1,313 prompts matching "Structured question: find fg(x) and gf(x)"
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Solve simultaneous equations with Cramer's rule (order 2) #1
I am in SS 3. Use Cramer's rule to solve 2x + 3y = 7 and x - y = 1. Set up the coefficient
Solve simultaneous equations with Cramer's rule (order 2) #4
Use Cramer's rule to solve 5x + 2y = 16 and x - 3y = -7. Set up the coefficient determinan
Solve a 3x3 simultaneous equation system with Cramer's rule #1
I am in SS 3. Use Cramer's rule to solve the system x + y + z = 6, 2x - y + z = 3, x + 2y
Explain why a matrix with zero determinant has no inverse
I am in SS 3. Explain why a matrix cannot be inverted when its determinant is zero, and gi
Show all working: the determinant of a three by three matrix
You are my SS3 Further Mathematics tutor. Teach me the determinant of a three by three mat
Solve simultaneous equations using an inverse matrix #2
I am in SS 3. Show me how to write 4x + y = 9 and 2x + 3y = 8 as a matrix equation, find t
Solve simultaneous equations using an inverse matrix #3
Show me how to write 3x - 2y = 4 and x + y = 6 as a matrix equation, find the inverse of t
Quiz me on units of force
Quiz me on the SI unit of force and how it is derived from mass and acceleration, then giv
Explain the parallelogram of forces
Explain the parallelogram law for finding the resultant of two forces, with a labelled dia
Solve a binomial probability problem #1
Give me a binomial distribution problem where n=8, p=0.3, find P(X=3), using the binomial
Solve a binomial probability problem #4
I am in SS 3. Give me a binomial distribution problem where n=12, p=0.4, find P(X=5), usin
Solve a binomial probability problem #5
I am in SS 3. Give me a binomial distribution problem where n=5, p=0.6, find the probabili
Solve a Poisson distribution problem #1
I am in SS 3. Give me a Poisson distribution problem where the mean rate of 4 per hour, fi
Solve a Poisson distribution problem #2
I am in SS 3. Give me a Poisson distribution problem where the mean rate of 3 defects per
Solve a Poisson distribution problem #3
I am in SS 3. Give me a Poisson distribution problem where the mean rate of 5 calls per mi
Solve a Poisson distribution problem #4
I am in SS 3. Give me a Poisson distribution problem where the mean rate of 2.5 accidents
Solve a three coplanar forces in equilibrium problem #3
I am in SS 3. Give me a problem involving a particle held in equilibrium by three forces a
Quiz me on unit vectors
I am in SS 3. Quiz me on finding unit vectors from given vectors in 2D and 3D, and check w
Complex number arithmetic practice #1
I am in SS 3. Give me a complex number problem where z1 = 3 + 2i and z2 = 1 - 4i, find z1
Complex number arithmetic practice #2
I am in SS 3. Give me a complex number problem where z1 = 2 - i and z2 = 4 + 3i, find z1 x