What is the slope of the line represented by the equation y = x

Let f(x) be a func. satisfying f(-x)=f(x) for all real x.if f"(x) exist, find its value.

OverLord2011 [107]

Answer:

$f''(x)=f''(-x)$

Step-by-step explanation:

A function satisfying the equation $f(x)=f(-x)$ is said to be an even function. This denomination comes from the fact that the same relation is satisfied for functions of the form $x^{n}$ with $n$ even. Observe that if $f$ is twice differentiable we can derivate using the chaing rule as follows:

$f(x)=f(-x)$ implies $f'(x)=f'(-x)\cdot (-1)=-f'(-x)$

Applying the chain rule again we have:

$f'(x)=-f'(-x)$ implies $f''(x)=-f''(-x)\cdot (-1)=f''(-x)$

So we have that function $f''(x)$ is also an even function.

4 0

3 years ago

For each diagram, describe a translation, rotation, or reflection that takes line ℓ to line ℓ′. Then plot and label A′ and B′, t

inn [45]

Answer:

translate down 3
reflect across the horizontal line through A

Step-by-step explanation:

1. There are many transformations that will map a line to a parallel line. Translation either horizontally or vertically will do it. Reflection across a line halfway between them will do it, as will rotation 180° about any point on that midline.

In the first attachment, we have elected to translate the line down 3 units.

__

2. Again, there are many transformations that could be used. Easiest is one that has point A as an invariant point, such as rotation CW or CCW about A, or reflection horizontally or vertically across a line through A.

Any center of rotation on a horizontal or vertical line through A can also be used for a rotation that maps one line to the other.

In the second attachment, we have elected to reflect the line across a horizontal line through A.

6 0

3 years ago

Courtney is twice as old as Andre and three years older than Natalie. Courtney is half Shari's age. The difference between Shari

lesantik [10]

The question does not seem complete, but I'll represent the statement mathematically and look for their ages each. This is because the worst they can ask for is their ages.

Let C stand for Courtney's age, A for Andrei's age, N for Natalie's age and S for Shari's age. From the question we can deduce the following:

C = 2A

C = N + 3

C = S/2

S - N = C + A

S = 2C, N = C - 3 and A = C/2, therefore we have

2C - (C - 3) = C + C/2

C + 3 = C + C/2

C/2 = 3 and C = 6

A = C/2

A= 6/2

A = 3

N = C - 3

N = 6 - 3

N = 3

S = 2C

S = 2 x 6

S = 12.

C = 6, A = 3, N = 3 and S = 12

8 0

2 years ago

1. The dimensions of Mr. Bell's living room are 10 feet x 8 feet x 2 feet, and the dimensions of his kitchen are 20 feet x 2 fee

romanna [79]

Answer:

more detail

Step-by-step explanation:

8 0

3 years ago

Given a data set consisting of 33 unique whole number observations, its five-number summary is:

Lemur [1.5K]

Answer:

given a data set of 33 unique whole number observation,its five number sumary is [16, 29, 40 ,54, 67]

Step-by-step explanation:

The p-th percentile in an ordered (from low to high) data set is a value such that p% of the data is less than that value. The quartiles of a data set are the 25th, 50th and 75th percentiles. (The 25th percentile is usually called the first quartile, the 50th percentile is usually called the median, and the 75th percentile is usually called the third quartile.)

The formula for finding the location (or position) of the (approximate) pth percentile in an ordered (from low to high) data set is

L p=(n+1).p/100

For example, in the data set [2,4,6,8,10,12,14,16,18]

the (approximate) 60th percentile is located at position

L 60=(9+1).60/100=6

that is, the sixth data point (the value 12) is at the (approximate) 60th percentile.(Actually, only 55.6% of the data is below a 12.)

3 0

3 years ago

What is the slope of the line represented by the equation y = x - 3?