Part 1 , i really need help if anyone have the items for these please help

Solve the differential equation. (y^2 + xy^2)y' = 1

stira [4]

$(y^2 + xy^2)y' = 1 \ \Rightarrow\ (y^2 + xy^2)\frac{dy}{dx}= 1 \ \Rightarrow\\ \\
y^2(1 + x) \frac{dy}{dx} = 1 \ \Rightarrow\ y^2 dx = \frac{dx}{1 + x}\ \Rightarrow \\ \\
\int y^2 dx =\int \frac{dx}{1 + x} \ \Rightarrow\ \frac{1}{3}y^3 = \ln|1+x| + C\ \Rightarrow \\ \\
y^3 = 3 \ln|1 + x| + 3C\ \Rightarrow\ y = \sqrt[3]{3\ln|1+x| + K},\ \text{where $K = 3C$}
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6 0

3 years ago

F(x)=-2x-1 and g(x)=x^2-1. Find (fog)(-5).

serg [7]

Answer: - 49

Step-by-step explanation:

f(x) = -2x - 1

g(x) = $x^{2}$ - 1

fg(x) = f ( $x^{2}$ - 1) , we just put in the value of g(x) , the next thing is to substitute $x^{2}$ - 1 for the value of x in f(x) , that is

fg(x) = -2( $x^{2}$ - 1) - 1

fg(x) = -2 $x^{2}$ + 2 - 1

fg(x) = -2 $x^{2}$ + 1

Therefore : fg(-5) means we will substitute -5 for x in fg(x) , that is

fg(-5) = -2 ( $(-5)^{2}$ + 1

fg(-5) = -2(25) + 1

fg(-5) = -50 + 1

fg(-5) = -49

7 0

4 years ago

I NEED HELP PLEASE, THANKS! :)

Alenkasestr [34]

Answer:

Option A

Step-by-step explanation:

This is a great question!

The first thing we want to do here is to graph the system of " inequalities " -

$\begin{bmatrix}2x+9y\le \:100\\ 9x+y\le \:54\end{bmatrix}$

As x is ≥ 0, respectively y ≥ 0, it makes things a lot simpler, as it kind of restricts us to quadrant 1, but not entirely.

First change each inequality to " slope - intercept " form, as such -

$2x + 10y \leq 100,\\10y \leq 100 - 2x,\\y \leq - 1 / 5x + 10\\----------\\9x + y \leq 54,\\y \leq - 9x + 54$

The graphed solutions would be in the attachment. I have colored the region with which the two intersect, and the fact that we are limited to quadrant 1. In this colored region there are 3 major points, ( 5, 9 ), ( 0, 10 ), and ( 6, 0 ). We have to determine which of these are are maximum points, as the minimum are the same. Substitute these values ( ( 5, 9 ), ( 0, 10 ), and ( 6, 0 ) ) into the equation f( x, y ) = 10x + 4y,

$f ( x, y ) = 10( 5 ) + 4( 9 ),\\f ( x, y ) = 86 -\\f ( x, y ) = 10( 0 ) + 4( 10 ),\\f ( x, y ) = 40 -\\f ( x, y ) = 10( 6 ) + 4( 0 ),\\f ( x, y ) = 60$