The path of a total solar eclipse is modeled by f (t )equals 0.00223 t squared minus 0.558 t plus 41.395, where f(t) is the la

Question

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The path of a total solar eclipse is modeled by f (t )equals 0.00223 t squared minus 0.558 t plus 41.395, where f(t) is the la

titude in degrees south of the equator at t minutes after the start of the total eclipse. What is the latitude closest to the equator, in degrees, at which the total eclipse will be visible.

Mathematics

1 answer:

Leona [12.6K] · Answer 1 · 2026-04-11T12:02:38+03:00

Response:

Thus, the latitude nearest to the equator is approximately 6.49°.

Step-by-step rationale:

The solar eclipse path is modeled by

$f(t)=0.00223t^2-0.558t+41.395$

where f(t) denotes latitude in degrees south of the equator corresponding to t minutes.

We acknowledge that

The minimum or maximum of a function represented by y(t) =at²+bt+c

occurs when $t=-\frac{b}{2a}$

Here, a= 0.00223, b= - 0.558, and c= 41.395.

Thus, the minimum of f(t)

occurs at $t=-\frac{( - 0.558)}{2\times 0.00223}$

=125.11

Consequently, the latitude closest to the equator can be determined as

f(125.11)=0.00223(125.11)²-0.558×125.11+41.395

≈6.49

The path of a total solar eclipse is modeled by f (t )equals 0.00223 t squared minus 0.558 t plus 41.395​, where​ f(t) is the la

The path of a total solar eclipse is modeled by f (t )equals 0.00223 t squared minus 0.558 t plus 41.395, where f(t) is the la