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2 years ago

54,872 in expanded form

Mathematics

2 answers:

lina2011 [118]2 years ago

3 0

Answer:

54,000+800+70+2

Step-by-step explanation:

Finger [1]2 years ago

3 0

Answer:

Here is an answer

54,000+800+70+2

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Use the Laplace transform to solve the given initial value problem. y' + 6y = e^4t ; y(0)=2 ...?

TiliK225 [7]

Performing laplace transform of the equation.

sY(s) - y(0) + 6Y(s) = 1/(s-4)
(s+6)Y(s) - 2 = 1/(s-4)
Y(s) = 2/(s+6) + 1/(s-4)(s+6), by partial fraction decomposition
Y(s) = 2/(s+6) + 1/10 * (1/(s-4) + 1/(s+6))
Y(s) = 0.1/(s-4) + 2.1/(s+6)

Performing inverse laplace transform,
y(t) = 0.1e^4t + 2.1e^(-6t)

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4 0

3 years ago

Marco purchased a large box of comic books for $300. He gave 15 of the comic books to his brother and then sold the rest on an i

Yuri [45]

Answer: There are 75 books.

Price of each book = $4.

Step-by-step explanation:

Let x = Number of books in the box.

Then as per given,

Cost of x books = $300

Cost of one book = $\$(\dfrac{300}x)$

Books left after giving 15 of them = x-15

Selling price of (x-15) books= $330

Selling price of one book = $\$(\dfrac{330}{x-15})$

Profit on each book= $1.50

Profit = selling price - cost price

$\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}]$

$\Rightarrow (x+40)(x-75)=0\\\\\Rightarrow\ x=-40,75$

Number of books cannot be negative.

So, there are 75 books.

Price of each book = $\dfrac{300}{75}=\$4$

So price of each book = $4.

5 0

3 years ago

Totsaken sold half of his comic books and bought ten more. He now has 40. With how many did he begin?

AURORKA [14]

The answer is 60 because

40-10*2=60

hope it helps

8 0

3 years ago

Read 2 more answers

Please help me find limit

cluponka [151]

9514 1404 393

Answer:

-13/11

Step-by-step explanation:

Straightforward evaluation of the expression at x=1 gives (1 -1)/(1 -1) = 0/0, an indeterminate form. So, L'Hopital's rule applies. The ratio of derivatives is ...

$\displaystyle\lim_{x\to 1}\dfrac{n}{d}=\dfrac{n'}{d'}=\left.\dfrac{\dfrac{4}{3\sqrt[3]{4x-3}}-\dfrac{7}{2\sqrt{7x-6}}}{\dfrac{5}{2\sqrt{5x-4}}-\dfrac{2}{3\sqrt[3]{2x-1}}}\right|_{x=1}=\dfrac{4/3-7/2}{5/2-2/3}=\dfrac{8-21}{15-4}\\\\=\boxed{-\dfrac{13}{11}}$

4 0

3 years ago

A doorway is 7 1/2 feet tall. How many inches tall is the doorway?

neonofarm [45]

Answer:

6.07/212

Step-by-step explanation:

5 0

2 years ago

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