Ask question

Ask question

All categories

3 years ago

10

What is the domain of the relation?

1 answer:

Illusion [34]3 years ago

4 0

Answer:

A

Step-by-step explanation:

The domain of a relation is all the x values in it. Therefore, since the only x values in this relation are -4, -2, 1, and 4 that is the answer.

hope this helps :)

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

A mechanic works on the overhaul of a transmission. He starts at 8:25 AM and finishes

Mama L [17]

$56.25

8:25 - 4:25 = 4 hours

4 hours - 1 hour for lunch = 3 hours

$18.75 x 3 = $56.25

3 0

1 year ago

A rectangular yoga mat has a perimeter of 179 inches. The width of the mat is eight less than half the length. Find the width, i

lianna [129]

Answer:

The width is $24.5in$

Step-by-step explanation:

The perimeter of the rectangular yoga mat can be found using the formula;

$P=2l+2w$ .

$\Rightarrow 179=2l+2w...(1)$ .

It was given that the width of the mat is eight less than half the length.

$w=\frac{1}{2}l-8...(2)$

We put equation (2) into equation (1) to get;

$179=2l+2(\frac{1}{2}l-8)$ .

$\Rightarrow 179=2l+l-16$ .

$\Rightarrow 179+16=2l+l$ .

$\Rightarrow 3l=195$

Divide both sides by 3;

$l=65$

We put $l=65$ into equation 2 to get;

$w=\frac{1}{2}\times65-8$

$w=32.5-8$

$w=24.5in$

4 0

2 years ago

Find the value of x.<br> x<br> x = [?]<br> Enter

liberstina [14]

Answer:

x = 14

Step-by-step explanation:

From the given figuer...

x = 7 + 7
x = 14

Therefore, the value of x is 14.

<u>------------------------</u>

8 0

1 year ago

Josea’s recipe calls for 1/3 cup of milk

Goshia [24]

I think its 1/6 because if yoh do 1/3 times 1/2 it equals 1/6???????? not sure

3 0

2 years ago