Mathematics, 30.10.2019 22:31 Nakieapowell1276

Use linear approximation to estimate 15^.25

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Answer from: Vanina2001

Let f(x) = sqrt(x). Use linear approximation about x = 25, since 24 is close to 25, and since it is easy to take the square root of 25. Note that f ' (x) = 1/[2sqrt(x)] from the power rule. About x = 25, f(x) is approximately f(25) + f ' (25)(x - 25). So sqrt(24) = f(24) is approximately f(25) + f ' (25)(24 - 25) = sqrt(25) + {1/[2sqrt(25)]}(-1) = 5 - 1/10 = 4.9 .

Answer from: Fahaddie

A linear approximation of f(x) in a neighborhood of a

f(x) ~ f(a) + f'(a) (x-a)

f(x) = x^1/4

2^4 = 16 i.e. a = 16

f(15) ~ f(16) + f'(16) (15-16)

f'(x) = 1/4 x^(-3/4)

f(15) ~ 2 + 1/4 (16)^-3/4 (-1)

~ 2 - 1/(32) = 1.96875

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Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

The answer is b) 32 your welcome

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