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Doug C.'s Resources

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Hi Michelle,   Hopefully you see how to get to here:      3              3 --------   -   ----  (7+h)          7 --------------------      ...

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Hi Neal,   One technique to try is writing the difference between successive terms to see if a pattern develops. For example the difference between 3 and 0 is 3, the difference between 8 and 3 is 5, between 15 and 8, 7.   So we have 3, 5, 7... Checking one more difference...

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6x - 38 must be greater than 0 too, because otherwise taking the square root of a negative number.   Check out this graph:   https://www.desmos.com/calculator/qgvcaurvrk    

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Hi Claire,   Take a look at this graph to get the idea of what is happening. This problem is an example of the "area between two curves". To find the height of a "typical rectangle" use "top" - "bottom".   https://www.desmos.com/calculator/mmynniltq1   Hopefully...

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Another option for finding the area of any triangle when you know all three sides is to use Heron's formula.   First make sure that the numbers a,b,c (sides of the triangle) actually form a triangle. The sum of any two sides must be greater than the 3rd side.   Find the...

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Dice experiment (answer)

Hi Jovan,   One way to look at it:   You might try drawing a tree diagram where Even has a probability of 1/2 and Odd has a probability of 1/2.   Some possible outcomes {E,E,E}, {O,O,O}, {E,O,E}, etc. The probability of each of those outcomes is (1/2)(1/2)(1/2)=...

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Hi Cayce,   To determine the slope of the line passing through two points use the formula for slope.   The following graph shows the results of two different ways to do the calculation.   https://www.desmos.com/calculator/5pvn8xfhg7   The graph...

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Optimisation (answer)

Hi Vans,   Here are some ideas to get you started.   Let x = the height of a locker. Let y = the width.   Then the area of one locker will be A = xy.   The trick is to come up with a relationship between x and y so that A can be written as the...

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Optimisation (answer)

Hi Vans,   You need a function that determines the length of the wire for any given point at which the wires are staked between 0 and 24 meters. The assumption is that this point is on the line connecting the bases of the two poles. If you draw a sketch you will see that the two separate...

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Hi Karen,   Imagine two piles of coffee. One contains 10 pounds and each pound is worth $5. So that pile is worth $50.   The second pile we do not know the number of pounds so let's call that x. That pile is worth $8 for each pound. If we multiply x by 8 we will have the...

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Hi Vagif,   First thing I would recommend is to use specific values for a, b, c to get an idea of what is going on. The following graph has sliders for a,b,c so you can adjust them to get different pictures:   https://www.desmos.com/calculator/2gzw4cq72y   Notice...

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Hi Marcio,   The easiest way to solve this problem is to use the washer method, but integrating along the y-axis. The problem has already solved the for x in terms of y. Remember "outer radius squared minus inner radius squared".   This graph should give you the...

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Hi Lexie,   The idea behind logarithmic differentiation is to simplify finding y' when complicated product/quotient rule is required. Take the natural log of both sides, use properties of logarithms to expand the ln f(x) into separate terms, then take the derivative of both sides...

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Find y-values. (answer)

Hi Madeline,   You might want to start using the Desmos online graphing calculator to help answer questions like this.   Here is a graph containing the parent function (y=|x|), a vertical stretch for the parent (y=3|x|), and the function for this question.   https://www...

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