All categories

3 years ago

What is 4x² / 4x² ? Is the answer still a polynomial?

Mathematics

2 answers:

seraphim [82]3 years ago

4 0

Answer:

4x² / 4x² = 1

Step-by-step explanation:

Anything divided by itself is always 1

Yanka [14]3 years ago

3 0

The answer is definitely 1

You might be interested in

Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w

siniylev [52]

Solution :

a). The level curves of the function :

$C(x,y) = e^{-(x^2+2y^2)/10^4}$

are actually the curves

$e^{-(x^2+2y^2)/10^4}=k$

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$

which is a family of ellipses.

We sketch the level curves for K =1,2,3 and 4.

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.

$r(t)=x(t)i+y(t)j$ is a parametrization of the most $\text{rapid increase curve}$ , then

$\frac{dx}{dt}=\frac{dx}{dt}i+\frac{dy}{dt}j$ is a tangent to the curve.

So then we have that $\frac{dr}{dt}=\lambda \triangledown C$

$\Rightarrow \frac{dx}{dt}=-\frac{2\lambda x}{10^4}e^{-(x^2+2y^2)/10^4}, \frac{dy}{dt}=-\frac{4\lambda y}{10^4}e^{-(x^2+2y^2)/10^4}$

∴ $\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2y}{x}$

Using separation of variables,

$\frac{dy}{y}=2\frac{dx}{x}$

$\int\frac{dy}{y}=2\int \frac{dx}{x}$

$\ln y=2 \ln x$

⇒ y = kx^2 for some constant k

but we know that $y(x_0)=y_0$

$\Rightarrow kx_0^2=y_0$

$\Rightarrow k =\frac{y_0}{x_0^2}$

∴ The path of the shark will follow is along the parabola

$y=\frac{y_0}{x_0^2}x^2$

$y=y_0\left(\frac{x}{x_0}\right)^2$

7 0

2 years ago

Please Help I'm not really good at math

UkoKoshka [18]

The true statements about the triangles RST and DEF are: (a), (d) and (e)

<h3>How to determine the true statements?</h3>

The statement ΔRST ≅ ΔDEF means that the triangles RST and DEF are congruent.

This above implies that:

The triangles can be mapped onto each other by rigid transformations such as reflection, translation and rotation
The transformation does not include dilation
Corresponding sides are congruent

The above means that the possible true statements are: (a), (d) and (e)

Read more about transformation at:

brainly.com/question/4289712

#SPJ1

3 0

2 years ago

Choice 3: Kyra makes $700.00 a week in her job. She did such a great job this week that she is going to get a 15% raise next wee

nikklg [1K]

Answer:

15/100 x 700 = 105

Step-by-step explanation:

Consider 15% as 15 because you always consider a percent out of 100, you can remember by the word 'cent' meaning 100.

You need to FIRST find out what the percentage is OF whenever coming across these types of problems.

And the keyword 'of' means to multiply.

5 0

2 years ago

Alex rolls a six-sided number cube 570 times. Approximately how many times can he expect to roll a 5?

madreJ [45]

Answer:

95 times

Step-by-step explanation:

Probability of rolling a 5 =1/6

So no. of times 5 is expected when the number cube is rolled out 570 times = 570*1/6 = 95 times

5 0

3 years ago

Read 2 more answers

Dan multiplied 1,563 by 4 and got the incorrect product of 2,252. Find the correct product and explain what Dan did wrong. Pleas

Morgarella [4.7K]

Answer:

The correct product is 6,252.

I don't know what Dan did wrong lol

8 0

2 years ago