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3 years ago

Please help, thanks if you do :)

Mathematics

1 answer:

Evgen [1.6K]3 years ago

8 0

Answer: No solution

Explanation: It is completely parallel. If it intersects, it has 1 solution. If it is exactly the same, giving the appearance of one line, it has infinite. When it’s parallel, it has none.

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Determine whether each first-order differential equation is separable, linear, both, or neither. 1. ????y????x+????xy=x2y2 2. y+

Mkey [24]

Answer:

a) Linear

b) Linear

c) Linear

d) Neither

See explanation below.

Step-by-step explanation:

a) $\frac{dy}{dx} +e^x y = x^2 y^2$

For this case the differential equation have the following general form:

$y' +p(x) y = q(x) y^n$

Where $p(x) =e^x$ and $q(x) = x^2$ and since n>1 we can see that is a linear differential equation.

b) $y + sin x = x^3 y'$

We can rewrite the following equation on this way:

$y' -\frac{1}{x^3} y= \frac{sin (x)}{x^3}$

For this case the differential equation have the following general form:

$y' +p(x) y = q(x) y^n$

Where $p(x) =-\frac{1}{x^3}$ and $q(x) = \frac{sin(x)}{x^3}$ and since n=0 we can see that is a linear differential equation.

c) $ln x -x^2 y =xy'$

For this case we can write the differential equation on this way:

$y' +xy = \frac{ln(x)}{x}$

For this case the differential equation have the following general form:

$y' +p(x) y = q(x) y^n$

Where $p(x) =x$ and $q(x) = \frac{ln(x)}{x}$ and since n=0 we can see that is a linear differential equation.

d) $\frac{dy}{dx} + cos y = tan x$

For this case we can't express the differential equation in terms:

$y' +p(x) y = q(x) y^n$

So the is not linear, and since we can separate the variables in order to integrate is not separable. So then the answer for this one is neither.

4 0

3 years ago

<img src="https://tex.z-dn.net/?f=Expand%20%24%28a%20%2B%202%29%283a%5E2%20%2B%2012%29%28a%20-%202%29.%24" id="TexFormula1" titl

sashaice [31]

Answer:

3 $a^{4}$ - 48

Step-by-step explanation:

Given

(a + 2)(3a² + 12)(a - 2)

= (a + 2)(a - 2)(3a² + 12) ← expand the first pair of parenthesis using FOIL

=(a² - 4)(3a² + 12) ← expand using FOIL

= 3 $a^{4}$ + 12a² - 12a² - 48 ← collect like terms

= 3 $a^{4}$ - 48

5 0

3 years ago

What is the volume of this rectangular prism?

kolezko [41]

Answer:

105 in³.

Step-by-step explanation:

Given numbers:

7, 3, and 5.

Given equation:

7 * 3 * 5.

Solve:

7 * 3
= 21 * 5
= 105.

Volume is 105 in³.

4 0

2 years ago

Read 2 more answers

Given that 196k is a perfect cube , find the smallest possible value of k

kaheart [24]

Factor 196k
196k=2*2*7*7*k
we need to get something like x^3
hmm
we right now have
(2*7)^2
if we multiply that by (2*7)^1, we can beg (2*7)^3,
therefor k=2*7=14

tha tnumber is 14

or

if k can be any number
k can be 1/196, to make it 1, and 1 is a perfect cube

or

my bro had an epic idea: what if k is negative
the cube root of a negative number is negative
so the smallest one would be negative infinity or something

I think the answer you're looking for is k=14

3 0

4 years ago

Find the difference 67/8 - 43/8=

dmitriy555 [2]

Answer: 3

Step-by-step explanation:

Since the denominator of the two fractions are already the same, we do not have to alter the fractions at all

Because the denominators are the same, all we have to worry about is the numerator, so take 67 and subtract 43 from it to get 24

$\frac{67}{8} -\frac{43}{8} =\frac{24}{8}$

As you know, 24/8 = 3, and that would be your final answer

7 0

3 years ago