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Find the angle between the diagonal of a cube of side length 19 and the diagonal of one of its faces, so that the two diagonals have a common vertex. The angle should be measured in radians.
find the equation of the largest sphere that passes through the point (-1,1,4) and is such that each of the points (x,y,z) inside the sphere satisfies the condition x^2+y^2+z^2
where cosh(x)=(e^x+e^-x)/2 is the hyperbolic cosine, which is an important function in physics and engineering.
the length of a rectangular parking lot is 10 meters less than twice its width, and the perimeter is 448 meters, find the length of the parking lot.
the fence around a rectangular piece of property is 156 m long. if the area of the property is 1505 meters squared, find the dimensions of the property.
A brief and an original writeup has been provided to explain the student community the concept of vertical lines. A graphical example of equation x=4 has been attached to aid the understanding of the concept.
Which of the following can be solved by using a system of equations? Laura and Mark went to the movies and spent $29 on movie tickets and snacks. Mark paid $10 more than Laura. How much did each spend?
Find the length of the sides parallel to the store and perpendicular that will maximize the total area of the outdoor enclosure.
Find the largest possible product of such numbers.
The volume of a square-based rectangular cardboard box needs to be 1000 cm^3. Determine the dimensions that require the minimum amount of material to manufacture all six faces.
the bottom of a storage tank at a rate of r(t) = 200-4t liters per minute, where 0≤ t ≤ 66. Find the amount of water that flows from the tank during the first 66 minutes.
What are the four steps for solving an equation? Should any other factors be accounted for when solving an equation? Should any factors be accounted for when explaining how to solve an equation? Explain your answer.
The importance of geometry's role in the math curriculum is debated in many high schools and colleges. Some schools offer the course while others have done away with it.
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