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To make a conjecture about the tangent lines and the graph with the proof of the conjecture.
Conjecture consider the functions f(x) = ½ x2 and g(x) = 1/16 x4 - ½ x2 on the domain [0,4].
Make a conjecture about the relationship between tangent lines to the graphs of two functions at the value of x at which the vertical distance between the functions is greatest, and prove your conjecture.
a company wants to construct a box that will hold exactly 200 one inch cubes. find the dimensions of all possible boxes. which size box do you think the company should make? why?
The width of a rectangular garden is 2 feet shorter than one-half its length. If the perimeter of the garden is 32 ft., what are the dimensions of the garden?
At noon, ship A is 50 km west of ship B. Ship A is sailing south at 45 km/h and ship B is sailing north at 25km/h. How fast is the distance between the ships changing at 4:00pm.
a man invests 20000at an annual interest rate of 7%, and 12000 at an annual interest rate of 7.5%. what was his annual income in the two investments?
Buying a Cottage A group of friends decides to buy a vacation home for $120,000, sharing the cost equally. If they can nd one more person to join them, each persons contribution will drop by $6000. How many people are in the group?
How to compute the derivative of a summation?
Kent worked in the housewares section of a department store. This year he set a record high for vacuum sales with 567 vacuums sold. The previous high was last year, when 540 vacuums were sold. What is the percent of increase in sales from last yea..
Two observation points A and B are 1500 feet apart. From those points the angles of elevation of a hot-air balloon are 43° and 47°. Find the height of the balloon to the nearest foot.
Indicate whether each system is independent, inconsistent or dependent
Probability of cycle time, The cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 40 to 60 minutes
The frame around the picture has a uniform width of 2 inches and an area of 96 square inches. What are the dimensions of the picture?
Kno withinknowing that this number, the golden ratio is present not just in mathematics but also be present within your own brain and body at the atomic or subatomic levelwhat do you think it means? Is this number evidence of a grand design, a mas..
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