URGENT PLEASE HELP ME ON THIS QUESTION.!!! the first term of a sequence of numbers is 18

1 answer:

3 0

Well this problem can be solved with Algebra

the rule here is that for every incrementing sequence you increase your number by 6.

T(n)=18+6(n-1)

for 603 to be in the sequence, it has to male sense with the function above

603=18+6(n-1)

603-18=585

585=6(n-1)

n-1=(585/6)

n=(585+6)/6

n=591/6

here is your answer.

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You want to get from a point A on the straight shore of the beach to a buoy which is 54 meters out in the water from a point B o

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$x =\dfrac{45 \sqrt{6}}{ 2}$

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

$\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}$

In order to estimate the point along the shore, x meters from B, the runner should stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

= $\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0$