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Rama09 [41]
3 years ago
11

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

Mathematics
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>

3 0
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
5 0
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
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