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
Viktor [21]
1 year ago
12

Suppose that the derivable functions x=x(t) and y=y(t) satisfy xcosy=2.

Mathematics
1 answer:
ololo11 [35]1 year ago
4 0

Applying implicit differentiation, it is found that dy/dt when y=π/4 is of:

a-) -√2 / 2.

<h3>What is implicit differentiation?</h3>

Implicit differentiation is when we find the derivative of a function relative to a variable that is not in the definition of the function.

In this problem, the function is:

xcos(y) = 2.

The derivative is relative to t, applying the product rule, as follows:

\cos{y}\frac{dx}{dt} - x\sin{y}\frac{dy}{dt} = 0

\frac{dy}{dt} = \frac{\cos{y}\frac{dx}{dt}}{x\sin{y}}

Since dx/dt=−2, we have that:

\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}

When y = π/4, x is given by:

xcos(y) = 2.

x = \frac{2}{\cos{\frac{\pi}{4}}} = \frac{2}{\frac{\sqrt{2}}{2}} = \frac{4}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = 2\sqrt{2}

Hence:

\frac{dy}{dt} = -2\frac{\cos{y}}{x\sin{y}}

\frac{dy}{dt} = -\frac{1}{\sqrt{2}}\cot{y}

Since cot(pi/4) = 1, we have that:

\frac{dy}{dt} = -\frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = -\frac{\sqrt{2}}{2}

Which means that option a is correct.

More can be learned about implicit differentiation at brainly.com/question/25608353

#SPJ1

You might be interested in
ΔABC will undergo two transformations to give ΔA′B′C′. Which pair of transformations will give a different image of ΔABC if the
Marta_Voda [28]
<span>a rotation 90° counterclockwise about the origin followed by a reflection across the y-axis</span>
4 0
3 years ago
Copies of a famous painting were created at the local art museum for visitors to purchase. The copies had a 20% smaller area tha
oee [108]
Original painting was 39 ft²
(1.00-.2)39=39(.8)=31.2 ft²
☺☺☺☺
4 0
3 years ago
Please help me I'll give you a brainliest
astraxan [27]
Okay try to round the whole number and see if you can solve that should help you
7 0
2 years ago
Which of the following are prime factors of both 24 and 42? Select all that apply.
BlackZzzverrR [31]

Answer:

2 and 3

Step-by-step explanation:

So, 24=2x2x2x3

42=2x3x7

3 and 2

4 0
2 years ago
Read 2 more answers
Let x and y be inversely related. if x is 5 when y is 6, find y when x is 3​
VLD [36.1K]

Answer:

when its to the left

Step-by-step explanation:

5 0
2 years ago
Other questions:
  • I need help on question 2 and 3
    11·1 answer
  • I need help again. once again due TM helppp
    6·2 answers
  • Use long division to find the quotient below. (x2 + x – 20) ÷ (x – 4)
    11·1 answer
  • • Clare mixes 2 cups of water with
    13·2 answers
  • If the graph of f(x) is:<br><br><br><br> Which of the following is the graph of −f(−x)?
    10·1 answer
  • A plumber had two pipes. The ratio of the length of the longer pipe to the
    13·1 answer
  • What is the equation for this graph pls help me and pls make sure it’s right:))
    12·2 answers
  • What is the equation for the line shown on this graph?
    12·1 answer
  • Last week Fred had
    9·2 answers
  • 7. Three vertices of a parallelogram are (0, 0), (−4,0) and (0, 5). Find all 3 possible coordinates for
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!