Anyone know how to do this?
2 answers:
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Answer:
The number of seashells he have in his collection all together is 140.
Step-by-step explanation:
Given:
Stanley has a collection of seashells. He found 35% of his collection on Florida beaches.
Stanley has 49 seashells from Florida.
Now, to find the number of seashells of his collection altogether.
Let the number of seashells all together be
Percentage of seashells found on Florida beaches = 35%.
Number of seashells found on Florida beaches = 49.
Now, to get the number of seashells altogether we put an equation:
⇒
⇒
⇒
Dividing both sides by 0.35 we get:
⇒
Therefore, the number of seashells he have in his collection all together is 140.
Your calculator's cubic regression function can tell you the equation is
... f(x) = 2x³ + 5x² -12x = x(x +4)(2x-3)
The x-intercepts are -4, 0, +1.5.
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If you want to solve this "by hand", you can first of all recognize that since there is an x-intercept at 0, the cubic will only have three coefficients. That is, you can write the equation as
... f(x) = ax³ + bx² + cx
Substituting the given points (except (0, 0)) gives three linear equations in a, b, c.
... -a +b -c = 15 . . . . . for x=-1
... a + b + c = -5 . . . . for x=1
... 8a +4b +2c = 12 . . for x=2
adding the first two equations gives 2b=10, or b=5. Now, you can reduce the system to
... a + c = -10
... 4a +c = -4
Subtracting the first of these equations from the second gives 3a=6, or a=2. That tells you c=-12 (from a+c=10).
Then your equation is
... f(x) = x(2x² +5x -12)
Factoring by any of the usual techniques, or graphing, or using the quadratic formula will tell you the zeros (x-intercepts) are as above.
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Since the input values are sequential, you can also develop the function from differences of the output values. Those are 15, 0, -5, 12. First differences are -15, -5, +17. Second differences are +10, +22. The third difference is 12. Using the first of these differences in appropriate places in the interpolating polynomial formula, we have
... f(x) = 15 + (x+1)(-15 + (x)/2·(10 + (x-1)/3·(12))) = 2x³ +5x² -12x . . . . as above
