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2 years ago

= Use <, >, or = to make the statements true. 1 km 3,000 m 4L 4,000 mL

Mathematics

1 answer:

quester [9]2 years ago

3 0

Answer:

1 km < 3,000 m and 4L = 4,000 mL

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In this problem we consider an equation in differential form Mdx+Ndy=0. (4x+2y)dx+(2x+8y)dy=0 Find My= 2 Nx= 2 If the problem is

zheka24 [161]

Answer:

$f(x,y)=2x^2+4y^2+2xy=C_1\\\\Where\\\\y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )$

Step-by-step explanation:

Let:

$M(x,y)=4x+2y\\\\and\\\\N(x,y)=2x+8y$

This is and exact equation, because:

$\frac{\partial M(x,y)}{\partial y} =2=\frac{\partial N}{\partial x}$

So, define f(x,y) such that:

$\frac{\partial f(x,y)}{\partial x} =M(x,y)\\\\and\\\\\frac{\partial f(x,y)}{\partial y} =N(x,y)$

The solution will be given by:

$f(x,y)=C_1$

Where C1 is an arbitrary constant

Integrate $\frac{\partial f(x,y)}{\partial x}$ with respect to x in order to find f(x,y):

$f(x,y)=\int\ {4x+2y} \, dx =2x^2+2xy+g(y)$

Where g(y) is an arbitrary function of y.

Differentiate f(x,y) with respect to y in order to find g(y):

$\frac{\partial f(x,y)}{\partial y} =2x+\frac{d g(y)}{dy}$

Substitute into $\frac{\partial f(x,y)}{\partial y} =N(x,y)$

$2x+\frac{dg(y)}{dy} =2x+8y\\\\Solve\hspace{3}for\hspace{3}\frac{dg(y)}{dy}\\\\\frac{dg(y)}{dy}=8y$

Integrate $\frac{dg(y)}{dy}$ with respect to y:

$g(y)=\int\ {8y} \, dy =4y^2$

Substitute g(y) into f(x,y):

$f(x,y)=2x^2+4y^2+2xy$

The solution is f(x,y)=C1

$f(x,y)=2x^2+4y^2+2xy=C_1$

Solving y using quadratic formula:

$y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )$

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3 years ago

Graph this piecewise function:

Pepsi [2]

Consider the function f(x) = 2 x + 1. We recognize the equation y = 2 x + 1 as the Slope-Intercept form of the equation of a line with slope 2 and y-intercept (0,1). Think of a point moving on the graph of f. As the point moves toward the right it rises.
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3 years ago

Can anyone help?............

sertanlavr [38]

Answer:

52+46

Step-by-step explanation:

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3 years ago

A tennis ball travels at speed of 120 miles per hour.convert this rate to feet per second

Vanyuwa [196]

$120\frac{mile}{hour}\\\\
1 \ mile=5280\ feet\\
1\ hour=3600\ seconds\\\\
120\frac{mile}{hour}=120*\frac{5280}{3600}=\frac{120*5280}{3600}=\frac{633600}{3600}=176\frac{feet}{second}\\\\
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40 and 400 The value of 4 in ___ is______ times the value of 4 in _____

Nat2105 [25]

The value of 4 in the 400 is ten times the value of 4 in the 40's place

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