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2 years ago

15

Write the prime factorization of 27. Use exponents when appropriate and order the factors from least to greatest (for example, 2

235).

1 answer:

Maksim231197 [3]2 years ago

4 0

Answer:

least - 3 * 3 * 3

Step-by-step explanation:

3 * 3 * 3

9 * 3

27

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Y" +2y' +17y=0; y(0)=3, y'(0)=17

Ronch [10]

Answer:

The solution is $y(t)=e^{-t}(\cos 32t + (\frac{5}{8}) \sin 32t)$

Step-by-step explanation:

We need to find the solution of $y''+2y'+17y=0$ with

condition $y(0)=3,\ y'(0)=17$

This is a homogeneous equation with characteristic polynomial

$r^{2}+2r+17=0$

using quadratic formula $x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

$r=\frac{-2\pm \sqrt{2^{2}-4(1)(17)}}{2(1)}$

$r=\frac{-2\pm \sqrt{4-68}}{2}$

$r=\frac{-2\pm \sqrt{-64}}{2}$

$r=\frac{-2\pm 64i}{2}$

$r=-1 \pm 32i$

The general solution for eigen value $a \pm ib$ is

$y(t)=e^{at}(A \cos bt + B \sin bt)$

$y(t)=e^{-t}(A \cos 32t + B \sin 32t)$

Differentiate above with respect to 't'

$y'(t)=-e^{-t}(A \cos 32t + B \sin 32t) + e^{-t}(-32A \sin 32t + 32B \cos 32t)$

Since, y(0)=3

$y(0)=e^{0}(A \cos(0) + B \sin(0))$

$3=(A \cos(0) +0)$

so, A=1

Since, y'(0)=17

$y'(0)=-e^{0}(3 \cos(0) + B \sin(0)) + e^{0}(-32(3) \sin(0) + 32B \cos (0))$

$17=-(3 \cos(0)) + (0 + 32B \cos (0))$

$17=-3 + 32B$

add both the sides by 3,

$17+3 = 32B$

$20= 32B$

divide both the sides, by 32,

$\frac{20}{32}= B$

$\frac{5}{8}= B$

Put the value of constants in $y(t)=e^{-t}(A \cos 32t + B \sin 32t)$

$y(t)=e^{-t}((1) \cos 32t + (\frac{5}{8}) \sin 32t)$

Therefore, the solution is $y(t)=e^{-t}(\cos 32t + (\frac{5}{8}) \sin 32t)$

8 0

3 years ago

What is the cube root of 216x^9y^18?

PilotLPTM [1.2K]

Answer:

The cube root of given expression is $6x^3y^6$ .

Step-by-step explanation:

The given expression is

$\sqrt[3]{216x^9y^{18}}$

It can be written as

Use the exponent property: $a^{mn}=(a^m)^n$

$\sqrt[3]{216x^9y^{18}}=\sqrt[3]{6^3(x^3)^3(y^6)^{3}}$

$\sqrt[3]{216x^9y^{18}}=\sqrt[3]{(6x^3y^6)^{3}}$

$\sqrt[3]{216x^9y^{18}}=6x^3y^6$

Therefore the cube root of given expression is $6x^3y^6$ .

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3 years ago

2. LIST THREE DIFFERENT TYPES OF ORGANISMS THAT USE CELLULAR RESPIRATION? MAKE THEM AS DIFFERENT AS POSSIBLE.

OLEGan [10]

<h2>1) Plants</h2><h2>2) Animals</h2><h2>3) Humans</h2>

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3 years ago

-4 , 5/8 , 3 and 2.9 order the following Greatest to least

sladkih [1.3K]

Answer:

-4, 5/8, 2.9 3

Step-by-step explanation:

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3 years ago

How does the multiplicity of a zero determine the behavior of the graph at that zero?

grin007 [14]

If the graph crosses the x-axis and appears almost linear at the intercept, it is a single zero. If the graph touches the x-axis and bounces off of the axis, it is a zero with even multiplicity. If the graph crosses the x-axis at a zero, it is a zero with odd multiplicity. The sum of the multiplicities is the degree

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2 years ago