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
siniylev [52]
3 years ago
12

Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. x2 + y2 = 25 (a) Fin

d dy/dt, given x = 3, y = 4, and dx/dt = 5. dy/dt = -3/4 Incorrect: Your answer is incorrect. (b) Find dx/dt, given x = 4, y = 3, and dy/dt = –5.
Mathematics
1 answer:
Artemon [7]3 years ago
5 0

Answer:

(a) \frac{dy}{dt}=-3\frac{3}{4}

(b) \frac{dx}{dt}=3\frac{3}{4}

Step-by-step explanation:

x^{2} +y^{2}=25

Take \frac{d}{dt} of of each term.

\frac{d}{dt}(x^{2})+\frac{d}{dt}(y^{2})=\frac{d}{dt}(25)\\\\(\frac{d}{dx}(x^{2})*\frac{dx}{dt}) +(\frac{d}{dy}(y^{2})*\frac{dy}{dt})=\frac{d}{dt}(25)\\\\2x\frac{dx}{dt} +2y\frac{dy}{dt} = 0\\\\

For Question a

2y\frac{dy}{dt}=-2x\frac{dx}{dt}\\\\\frac{dy}{dt}=\frac{-2x\frac{dx}{dt}}{2y} \\\\\frac{dy}{dt}=-\frac{x}{y}\frac{dx}{dt}

Given that x = 3, y = 4, and dx/dt = 5.

\frac{dy}{dt}=-\frac{3}{4}*5=-\frac{15}{4}\\   \\\frac{dy}{dt}=-3\frac{3}{4}

For Question b

2x\frac{dx}{dt}=-2y\frac{dy}{dt}\\\\\frac{dx}{dt}=\frac{-2y\frac{dy}{dt}}{2x} \\\\\frac{dx}{dt}=-\frac{y}{x}\frac{dy}{dt}

Given that x = 4, y = 3, and dx/dt = -5.

\frac{dx}{dt}=-\frac{3}{4}*-5=\frac{15}{4}\\   \\\frac{dx}{dt}=3\frac{3}{4}

You might be interested in
What is 4× 10 in standard notation
riadik2000 [5.3K]
400000 10 to the fifth power is 100000, so when you switch out the 1 for a 4, it become 400000.
6 0
3 years ago
A probability experiment is conducted in which the sample space of the experiment is upper s equals startset 4 comma 5 comma 6 c
olchik [2.2K]
The correct question statement is:

A probability experiment is conducted in which the sample space of the experiment is S = {4,5,6,7,8,9,10,11,12,13,14,15}. Let event E={7,8,9,10,11,12,13,14,15}. Assume each outcome is equally likely. List the outcomes in E^{c}. Find P(E^{c}).

Solution:

Part 1:

E^{c} means compliment of the set E. A compliment of a set can be obtained by finding the difference of the set from the universal set. The universal set is the set which contains all the possible outcomes of the events which is S in this case.

So, compliment of E will be equal to S - E. S - E will result in all those elements of S which are not present in E. So, we can write:

E^{c}=S-E \\  \\ 
E^{c}=(4,5,6,7,8,9,10,11,12,13,14,15)-(7,8,9,10,11,12,13,14,15) \\  \\ 
E^{c}=(4,5,6)

Thus the set compliment of E will contain the elements {4,5,6}.So

E^{c} = {4,5,6}

Part 2)

P(E^{c}) means probability that if we select any number from the Sample Space S, it will belong the set E compliment.

P(E^{c}) = (Number of Elements in E^{c})/Number of elements in S

Number of elements in set S = n(S) = 12
Number of elements in set E^{c} = n(E^{c})=3

So, 

P(E^{c})= \frac{n(E^{c}) }{n(S)} \\  \\ 
P(E^{c})= \frac{3}{12} \\  \\ 
P(E^{c})= \frac{1}{4}
7 0
3 years ago
Daria's goal is to run 7 miles each weekend.she ran 3 and 1/3 mules on saturday and 3 and 3/4 on Sunday. by how much did she bea
oksano4ka [1.4K]
She beat her goal. her total was 7 miles and 1/12 as she ran .1 miles longer find the lcd of 4 and 3 wich is 12 and add the num. to get 13 and that simplifed is 1 1/12+6 which is 7.1 or
7 1/12 mules
5 0
3 years ago
X = mb + y <br><br> Is this written out in slope intercept form?
Anna [14]

Answer:

no

Step-by-step explanation:

y=mx+b

hope this helps

8 0
3 years ago
Read 2 more answers
What's is the converse of the statement?If x is odd, then 2x is even.
dsp73
If you have two statements p and q and p\Rightarrow q is true, then  \neg q\Rightarrow \neg p is also true.

In your case, statements are p - "x is odd" and q -  "2x is even".

 Then \neg p - "x is not odd" and \neg q - "2x is not even."


Hence \neg q\Rightarrow \neg p sounds as: "If 2x is not even, then x is not odd".
Answer: correct choice is D.







7 0
3 years ago
Other questions:
  • What is the fifth term of a sequence whose first term is 5 and whose common ratio is 3
    12·1 answer
  • Solve for u<br> -1/5 + 1/2 u = -2/3
    13·1 answer
  • 1 Find the equation of the axis of symmetry and the coordinates of the vertex of the
    8·1 answer
  • A photocopy machine can reduce copies to 80% of their original size. By copying an already reduced copy, further reductions can
    14·1 answer
  • What is the minimum number of degrees that a regular hexagon can be rotated before it carries onto itself?
    13·2 answers
  • The Questions above.
    8·1 answer
  • A piece of art weighing 30 pounds is hung from two wires as shown below. Each wire is supporting half of the weight of the pictu
    13·1 answer
  • Beth is putting liquid fertilizer on the plants in three flower pots her measuring Spoon holds 1/8 teaspoon the directions say t
    6·1 answer
  • Is -2 more than -1? or is it the other way around
    13·2 answers
  • Mabel is working with other students from her class on a project their teacher gave them. The project is to bake a cake that use
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!