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3 years ago

Point V lies between points U and W on .

Mathematics

1 answer:

malfutka [58]3 years ago

3 0

Answer:

$\boxed{5}$

Step-by-step explanation:

$\begin{array}{rcl}UW & = & UV + VW\\9x - 9 & = & 2x - 4 + 4x + 10\\9x - 9 & = & 6x + 6\\3x - 9 & = & 6\\3x & = & 15\\x & = & \mathbf{5}\\\end{array}\\UW = \boxed{\mathbf{5}}$

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Find a homogeneous linear differential equation with constant coefficients whose general solution is given by

frez [133]

Answer:

$y" + 2y' + 2y = 0$

Step-by-step explanation:

Given

$y=c_1e^{-x}cosx+c_2e^{-x}sinx$

Required

Determine a homogeneous linear differential equation

Rewrite the expression as:

$y=c_1e^{\alpha x}cos(\beta x)+c_2e^{\alpha x}sin(\beta x)$

Where

$\alpha = -1$ and $\beta = 1$

For a homogeneous linear differential equation, the repeated value m is given as:

$m = \alpha \± \beta i$

Substitute values for $\alpha$ and $\beta$

$m = -1 \± 1*i$

$m = -1 \± i$

Add 1 to both sides

$m +1= 1 -1 \± i$

$m +1= \± i$

Square both sides

$(m +1)^2= (\± i)^2$

$m^2 + m + m + 1 = i^2$

$m^2 + 2m + 1 = i^2$

In complex numbers:

$i^2 = -1$

So, the expression becomes:

$m^2 + 2m + 1 = -1$

Add 1 to both sides

$m^2 + 2m + 1 +1= -1+1$

$m^2 + 2m + 2= 0$

This corresponds to the homogeneous linear differential equation

$y" + 2y' + 2y = 0$

6 0

3 years ago

hudson pick 1 1/4 baskets of apple suzy pick 2 basket of apple how muck more basket apple did suzy pick than hudson.

Vinvika [58]

Answer:

3/4

Step-by-step explanation:

Hudson = 1 1/4 baskets

Suzy = 2 baskets

How much more apple Suzy picked than Hudson :

Suzy - Hudson

2 - 1 1/4

2 - 5/4

L. C. M = 4

(8 - 5) / 4

3 /4 apples

Suzy picked 3/4 more apples Than Hudson

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3 years ago

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belka [17]

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8 0

3 years ago

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Reika [66]

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3 0

3 years ago

Read 2 more answers

Determine if each statement is True or False. If False, determine what needs to be

kicyunya [14]

Answer:

a. False. A constant is a number on it's own, and 5 would be the coefficient of x. 8 would be the constant.

b. False. -6.5 would be the constant, since it's on its own. But actually, x would be carrying on a coefficient of 1. Letters are variables, not constants.

c. True.

8 0

3 years ago