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3 years ago

Translations, reflections and rotations are all known as

Mathematics

1 answer:

taurus [48]3 years ago

8 0

transformations

hope it helps you

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Section 5.2 Problem 17:

Elina [12.6K]

This DE has characteristic equation

$4r^2 - 12r + 9r = (2r - 3)^2 = 0$

with a repeated root at r = 3/2. Then the characteristic solution is

$y_c = C_1 e^{\frac32 x} + C_2 x e^{\frac32 x}$

which has derivative

${y_c}' = \dfrac{3C_1}2 e^{\frac32 x} + \dfrac{3C_2}2 x e^{\frac32x} + C_2 e^{\frac32 x}$

Use the given initial conditions to solve for the constants:

$y(0) = 3 \implies 3 = C_1$

$y'(0) = \dfrac52 \implies \dfrac52 = \dfrac{3C_1}2 + C_2 \implies C_2 = -2$

and so the particular solution to the IVP is

$\boxed{y(x) = 3 e^{\frac32 x} - 2 x e^{\frac32 x}}$

8 0

2 years ago

A cube has a volume of 64 cubic meters what is the length of each edge

Murljashka [212]

Answer:

The length of each side is 4 m

Step-by-step explanation:

The volume of a cube is given by

V = s^3 where s is the side length

64 = s^3

Take the cube root of each side

64 ^ (1/3) = s^3 ^ (1/3)

4 = s

The length of each side is 4 m

7 0

3 years ago

Read 2 more answers

Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 16.

navik [9.2K]

The transformations are

(b) A vertical shift 16 units downward.
(d) A horizontal shift 16 units to the right

<h3>How to determine the transformation?</h3>

The functions are given as:

f(x) = x

g(x)= x - 16

When a function is shifted right, the transformation rule is:

(x, y) = (x - h, y)

This means that the transformation is (d) A horizontal shift 16 units to the right

Since the parent function is a base linear function.

The transformation can also be represented as:

(x, y) = (x, k - h)

This gives

g(x)= x - 16

This means that the transformation is (b) A vertical shift 16 units downward.

Hence, the transformations are (b) and (d)