Math Solutions
All Solutions
492 solutions\frac{\partial g_{ij}}{\partial t} = -2 R_{ij} = -2 (\theta_k \Gamma^k_{ij} - \partial_j \Gamma^k_{ik} + \Gamma^k_{il} \Gamma^l_{kj} - \Gamma^k_{jl} \Gamma^l_{ik})
A ball is thrown from a 50-meter tall building at 20 m/s at a 60° angle. Find when and where it hits the ground.
Show how the transformation T(x) = [[2, 1], [1, 2]]x transforms the unit square
Find all critical points of f(x) = x³ - 6x² + 9x + 2 and classify them
A ball is thrown from a 50-meter tall building at 20 m/s at a 60° angle. Find when and where it hits the ground.
A kite of mass 50 g is flying at a height of 300 m when its string is cut. The wind blows horizontally toward a building at a constant speed of 60 km/h. At the moment the string is cut, the kite has: height: 300 m horizontal distance to a 12-storey building: 20 m height of each storey: 1.5 m Assume: the wind gives the kite a constant horizontal speed of 60 km/h, the kite initially has no vertical speed when cut, it then falls freely under gravity with 𝑔 ≈ 9.8 m/s 2 g≈9.8 m/s 2 , air resistance (other than the horizontal push of wind) is ignored. Question: Does the kite hit the building? If yes, at what height (which floor)?
Lisa is 16 years younger than Kathy. If the sum of their ages is 30, how old is Lisa? (Sum of ages and age difference problem)
Lisa is 16 years younger than Kathy. If the sum of their ages is 30, how old is Lisa? (Sum of ages and age difference problem)
A ball is thrown from a 50-meter tall building at 20 m/s at a 60° angle. Find when and where it hits the ground.
A ball is thrown from a 50-meter tall building at 20 m/s at a 60° angle. Calculate when and where it hits the ground.
What comes next in the pattern: 2, 4, 8, 16, ___?
A rectangle has length 6 and width 4. What is its area and perimeter?
Plot these points on a coordinate grid: (2,3), (5,1), (3,7)
What is 15% of 80? Show multiple solution methods
Solve the system using matrices: 2x + y - z = 3, x - y + 2z = 1, 3x + 2y + z = 4
Simplify: (x² - 9)/(x² + 6x + 9)
Solve for x: |2x - 3| = 7
Compare 3/4 and 2/3 using visual bars
Compare 3/4 and 2/3 using visual bars
If I have 3 groups of 4 apples, how many apples total? Show with pictures