What is the most reasonable estimate for the sum? 9/11 + 3/5

Mathematics

2 answers:

Eddi Din [679]3 years ago

7 0

The exact answer would be 78/55, or 1 23/55

PilotLPTM [1.2K]3 years ago

5 0

While this is not an estimate, I can give you this= 1 23/55 78/55

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Use Laplace transform methods to solve the differential equation: The initial conditions are f(0) = 0 and <img src="https://tex.

Llana [10]

Answer:

Step-by-step explanation:

$\frac{d^2 y}{dt^2} +12\frac{dy}{dt} +32y = 10e^{-2t}$ where f(x) is replaced by y

Take Laplace on both sides

$s^2 Y -s(0)-0 +12s Y-0+32Y = \frac{10}{s+2} \\Y(s^2+12s+32) = \frac{10}{s+2}\\Y = \frac{10}{(s+2)(s+4)(s+8)}$

We can resolve into partial fraction to get Y = L(y)

Let this equals

$\frac{A}{s+2} +\frac{B}{s+4} +\frac{C}{s+8} \\10 = A(s+4)(s+8) + B(s+2)(s+8) +Cs+4)(s+2) \\$

Solving we get

s=-9

24C = 10 or C =5/12

s=-2: A=10/12=5/6

s=-4: B = -5/4

Taking inverse Laplace

$y(t) = \frac{-5e^{-4t} }{4} + \frac{5e^{-8t} }{12} +\frac{-5e^{-2t} }{6}$

6 0

3 years ago

The shorter leg of a 30 60 90 triangle is 6.4 inches long. Find the perimeter.

kogti [31]

The perimeter is 38.4 inches

8 0

3 years ago

What is 1 1/4÷ by 3 4/5

spin [16.1K]

let's firstly convert the mixed fractions to improper fractions and then divide.

$\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{3\frac{4}{5}}\implies \cfrac{3\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{19}{5}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{4}\div\cfrac{19}{5}\implies \cfrac{5}{4}\cdot \cfrac{5}{19}\implies \cfrac{25}{76}$