Mathematics, 02.10.2019 17:10 asdf334asdf334

Numerically estimate the slope of y = f(x) at r = a. 1. f(x) = x^2 - 2x, a = 2 2. f(x) = sin 2x, a = 0

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Answer from: 61497

1. Slope at a=2 is 2.

2. Slope at a=0 is 2.

Step-by-step explanation:

We need to find the slope of y = f(x) at x = a.

The given function is

f(x)=x^2-2x

It can be written as

y=x^2-2x

Differentiate with respect to x.

y'=2x-2

Substitute x=2 to find the slope of y = f(x) at a=2.

y'=2(2)-2

y'=4-2

y'=2

Therefore the slope of function at a=2 is 2.

The given function is

$f(x)=\sin 2x$

It can be written as

$y=\sin 2x$

Differentiate with respect to x.

$y'=2\cos 2x$

Substitute x=0 to find the slope of y = f(x) at a=0.

$y'=2\cos 2(0)$

y'=2(1)

y'=2

Therefore the slope of function at a=0 is 2.

Answer from: Quest

to find the unit price, we must figure out the cost of one item (in this case one dish towel). to do this, we divide the total price ($7.92) by the number of items bought (for this problem it is 8, because there are eight dish towels in one pack).

$7.92/8 = $0.99

therefore, the unit price, or the price of one dish towel, is $0.99.

hope this !

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.

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Numerically estimate the slope of y = f(x) at r = a. 1. f(x) = x^2 - 2x, a = 2 2. f(x) = sin 2x, a =...