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elena-14-01-66 [18.8K]

3 years ago

10

Solve using the systems of linear inequalities

la1" title="4x + y \geqslant 2" alt="4x + y \geqslant 2" align="absmiddle" class="latex-formula">

1 answer:

Archy [21]3 years ago

5 0

The linear inequality for x is x ≥ 1/2-y/4
The linear inequality for y is y ≥ 2-4x

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What is the answer to number 12

egoroff_w [7]

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2 years ago

The amount of time that American astronauts spent on space is about 13,507,804 minuets. What is the word form of that number

eduard

The amount of time that American astronauts spent on space is about

["Thirteen million, five hundred seven thousand, eight hundred four"]

8 0

2 years ago

Given the second order homogeneous constant coefficient equation y′′−4y′−12y=0 1) the characteristic polynomial ar2+br+c is r^2-

Vitek1552 [10]

Answer:

The initial value problem $y(x) = 4 e^{-2x} -3 e^{6 x}$

Step-by-step explanation:

<u>Step1:</u>-

a) Given second order homogenous constant co-efficient equation

$y^{ll} - 4y^{l}-12y=0$

Given equation in the operator form is $(D^{2} -4D-12)y=0$

<u>Step 2</u>:-

b) Let f(D) = $(D^{2} -4D-12)y$

Then the auxiliary equation is $(m^{2} -4m-12)=0$

Find the factors of the auxiliary equation is

$m^{2} -6m+2m-12=0$

m(m-6) + 2(m-6) =0

m+2 =0 and m-6=0

m=-2 and m=6

The roots are real and different

The general solution $y = c_{1} e^{-m_{1} x} + c_{2} e^{m_{2} x}$

the roots are $m_{1} = -2 and m_{2} = 6$

The general solution of given differential equation is

$y = c_{1} e^{-2x} + c_{2} e^{6 x}$

<u>Step 3</u>:-

C) Given initial conditions are y(0) =1 and y1 (0) =-26

The general solution of given differential equation is

$y(x) = c_{1} e^{-2x} + c_{2} e^{6 x}$ .....(1)

substitute x =0 and y(0) =1

$y(0) = c_{1} e^{0} + c_{2} e^{0}$

$1 = c_{1} + c_{2}$ .........(2)

Differentiating equation (1) with respective to 'x'

$y^l(x) = -2c_{1} e^{-2x} + 6c_{2} e^{6 x}$

substitute x= o and y1 (0) =-26

$-26 = -2c_{1} e^{0} + 6c_{2} e^{0}$

$-2c_{1} + 6c_{2} = -26$ .............(3)

solving (2) and (3) by using substitution method

$substitute c_{2} =1- c_{1}$ in equation (3)

$-2c_{1} + 6(1-c_{1}) = -26$

on simplification , we get

$-2c_{1} + 6(1)-6c_{1}) = -26$

$-8c_{1} = -32$

dividing by'8' we get $c_{1} =4$

substitute $c_{1} =4$ in equation $1 = c_{1} + c_{2}$

so $c_{2} = 1-4 = -3$

now substitute $c_{1} =4 and c_{2} =-3$ in general solution

$y(x) = c_{1} e^{-2x} + c_{2} e^{6 x}$

$y(x) = 4 e^{-2x} -3 e^{6 x}$

now the initial value problem

$y(x) = 4 e^{-2x} -3 e^{6 x}$

7 0

3 years ago

Evaluate: \frac{23}{56} + \frac{3}{8} - ( - \frac{4}{28} )

MrMuchimi

I think this is what you mean. I don't know why the Latex didn't work. Good for you that you can use it.

$\frac{23}{56} + \frac{3}{8} - \frac{-4}{28}$
$\frac{23}{56} + \frac{3}{8} - \frac{-4}{28}$ Reduce the 4/28 to 1/7
$\frac{23}{56} + \frac{3}{8} - \frac{-1}{7}$ Make the 2 minuses into a +
$\frac{23}{56} + \frac{3}{8} + \frac{1}{7}$ 56 is the common denominator.
$\frac{23}{56} + \frac{21}{56} + \frac{8}{56}$

Answer = [23 + 21 + 8] / 56 = 52 / 56 = 13 / 14 When both numerator and denominator are divided by 4

13 / 14 <<<< answer.

5 0

2 years ago

A pet-sitting company charges $25 to board a pet for one day. It also charges all customers an extra $7.50 to trim the pet's nai

Mrac [35]

2 weeks = 14 days

14 * 25 = 350

350 + 7.50 = 357.50

Answer is C

6 0

3 years ago