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
Mekhanik [1.2K]
3 years ago
8

Suppose a tub has the shape of an elliptical paraboloid given by z = ax2+by2 (where a, b are some positive constants). If a marb

le were released at the point (1, 1, a + b) on the inside surface of the tub, in what direction would it begin to roll? Your answer should be a unit vector in the requested direction.
Mathematics
1 answer:
Umnica [9.8K]3 years ago
6 0

Answer:

It would roll in this direction.

\nu  =  (-a/\sqrt{a^2+b^2},-b/\sqrt{a^2+b^2})

Step-by-step explanation:

It would roll to the direction of maximum decrease, which is the -1 times the direction of maximum increase, which is given by the gradient of the function.  

Since  

z =  ax^2  + by^2

For this case, the gradient of your function would be

\nabla z  = (2ax , 2by)

And  -1  times the gradient of your function would be

-\nabla z  = (-2ax , -2by)\\

Then, at

 (1,1,a+b),\\x = 1 \\y = 1

So it would go towards

v = (-2a,-2b)

The magnitud of that vector is

|v| =  2\sqrt{a^2+b^2}

and to conclude it would roll in this direction.

\nu  =  (-a/\sqrt{a^2+b^2},-b/\sqrt{a^2+b^2})

You might be interested in
A student skipped a step when she tried to convert 18 hours into seconds and she got the following result:
Kitty [74]

Multiply 18hours by 60 seconds, the answer is 2880 seconds.

6 0
3 years ago
The area of a rectangular soccer field is 5000 yd^2. The length of the field is twice the length. Find the dimensions of the fie
harina [27]
You can divide the field into two squares of area 2500 yd^2. The side of each of those will be √2500 = 50 yd.

The dimensions of the field are 50 yd by 100 yd.
4 0
3 years ago
Read 2 more answers
4a + 3 - 9 = -7 + 2 + a
rjkz [21]
4a + 3 - 9 = -7 + 2 + a
4a - 6 = -5 + a
4a - a = -5 + 6
3a = 1 / : 3
a = 1/3

6 0
3 years ago
Read 2 more answers
The sum of one-fifth of a number and two is five
Veseljchak [2.6K]

Answer:

15

Step-by-step explanation:

Let us first write an equation where the unknown number is represented with variable x. <em>The sum of a fifth of x and two is five:</em>

\frac{1}{5} x+2=5

Great! Let's solve for x by isolating the variable.

\frac{1}{5}x=3\\x=15

<u>Therefore, the unknown number is 15.</u>

<u />

<em>I hope this helps! Let me know if you have any questions :)</em>

3 0
3 years ago
Factor the expression using the GCF.<br><br> 18h+30k<br><br> The factored form is <br> .
Murljashka [212]

Answer:

6(3h+5k)

Step-by-step explanation:

18h+30k

Factors of 18:

1, 2, 3, 6, 9, 18

Factors of 30:

1, 2, 3, 5, 6, 10, 15, 30

GCF of 18 and 30: 6

18h+30k = 6(3h+5k)

Check your answer:

6(3h+5k)

6(3h) + 6(5k)

18h + 30k

Hope this helps!

7 0
2 years ago
Other questions:
  • VERY EASY HELP QUICKLY PLEASE!! Write 6.012 as a mixed number in simplest form.
    12·1 answer
  • If a road has a grade of 30°, this means that it's angle of elevation is 30°. If you travel 1.5 miles on this road, how much ele
    9·1 answer
  • Can anyone help me with a problem on my math assignment. I need to find the surface area
    7·1 answer
  • Your friend approaches with three, fair 5-sided dice (labeled 1 to 5). You get to roll them and your friend gives you money base
    6·1 answer
  • Help ASAP!!!! 10 points
    6·2 answers
  • 1. What is percent of change formula
    6·1 answer
  • Solve using EQUATIONS (with step by step explanation)<br><br> 3x+y=-9<br> y=5x+7
    15·1 answer
  • PLEASE HELP WITH ALGEBRA WILL GIVE BRAINLIEST
    8·1 answer
  • A rectangle has a length of 11.8 centimeters and a width of 8.2 centimeters.
    10·1 answer
  • Can someone please help me solve this question? Pls provide a step by step explanation too… Ty!
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!