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3 years ago

11

F(x) = x^2 What is g(x)?

1 answer:

Scilla [17]3 years ago

6 0

Answer:

Last option.

Step-by-step explanation:

The coordinates are (4 , 1)

x = 4

y = 1

Put x as 4, the output should be 1.

g(4) = (1/4(4))²

g(4) = 1²

g(4) = 1

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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:

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

4 0

3 years ago

What is the decimal equivalent of 7/16

Sever21 [200]

The answer is 0.4375

3 0

3 years ago

Read 2 more answers

A pond has 150 fish and the population decreases by 8% each day. How many days before there are 30 fish

nlexa [21]

Answer:

19 days

Step-by-step explanation:

Given

$a = 150$ --- initial

$r = 8\%$ -- rate

Required

Days when the fish gets to 30

The function is exponential and as such it follows;

$y = ab^x$

Where x represents the number of days and y the number of fishes

Because the fishes decreases;

$b = 1 - r$

So, we have:

$b = 1 - 8\%$

Express as decimal

$b = 1 - 0.08$

$b = 0.92$

In $y = ab^x$

$a =150$

$y = 30$

$b = 0.92$

So, we have:

$30 = 150 * 0.92^x$

Divide both sides by 150

$0.2 = 0.92^x$

Take log of both sides

$log(0.2) = log(0.92^x)$

Apply law of logarithm

$log(0.2) = x\ log(0.92)$

Make x the subject

$x = \frac{log(0.2)}{log(0.92)}$

$x = \frac{-0.6990}{-0.0362}$

$x = 19.309$

$x \approx 19$

<em>Hence, it takes approximately 19 days</em>

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3 years ago

Let w represent the sum of vectors u and v. Find the magnitude of w and the angle between w and u given the

tino4ka555 [31]

The angle between w and u is approximately

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2 years ago

You believe that eating an apple a day is healthy and want to design an experiment to find out. You have available 40 volunteers

Gwar [14]

The best design for this experiment would be a repeated measures design. This is ideal to determine if eating an apple makes you healthy.

<h3>What is an experimental design?</h3>

An experimental design refers to the general structure of an experiment including how people are distributed into the control and experimental group to test a specific phenomenon.

<h3>What is a repeated measures design?</h3>

In a repeated measures design all participants are both parts of the control group, in this case, people who do not eat apples, and the experimental group, or people who eat apples.

<h3>What does this design imply?</h3>

In the case of determining if eating an apple every day, this design implies:

All participants will be asked to not eat apples every day for a specific period such as one or two months, and health levels will be measured during this time.
After the first step, all participants will be asked to eat an apple every day during the period, and their health will be measured.
The researcher can compare the results of each participant, which is more accurate than comparing one participant to another.

Learn more about experiments in: brainly.com/question/1452319

7 0

2 years ago