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Andreyy89
3 years ago
11

Let f(x) = x^2 + -8x + 19 what is the minimum value of the function? Enter your answer in the box

Mathematics
2 answers:
Luden [163]3 years ago
8 0

Answer:

Let f(x) = x^2 + -8x + 19 what is the minimum value of the function? Enter your answer in the box?

Find the x-value the minimum occurs at. Use this value to find the minimum value.

(4,3)

crimeas [40]3 years ago
3 0
<h2>(4,3)</h2>

Function Template

ax^2 + bx + c

x^2 + -8x + 19

Max/Min Point Template

- (b / 2a)

- (-8 / 2 * 1)

- (-8 / 2)

- (-4)

4

Substitute the value into the function.

(x) = x^2 + -8x + 19

f(4) = 4^2 + -8(4) + 19

f(4) = 16 + (-32) + 19

f(4) = 3

Minimum point = (4,3)

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A cylindrical 2014-t6 aluminum alloy bar is subjected to compression-tension stress cycling along its axis; results of these tes
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Complete part of Question:

Assume a factor of safety of 3.0

The Maximum stress versus logarithm of the number of cycles to fatigue failure curve for 2014-T6 Aluminium bar is attached to this solution

Answer:

The maximum allowable load amplitude is 6403.33 N

Step-by-step explanation:

diameter of the bar, d = 12 mm

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Cross sectional area of the bar, A = πd²/4

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A = 0.000113 m²

From the Maximum stress versus logarithm of the number of cycles to fatigue failure for 2014-T6 Aluminium bar attached to this solution;

At 10⁷ cycles, Maximum stress, S = 170 MPa

S = 170 * 10⁶ Pa

Factor of safety, N = 3.0

The tensile stress is given by the formula:

\sigma = S/N\\\sigma = \frac{170 * 10^{6} }{3} \\\sigma = 56.67 * 10^{6} N/m^{2}

The tensile stress is also given by:

\sigma = F/A\\\sigma = F/0.000113

F/0.000113 = 56.67 * 10⁶

F = 56.67 * 10⁶ * 0.000113

F = 6403.33 N

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