Answer:
Step-by-step explanation:
Please find the attachment.
We have been given that ABC is a right triangle with sides of lengths a, b, and c and right angle at C.
To find the side length a, we will Pythagoras theorem, which states that the sum of squares of two legs of a right triangle is equal to the square of the hypotenuse of right triangle.
Upon substituting our given values in Pythagoras theorem, we will get:
Take square root of both sides:
Therefore, the length of side 'a' is units.
We know that tangent relates opposite side of a right triangle with adjacent side.
We can see that 'a' is opposite side of angle A and 'b' is adjacent side.
Therefore, the value of tan(A) is .
100/x=60/30 so x=100*30/60=50
(i) Use the formula for the determinant of a 2×2 matrix.
(ii) The adjugate matrix is the transpose of the cofactor matrix of A. (These days, the "adjoint" of a matrix X is more commonly used to refer to the conjugate transpose of X, which is not the same.)
The cofactor of the (i, j)-th entry of A is the determinant of the matrix you get after deleting the i-th row and j-th column of A, multiplied by . If C is the cofactor matrix of A, then
Then the adjugate of A is the transpose of C,
(iii) The inverse of A is equal to 1/det(A) times the adjugate:
(iv) The system of equations translates to the matrix equation
Multiplying both sides on the left by the inverse of A gives
(b) 2x² - 3x + 4
using synthetic division or long division to obtain the quotient 2x² - 3x + 4