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2 years ago

14

Sarah used 2.5 cups of cheese in a dish that serves 10 people. Amy used 1.6 cups of cheese in a dish that serves 8 people.

1 answer:

Black_prince [1.1K]2 years ago

5 0

2.5/10
For Sarah
Answer: 0.25

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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

In 1995, the total box office in U.S movie theaters was about $5.02 billion. From 1995 through 2008, the box office revenue incr

soldier1979 [14.2K]

Answer:

1.06 x $10^{10}$ (3sf)

Step-by-step explanation:

using compound interest formula A = P $(1+\frac{R}{100}) ^{n}$

from 95 to 08 is 13 yrs

Total Revenue = (5.02 x $10^{9}$ ) $(1 + \frac{5.9}{100}) ^{13}$ = 1.057 x $10^{10}$

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2 years ago

9:15 in ratio simplest form

olchik [2.2K]

0.6:1

Hope it helps yah (◕ᴗ◕✿)

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2 years ago

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Find the area of the right triangle.

disa [49]

54 is th answer because ther is 6 units on one side and 9 units in the other and when you times you get this I think

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3 years ago

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(5-8) (1,4) m = -3<br> find the slope

tatiyna

Answer:

slope is -3

Step-by-step explanation:

m is the slope, this may have been a trick question.

by the points given the slope is 1

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2 years ago