Bentley wants to determine the height of a tree. He is 5 and 1/2 feet tall.

Mathematics

1 answer:

Talja [164]2 years ago

4 0

Answer:

10.3 ft

Step-by-step explanation:

5.5/8 = x/15

multiply by 15

x=10.3 ft

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If a 16-foot silo casts a 12-foot shadow, what is the measure from the tip of the shadow to the top of the silo? 20 feet 400 fee

wlad13 [49]

Use the pythagorean theorm

16^2 + 12^2 = c^2
256 + 144 = c^2
400 = c^2
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3 years ago

Find the critical numbers of the function f(x) = x6(x − 1)5 what does the first derivative test tell you that the second derivat

patriot [66]

The given function is f(x) = x⁶(x-1)⁵

The first derivative is
f'(x) = 6x⁵(x-1)⁵ + 5x⁶(x-1)⁴
= x⁵(x-1)⁴(6x - 6 + 5x)
= x⁵(x-1)⁴(11x - 6)
The critical values are the zeros of f'(x). They are
x = 0, 6/11, and 1.
The critical values indicate that turning points exist for f(x) at the critical points. However, we do not know the nature of the turning points.

Write the first derivative in the form f'(x) = (x-1)⁴(11x⁶ - 6x⁵).
The second derivative is
f''(x) = 4(x-1)³(11x⁶ - 6x⁵) + (x-1)⁴(66x⁵ - 30x⁴)
= (x-1)³(44x⁶ - 24x⁵ + 66x⁶ - 30x⁵ - 66x⁵ + 30x⁴)
= (x-1)³(110x⁶ - 120x⁵ + 30x⁴)
= 10x⁴(x-1)³(11x² - 12x + 3)
The sign of f''(x) at the critical values tell us the nature of the turning point.

f''(0) = 0, therefore a point of inflection exists at x = 0.
f''(6/11) > 0, therefore a local minumum exists at x = 6/11.
f''(1) = 0, therefore a point of inflection exists at x=1.

The graphs shown below confirm these results.