fortdefruitI
2021-08-16
Answered

Designer functions Design a sine function with the given properties.
NKS
It has a period of 12 hr with a minimum value of $-4$ at $t=0$ hr and a maximum value of 4 at $t=6$ hr.

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Nathaniel Kramer

Answered 2021-08-17
Author has **78** answers

Step 1

Find the sine function satisying the properties.

The sine function:

Here

Sine function with period of 12 hr with minimum value of 10 at

We have

Step 2

Calculate A, d and c.

and

Substitute the values in the function:

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The graph shows one of the six basic functions of graphs and a ransformation of the function. Describe the transformation. Then use your description to write an equation for the transformation.

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Let $T:{R}^{2}\to {R}^{2}$ such that T(v) = Av + b, where A is a $2\to 2$ matrix. (Such a transformation is called an affine transformation.) Prove that T is a linear transformation if and only if b = 0.

asked 2022-02-12

Invariance of $d{s}^{2}$ and transformation properties of $dx}^{i$

Invariance of$d{s}^{2}$ and transformation properties of $dx}^{i$

$d{s}^{{}^{\prime}2}=d{s}^{2}$

$g}_{ij}^{{}^{\prime}}{dx}^{{}^{\prime}i}{dx}^{{}^{\prime}j}={g}_{ij}^{{}^{\prime}}\frac{\partial {x}^{{}^{\prime}j}}{\partial {x}^{k}}{dx}^{k}\frac{\partial {x}^{{}^{\prime}j}}{\partial {x}^{l}}{dx}^{l$

$={g}_{ij}^{{}^{\prime}}\frac{\partial {x}^{{}^{\prime}i}}{\partial {x}^{k}}\frac{\partial {x}^{{}^{\prime}j}}{{dx}^{l}}{dx}^{k}{dx}^{l}$

$={g}_{kl}{dx}^{k}{dx}^{l}$

where$g}_{ij$ is metric tensor

1) I want to ask that idea behind this transformation is because distance remains invariant under transformation to different coordinate system

2) How this new variable k,l are introduced the text i am reading is physics pages

Invariance of

where

1) I want to ask that idea behind this transformation is because distance remains invariant under transformation to different coordinate system

2) How this new variable k,l are introduced the text i am reading is physics pages

asked 2020-12-01

a) To find:

The images of the following points under under a

I.

II.

III, (m,n) interms of m and n

b)To show:

That under a half-turn with the origin as center, the image of a point

c) To find:

The image of

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What is the new equation for the pictured graph after transformations from the parent function f(x)=lxl showing the transformations

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Draw a graph for each expression.

a)$f(x)={2}^{x}$

b)$f(x)={2}^{-x}$

c)$f(x)=\text{}-{2}^{x}$

d)$f(x)=\text{}-{2}^{-x}$

a)

b)

c)

d)

asked 2021-11-21

(a) identify the transformation, and

(b) graphically represent the transformation for an arbitrary vector in$R}^{2$ .

T(x, y) = (x, 9x + y)

(b) graphically represent the transformation for an arbitrary vector in

T(x, y) = (x, 9x + y)