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
Rus_ich [418]
3 years ago
5

The differential equation of a certain system is 20⁢y′⁢′+c⁢y′+80⁢y=0

Mathematics
1 answer:
Sholpan [36]3 years ago
5 0

Answer:

c=80

Step-by-step explanation:

Based on my reading the critical damping occurs when the discriminant of the quadratic characteristic equation is 0.

So let's see that characteristic equation:

20⁢r^2+c⁢r+80⁢=0

The discriminant can be found by calculating b^2-4aC of ar^2+br+C=0.

a=20

b=c

C=80

c^2-4(20)(80)

We want this to be 0.

c^2-4(20)(80)=0

Simplify:

c^2-6400=0

Add 6400 on both sides:

c^2=6400

Take square root of both sides:

c=80 or c=-80

Based on further reading damping equations in form

a⁢y′⁢′+b⁢y′+C⁢y=0

should have positive coefficients with b also having the possibility of being zero.

You might be interested in
Can someone please help me with this?
Anettt [7]

Answersorry

Step-by-step explanation:sorry idk

7 0
3 years ago
E temperature t of a metal sphere is inversely proportional to the distance from the centre of the sphere (the origin (0, 0, 0))
olasank [31]

(-x, -y, -z) the vector form (x, y, z) to the origin, in the direction of the greatest increase.

<h3>How to calculate temperature?</h3>

The quantity or amount of radiation contained in material or item, as measured by a temperature or sensed by touch and stated on a numerical scale.

The temperature T of a ball bearing is inverse to the length first from the origin, which we consider to be the center of the ball. The temperature at the exact location

(x, y, z) is a point on the sphere, the temperature at this point is given by

T(x,y,z)= \dfrac{k}{(x^2 +y^2+z^2)^{1/2}}

Where k is constant, then we have

T(1, 2, 2) = k/3 = 170

k = 510

So

T(x,y,z)= \dfrac{510}{(x^2 +y^2+z^2)^{1/2}}

Then we have

\rm \triangledown T =  \left ( -\dfrac{510x}{(x^2 +y^2+z^2)^{1/2}}, -\dfrac{510y}{(x^2 +y^2+z^2)^{1/2}}, \dfrac{510z}{(x^2 +y^2+z^2)^{1/2}} \right )\\\\\\\triangledown T (1, 2, 2) = -\dfrac{510}{27} (1, 2, 2) =-\dfrac{170}{9} (1, 2, 2)

Then the direction will be from (1, 2, 2) to (4, 3, 5) will be (3, 1, 3)

So u = (3/√19, 1/√19, 3/√19)

Then we get

\rm \triangledown T \cdot u = \dfrac{-170}{9}(1, 2, 2) \cdot \left (\dfrac{3}{\sqrt{19}}, \dfrac{1}{\sqrt{19}}, \dfrac{3}{\sqrt{19}} \right )\\\\\\\triangledown T \cdot u = - \dfrac{170}{9\sqrt{19}} (3 + 2 + 6)\\\\\\\triangledown T \cdot u = -\dfrac{1870}{9\sqrt{19}}

The direction of the greatest inverse in the temperature is given by any vector parallel to and having the same direction \triangledownT. (-x, -y, -z) the vector form (x, y, z) to the origin, in the direction of the greatest increase.

More about the temperature link is given below.

brainly.com/question/11464844

#SPJ4

6 0
2 years ago
A stock worth $42 at the beginning of the day. The stock depreciates 15% every hour. How much will the stock be worth after 7 ho
liubo4ka [24]

Answer:

14.46

Step-by-step explanation:

first hour: 35.7

2 hour: 30.34

3 hour: 25.79

4 hour: 21.93

5 hour: 18.64

6 hour:15.85

7 hour:14.46

7 0
3 years ago
X=y^2+4y+4 solve for y
IrinaK [193]

Answer:

y=

x

​

−2

y=−

x

​

−2, x≥0

​

y=−

x−2, x≥0

​

Step-by-step explanation:

8 0
3 years ago
Help you will get 30 <br> Points
Stells [14]

Answer:

Line A is filling more quickly

Step-by-step explanation:

Hope this helps!!:)

8 0
3 years ago
Other questions:
  • Travis has decided to budget his spending money. He can spend no more than $143.15 every month. He has also decided to spend 5.2
    5·1 answer
  • Write an equation of the line, in point-slope form, that passes through the two given points. points: (–15, 7), (5, –3)
    14·1 answer
  • Circle the vertex of the angle.
    11·1 answer
  • jean paid 18,489 for a new car. Calculate the total cost of the car if she financed it at an interest rate 3.5% in 4 years
    9·1 answer
  • What is a solution to (x + 6)(x + 2) = 60?<br> 0 x = -6<br> 0 x = -4<br> 0 х = 4<br> 0 х = 12
    6·2 answers
  • Indicate the degree of the term.<br> a^10
    13·1 answer
  • Which is the simplified form of the expression<br> 3<br> 2<br> 21 12<br> x y12<br> 24
    8·1 answer
  • Solve the proportion. 8/11 = 4/y + 2
    11·1 answer
  • Use the information to answer the following question.
    8·1 answer
  • Step 4: Finding the percentage of a number using equivalent ratios
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!