Is the equation a literal equation t+8y=7

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

8 0

3 years ago

The projected number of employed writers and authors in 2016 is 153,000. 12. 4% of those will have some college experience but n

GuDViN [60]

Number of Writers and authors with bachelor's degree more than those with only some college experience and no degree is Option b: 109701

<h3>How to form mathematical expression from the given description?</h3>

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

<h3>How to find the percentage from the total value?</h3>

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

$\dfrac{a}{100} \times b$

For the given case, it is specified that:

Total number of employed writers and authors: 153,000
Some college experience but no degree : 12.4%
Bachelor's degree or higher : 84.1%

Let we have:

writers and authors with bachelor’s degree = N + writers and authors with some college experience and no degree

(so the number of writers and authors with bachelor’s degree is N more than writers and authors with some college experience but no degree)

Number of writers and authors with bachelor's degree = 12.4% of 153000

which is $\dfrac{153000}{100} \times 12.4 = 18972$

Number of writers and authors with some college experience but no degree = 84.1% of 153,000 which is $\dfrac{153000}{100} \times 84.1 = 128673$

Thus,

128,673 = N + 18972

or

N = 128,673 - 18972= 109,701

Thus,

Number of Writers and authors with bachelor's degree more than those with only some college experience and no degree is Option b: 109701

Learn more about percentage here:

brainly.com/question/11549320

3 0

3 years ago

Alexa has some dimes and some quarters. She has a minimum of 28 coins worth a maximum of $5.05 combined. If Alexa has 17 quarter

Lerok [7]

Answer:

There are no possible solutions

Step-by-step explanation:

Given:

Minimum number of coins Alexa has =28 coins

Number of quarters Alexa has = 17 quarters