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3 years ago

Please help on this question. thank you.

Mathematics

1 answer:

Zielflug [23.3K]3 years ago

5 0

There are a couple of ways to work this problem. Perhaps the easiest is to make use of secant rules.

The product of the two halves of the chord will be the product of the height of the segment and the missing length of the rest of the diameter (x). Then we have
.. (1180/2)^2 = 225.4*x
.. x = 590^2/225.4 ≈ 1544.4

The diameter is 225.4 +1544.4 ≈ 1770 . . . . feet.

____
Another way to solve it is to consider the right triangle formed by the radius and the chord. Let the radius be represented by r. Then the Pythagorean theorem tells you
.. r^2 = 590^2 + (r -225.4)^2
.. r^2 = 590^2 +r^2 -450.8r +225.4^2
.. 450.8r = 590^2 +225.4^2
.. r = 398,905.16/450.8
.. r ≈ 884.88
.. d = 2r ≈ 1770 . . . . feet

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3 years ago

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Step-by-step explanation:

For this case we have the following function:

$P(t) = 1.6 t^2 -11t +44$

Where P represent the annual net income for the period 2007-2011 and $2 \leq t \leq 7$

And t represent the time in years since the start of 2005

In order to find the lowet income we need to use the derivate, given by:

$P'(t) = 3.2 t -11$

And we can set equal this derivate to 0 in order to find the critical point and we got:

$3.2 t-11= 0$

$t = \frac{11}{3.2}= 3.4375$

And we can calculate the second derivate and we got:

$P''(t) = 3.2 >0$

So then w can conclude that the value of t = 3.4375 represent the minimum value for the function and we can replace in the original function and we got:

$P(3.4375) = 1.6(3.4375)^2 - (11*3.4375) +44 = 25.094$

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