ax+B (using the method of undetermined coefficients
y'p = A
y"p = 0
Substituting the differentials into the general DE to get the constants we have;
0-8A = 7x+1
Comparing coefficients
-8A = 1
A = -1/8
B = 0
yp = -1/8x+0
yp = -x/8 (particular integral)
y = yc+yp
y = A+Be^8x-x/8
