1,334 prompts matching "find the coefficient of x^4 in the expansion of (1+3x)^7"
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Spot my mistake in a matrix transpose
I am in SS 3. I found the transpose of A=[[1,2,3],[4,5,6]] as [[1,4],[2,5],[3,6]] — please
Show all working: adding three matrices in one question
Give me a Cambridge Additional-Mathematics style question that asks me to find A + B - 2C
Multi-part matrix question: add then multiply
Set me a two-part question: part (a) add two matrices A and B, part (b) multiply the resul
Evaluate a 2x2 determinant #1
I am in SS 3. Give me a 2x2 matrix like A=[[3,5],[2,4]] and ask me to evaluate its determi
Evaluate a 2x2 determinant #5
I am in SS 3. Give me a 2x2 matrix like A=[[8,1],[2,3]] and ask me to evaluate its determi
Compare expanding a determinant along different rows
I am in SS 3. Give me one 3x3 matrix and ask me to evaluate its determinant twice — once e
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
WAEC past-question practice: determinants #1
I am in SS 3. Give me a WAEC Further Mathematics past-question on evaluating a 3x3 determi
WAEC past-question practice: determinants #2
I am in SS 3. Set me a WAEC-style question that uses Cramer's rule to solve a pair of simu
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
Define mass, force and weight with correct units
I am in SS 3. Ask me to define mass, force and weight, state the SI unit of each, and expl
Define particle and rigid body in mechanics
Ask me to explain the difference between a particle and a rigid body in mechanics, with an
Resolve a force into horizontal and vertical components #1
Give me a resolution of forces problem with a force of 10N acting at 30 degrees to the hor
Resolve a force into horizontal and vertical components #2
Give me a resolution of forces problem with a force of 25N acting at 50 degrees above the
Resolve a force into horizontal and vertical components #3
I am in SS 3. Give me a resolution of forces problem with a force of 18N at 40 degrees to
Resolve a force into horizontal and vertical components #4
I am in SS 3. Give me a resolution of forces problem with a force of 12N at 70 degrees to
Teach me composition of coplanar forces
I am in SS 3. Teach me what composition of forces means in mechanics and how it differs fr
Teach me equilibrium of forces from scratch
I am in SS 3. Teach me what it means for forces to be 'in equilibrium' as if I have never
Solve a three coplanar forces in equilibrium problem #1
I am in SS 3. Give me a problem involving three forces of 8N, 10N and 12N acting at a poin
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