Nerdy Turtlez Math Test (Math Problem Sample)

Nerdy Turtlez Math Test
Name
Institution
Nerdy Turtles Math Test
Question One
Solution
Question Two
Solution
For A to be an identity matrix, A needs to be
Therefore,
Question Three
Solution
The line y = mx + 1 is a tangent to the curve y2 = 4x. Find the value of m.
since the equation of the tangent to the curve is
y = mx + 1
When we substitute the value of y in y² = 4x, it’s found
(mx + 1) 2= 4x
= m2xx2+ 1 + 2mx - 4x =0
= m2x2+ x (2m - 4) + 1 =0----------(1)
Now Since the curve is touched by the tangent at one point the root of equation (1) has to be equal.
Hence, we get
Discriminant = b2- 4ac = 0
(2m - 4)2 – 4(m2) (1) = 0 confirm from equation (1)
=4m2-16m + 16 - 4m2 =0
= -16m + 16 = 0
= m =1
Question Four
Solution
Questi