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zhannawk [14.2K]
3 years ago
5

Finding Derivatives Implicity In Exercise, find dy/dx implicity. x2 - 3 ln y + y2 = 10

Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
8 0

Answer:

\frac{dy}{dx}=-\frac{2xy}{2y^2-3}

Step-by-step explanation:

We are given that

x^2-3lny+y^2=0

Differentiate w.r.t x

2x-\frac{3}{y}\frac{dy}{dx}+2y\frac{dy}{dx}=0

By using formula

\frac{dx^n}{dx}=nx^{n-1}

\frac{d(lnx)}{dx}=\frac{1}{x}

\frac{dy^n}{dx}=ny^{n-1}\frac{dy}{dx}

\frac{dy}{dx}(-\frac{3}{y}+2y)+2x=0

\frac{dy}{dx}(-\frac{3}{y}+2y)=-2x

\frac{dy}{dx}=-\frac{2x}{-\frac{3}{y}+2y}

\frac{dy}{dx}=-\frac{2xy}{2y^2-3}

Hence, the derivative of function

\frac{dy}{dx}=-\frac{2xy}{2y^2-3}

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From a group of 21 astronauts that includes 12 people with previous experience in space flight, a 3-person crew is to be selecte
Vladimir79 [104]

Answer:

3

Step-by-step explanation:

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8 0
3 years ago
A student has four sticks of wood that measures 3 inches, 4 inches, 5 inches, and 6 inches.Can the student use any three of thes
saw5 [17]

Answer:

Yes, the student can use three of these sticks to make a right triangle.

Step-by-step explanation:

The measure of four sticks = 3 inches, 4 inches, 5 inches and 6 inches.

Now, in a right angled triangle, by PYTHAGORAS THEOREM the three sides of the triangle base, perpendicular and  hypotenuse are in the  given following relation :

(Base)^{2}  + (Perpendicular)^{2}   = (Hypotenuse)^{2}

Now, here among all four sticks

(3)^{2}  +(4)^{2}   = 9 + 16  = 25

and 25 = (5)^{2}

So, there exists three sticks of length 3 in, 4 in and 5 inches which satisft Pythagoras Theorem , such that:

(3)^{2}  + (4)^{2}   = (5)^{2}

So, the required length sticks are 3 inches, 4 inches and 5 inches.

Hence, the student use three of these sticks to make a right triangle.

5 0
3 years ago
5-9 please <br> Thanks for your time
o-na [289]
Five minus nine is negative four...
3 0
3 years ago
Read 2 more answers
Please help ASAP
Arisa [49]

Answer:

2 lessons per day for 27 days and 3 lessons a day for 4 days.

Step-by-step explanation:

66/31 = 2 4/31

Since 66 divided by 31 is 2 with remainder 4, you need to do 31 days of 2 lessons per day. To do the extra 4 lessons, do one more lesson per day for 4 of those days.

That results in:

2 lessons per day for 27 days and 3 lessons a day for 4 days.

Check:

2 lessons a day for 27 days = 2 * 27 = 54

3 lessons a day for 4 days = 3 * 4 = 12

54 + 12 = 66

If you do 2 lessons a day for 27 days and 3 lessons a day for 4 days, you will do the 66 lessons.

5 0
3 years ago
How to graph 200-25x=y
In-s [12.5K]
Simplifying
y = -25x + 200

Reorder the terms:
y = 200 + -25x

Solving
y = 200 + -25x

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Simplifying
y = 200 + -25x
4 0
3 years ago
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