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djverab [1.8K]
2 years ago
5

A seed company says that 4 out of every 5 of its seeds will grow. If Melissa plants

Mathematics
1 answer:
jarptica [38.1K]2 years ago
6 0

Answer:  I think the answer is 32.

Step-by-step explanation:

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Calc 3 iiiiiiiiiiiiiiiiiiiiiiiiiiii
Lilit [14]

Take the Laplace transform of both sides:

L[y'' - 4y' + 8y] = L[δ(t - 1)]

I'll denote the Laplace transform of y = y(t) by Y = Y(s). Solve for Y :

(s²Y - s y(0) - y'(0)) - 4 (sY - y(0)) + 8Y = exp(-s) L[δ(t)]

s²Y - 4sY + 8Y = exp(-s)

(s² - 4s + 8) Y = exp(-s)

Y = exp(-s) / (s² - 4s + 8)

and complete the square in the denominator,

Y = exp(-s) / ((s - 2)^2 + 4)

Recall that

L⁻¹[F(s - c)] = exp(ct) f(t)

In order to apply this property, we multiply Y by exp(2)/exp(2), so that

Y = exp(-2) • exp(-s) exp(2) / ((s - 2)² + 4)

Y = exp(-2) • exp(-s + 2) / ((s - 2)² + 4)

Y = exp(-2) • exp(-(s - 2)) / ((s - 2)² + 4)

Then taking the inverse transform, we have

L⁻¹[Y] = exp(-2) L⁻¹[exp(-(s - 2)) / ((s - 2)² + 4)]

L⁻¹[Y] = exp(-2) exp(2t) L⁻¹[exp(-s) / (s² + 4)]

L⁻¹[Y] = exp(2t - 2) L⁻¹[exp(-s) / (s² + 4)]

Next, we recall another property,

L⁻¹[exp(-cs) F(s)] = u(t - c) f(t - c)

where F is the Laplace transform of f, and u(t) is the unit step function

u(t) = \begin{cases}1 & \text{if }t \ge 0 \\ 0 & \text{if }t < 0\end{cases}

To apply this property, we first identify c = 1 and F(s) = 1/(s² + 4), whose inverse transform is

L⁻¹[F(s)] = 1/2 L⁻¹[2/(s² + 2²)] = 1/2 sin(2t)

Then we find

L⁻¹[Y] = exp(2t - 2) u(t - 1) • 1/2 sin(2 (t - 1))

and so we end up with

y = 1/2 exp(2t - 2) u(t - 1) sin(2t - 2)

7 0
2 years ago
You roll fair6-sided die what is P(roll a 2)?
creativ13 [48]

Answer:

1/6

Step-by-step explanation:

It is a 6 sided die, so you have 6 possibilities, so that is going to be you denominator.

There is only one number 2 on the die, so you have 1 as your numerator.

5 0
3 years ago
Read 2 more answers
Please i need to know if im correct with these questions
telo118 [61]

Answer: No Solution

<u>Step-by-step explanation:</u>

ln x - ln (x + 2) = 4             restrictions: x > 0  and  x + 2 > 0   →    x > 0

ln (\frac{x}{x + 2}) = 4

(\frac{x}{x + 2}) = e⁴

x = e⁴ (x + 2)

x = 54.5982 (x + 2)

x = 54.5982x + 109.1964

- 53.5982x = 109.1964

x = \frac{109.1964}{-53.5982}

x = -2.0373

-2.0373 is not greater than 0 so is not valid

**************************************************************************

Answer: 2.1972

<u>Step-by-step explanation:</u>

eˣ = 9

ln eˣ = ln 9

   x = ln 9

   x ≈ 2.1972

**************************************************************************

Answer: \frac{3}{2}

<u>Step-by-step explanation:</u>

log₂ (3x - 4) = -1

        3x - 4 = 2⁻¹

         3x - 4 = \frac{1}{2}

       <u>       +4 </u>   <u>+4 </u>

          3x     = 4\frac{1}{2}

          3x     = \frac{9}{2}

          \frac{3x}{3} = \frac{9}{2} * \frac{1}{3}

            x = \frac{3}{2}

**************************************************************************

Answer: 1.117519

<u>Step-by-step explanation:</u>

in the calculator, type in 1 ÷ 9.

Then hit the eˣ button.

 e¹⁾⁹

= e°¹¹¹¹¹¹

= 1.117519

rounded to 6 decimal places: 1.117519

6 0
2 years ago
The cosine of the complimentary angle to 58 degrees
lana [24]
Yes
Divide it by sixty and multiply
I hope this helps
5 0
2 years ago
Simplify the expression
erastova [34]

Answer : A

We need to simplify the given expression

Lets factor numerator first

2x^2-5x-3 =(2x+1)(x-3)

x^2+8x+15 =(x+5)(x+3)

Now we factor the denominator

x^2+x-20 =(x+5)(x-4)

2x^2+9x+4 =(2x+1)(x-4)

Now we simplify it

\frac{(2x+1)(x-3)}{(x+5)(x-4)} * \frac{(x+5)(x+3)}{(2x+1)(x-4)}

Now cancel out same factors. so we left with

\frac{(x+3)(x-3)}{(x+4)(x-4)} }

Now multiply the factors

\frac{x^2-9}{x^2-16} }



6 0
3 years ago
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