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3 years ago

What is this word problem as an algebraic equation? Please help me :)

Mathematics

1 answer:

konstantin123 [22]3 years ago

6 0

X=“number”

5 + 4x = 3x + 6

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A bookstore owner has 48 science fiction books and 30 mysteries.He wants the most books possible in each package, but all packag

likoan [24]

The bookstore owner can make six packages. There will be eight science fiction books and five mystery books in each package. This is because 6 is the highest common factor of both 48 and 30, and 6 x 8 = 48 and 6 x 5 = 30.

4 0

3 years ago

Read 2 more answers

Help me please. I'm not even sure if the answers I put down are even correct.

Evgen [1.6K]

2.50 cm X 82 cm = 205

The rest is correct

6 0

4 years ago

Write down the explicit solution for each of the following: a) x’=t–sin(t); x(0)=1

Kay [80]

Answer:

a) x=(t^2)/2+cos(t), b) x=2+3e^(-2t), c) x=(1/2)sin(2t)

Step-by-step explanation:

Let's solve by separating variables:

$x'=\frac{dx}{dt}$

a) x’=t–sin(t), x(0)=1

$dx=(t-sint)dt$

Apply integral both sides:

$\int {} \, dx=\int {(t-sint)} \, dt\\\\x=\frac{t^2}{2}+cost +k$

where k is a constant due to integration. With x(0)=1, substitute:

$1=0+cos0+k\\\\1=1+k\\k=0$

Finally:

$x=\frac{t^2}{2} +cos(t)$

b) x’+2x=4; x(0)=5

$dx=(4-2x)dt\\\\\frac{dx}{4-2x}=dt \\\\\int {\frac{dx}{4-2x}}= \int {dt}\\$

Completing the integral:

$-\frac{1}{2} \int{\frac{(-2)dx}{4-2x}}= \int {dt}$

Solving the operator:

$-\frac{1}{2}ln(4-2x)=t+k$

Using algebra, it becomes explicit:

$x=2+ke^{-2t}$

With x(0)=5, substitute:

$5=2+ke^{-2(0)}=2+k(1)\\\\k=3$

Finally:

$x=2+3e^{-2t}$

c) x’’+4x=0; x(0)=0; x’(0)=1

Let $x=e^{mt}$ be the solution for the equation, then:

$x'=me^{mt}\\x''=m^{2}e^{mt}$

Substituting these equations in c)

$m^{2}e^{mt}+4(e^{mt})=0\\\\m^{2}+4=0\\\\m^{2}=-4\\\\m=2i$

This becomes the solution m=α±βi where α=0 and β=2

$x=e^{\alpha t}[Asin\beta t+Bcos\beta t]\\\\x=e^{0}[Asin((2)t)+Bcos((2)t)]\\\\x=Asin((2)t)+Bcos((2)t)$

Where A and B are constants. With x(0)=0; x’(0)=1:

$x=Asin(2t)+Bcos(2t)\\\\x'=2Acos(2t)-2Bsin(2t)\\\\0=Asin(2(0))+Bcos(2(0))\\\\0=0+B(1)\\\\B=0\\\\1=2Acos(2(0))\\\\1=2A\\\\A=\frac{1}{2}$

Finally:

$x=\frac{1}{2} sin(2t)$

7 0

4 years ago

2. Simplify. 10(x + 2)(x – 3) 5(x - 3)(x + 6)

Mariana [72]

Answer:

$10(x + 2)(x - 3) \\ 10x + 20 \times x - 3 \\ 10 {x}^{2} + 17$

$5(x - 3)( x + 6) \\ 5x - 15 \times x + 6 \\ 5 {x}^{2} - 9$

8 0

3 years ago

Read 2 more answers

Ms. Williamson woke up one morning to find her basement flooded with water. She called two different plumbers to get their rates

Oliga [24]

Answer:

A. $148 for the first plumber for 4 hours. $256 for the second plumber for 4 hour

B. He did 5 hours

C. 1 hours because the flat rate plus the hourly fee adding it together will equal 64.

Step-by-step explanation:

Your welcome

6 0

3 years ago