1174.

]]>Thanks bob]]>

thanks Bob]]>

Thanks for providing me with ways to do this.

Bob

]]>Thus, I love the idea of generating creative and indulging short exercises regarding math concepts such as algebra, basic word problems, trigonometry, etc. However, there is one thing which we need to adapt, and that comes from the idea of websites. They have everything arranged in different sections for easy identification. Thus, having math problems, we must arrange them in specific sections only; thus, people easily begin an exercise knowing where their interest and strength lies.]]>

Hi,

Next integral:

hi gar

]]>

Thanks for another interesting puzzle.

Bob

]]>Thanks for your latest puzzle.

Bob

]]>As far as I know there is no totally algebraic way to solve this.

What I would do is to sketch two graphs, y = 2^x and y = 2x to see where these cross.

You can try this at https://www.mathsisfun.com/data/function-grapher.php

In this case they look like they cross at (1,2) and at (2,4); and it's easy to check by substitution that these are solutions **. But are they the only ones?

y = 2x is an increasing function, negative when x<0.

y = 2^x is also increasing but never negative. So we can rule out any negative solutions for x.

2x increases at a steady rate (constant gradient) whereas 2^x gets steeper as x goes up. So they will never cross again after (2,4) when the 2^x curve crosses y = 2x with an ever increasing gradient. So x = 1 and x = 2 are the only solutions.

Does it matter that I spotted the answer without complicated algebraic work? Well no actually. If you have shown a solution works and found any others and can prove you've got them all, then that's ok as a way to answer the question.

Bob

** You shouldn't assume x= 1 is the answer just from the graph. The 'correct' answer might be x = 0.9999997. From a graph alone you only know the answer is roughly 1 as graphs are only as accurate as your ability to draw them (thickness of the pencil; degree of accuracy with the calculator etc)

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IQR = Q3 - Q1. The interquartile range [link removed by moderator] shows how the data is spread about the median. It is less susceptible than the range to outliers and can, therefore, be more helpful.

]]>functions from A to B? Explain.

9. A = {0, 1, 2, 3} and B = {−2, −1, 0, 1, 2}

(a) {(0, 1), (1, −2), (2, 0), (3, 2)}

(b) {(0, −1), (2, 2), (1, −2), (3, 0), (1, 1)}

(c) {(0, 0), (1, 0), (2, 0), (3, 0)}

(d) {(0, 2), (3, 0), (1, 1)}

10. A = {a, b, c} and B = {0, 1, 2, 3}

(a) {(a, 1), (c, 2), (c, 3), (b, 3)}

(b) {(a, 1), (b, 2), (c, 3)}

(c) {(1, a), (0, a), (2, c), (3, b)}

(d) {(c, 0), (b, 0), (a, 3)}

NOTE: THIS IS EXTRA PRACTICE FOR MEMBERS. I AM NOT ASKING FOR HELP WITH 9 AND 10.

]]>mathland wrote:Find the distance between the points.

17. (−2, 6), (3, −6)

18. (8, 5), (0, 20)

19. (1, 4), (−5, −1)

20. (1, 3), (3, −2)

21. (1/2, 4/3) (2, −1)

22. (9.5, −2.6), (−3.9, 8.2)

___________________

would the formula be √ (x1 - x2)² + (y1 -y2)² ? edit: oop the link already said so

I posted the problems as extra practice for members.

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