1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Komok [63]
3 years ago
10

Solve the equation by completing the square. Round to the nearest hundredth if necessary.

Mathematics
1 answer:
sergejj [24]3 years ago
3 0

Answer

2

Step-by-step explanation:

(reorder terms)

<u>2x + 2x</u> = 8

collect like terms

<u>4x=8</u>

divide both sides of the equation

x = 2

You might be interested in
A bottle of water contains 500 ml.
podryga [215]

Answer:

650ml

Step-by-step explanation:

30% = 0.30

0.30 x 500 = 150

500 + 150 = 650

8 0
3 years ago
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
Which best describes the relationship between the successive terms in the sequence below?
zhuklara [117]

Answer:

You haven't displayed the full question

3 0
2 years ago
100 points!!! Please help with this math.
joja [24]

Answer:

12ft

Step-by-step explanation:

A prism is a 3D shape which has the same 2D shape repeated along its length (this is sometimes called the cross section).

The 2D shape at the ends of the prism is the base of the prism, so for this shape, the <u>bases</u> are the <u>triangles</u>.

The height of the prism is actually the length of the prism, so for this prism the height is 12 ft.

6 0
2 years ago
Read 2 more answers
A construction crew has just finished building a road. The crew worked for 4 2/7 days. If the road is 9 kilometers long, how man
Lana71 [14]
4 2/7 equals 30/7
30/7 divided by 9 equals 10/21
So the crew built 10/21 of a km everyday
4 0
3 years ago
Read 2 more answers
Other questions:
  • There is a traffic light at the intersection of Main Street and Durham Avenue. The traffic light on Main Street follows a cycle.
    9·1 answer
  • 0.1 x 23<br><br><br><br><br><br><br><br> Please help me
    8·2 answers
  • The faster a vehicle is going, the further it will continue to travel after the brakes are applied. Which is the dependent varia
    13·1 answer
  • The population of men at UMBC has a mean height of 69 inches with a standard deviation of 4 inches. The women at UMBC have a mea
    6·1 answer
  • I don't understand this, can someone help?
    9·1 answer
  • Vincent works 8 hours a day for 5 days. How much does he earn at the rate of $.97 per hour?
    6·2 answers
  • Find the area of the Trapezoid below please!
    12·1 answer
  • PLEASE PLEASE HELP I REALLY NEED IT <br> QUESTION 2
    13·2 answers
  • Can y’all help me with this plz
    5·1 answer
  • Find two positive angles and two negative angles that are coterminal with the given angle and less than 1080 but greater than 72
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!