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Tanzania [10]
3 years ago
5

Find the equation of the tangent of x^2- xy + y^2 =7 at (-1, 2)

Mathematics
2 answers:
Citrus2011 [14]3 years ago
8 0

Answer:

<u>It</u><u> </u><u>is</u><u> </u><u>3</u><u>y</u><u> </u><u>=</u><u> </u><u>4</u><u>x</u><u> </u><u>+</u><u> </u><u>1</u><u>0</u>

Step-by-step explanation:

Let's first get the slope of the curve.

[ slope is the derivative of the equation ]

{x}^{2}  - xy +  {y}^{2}  = 7

introduce dy/dx :

\frac{d}{dx} ( {x}^{2}  - xy +  {y}^{2} ) =  \frac{d}{dx} (7) \\  \\ 2x - (y +  \frac{dy}{dx} ) + 2y \frac{dy}{dx}  = 0

make dy/dx the subject:

2x - y -  \frac{dy}{dx}  + 2y \frac{dy}{dx}  = 0 \\  \\ 2y \frac{dy}{dx}  -  \frac{dy}{dx}  = y - 2x \\  \\  \frac{dy}{dx} (2y - 1) = y - 2x \\  \\  \frac{dy}{dx}  =  \frac{y - 2x}{2y - 1}

At point (-1, 2):

\frac{dy}{dx}  =  \frac{2 - 2( - 1)}{2(2) - 1}  \\  \\ slope =  \frac{4}{3}

but a tangent has the same slope as the curve:

y = mx + c

m is the slope

c is the y-intercept

At (-1, 2):

2 = ( - 1 \times  \frac{4}{3} ) + c \\  \\ c = 2 +  \frac{4}{3}  \\  \\ c =  \frac{10}{3}

equation:

y =  \frac{4}{3} x +  \frac{10}{3}  \\  \\ { \boxed{3y = 4x + 10}}

dsp733 years ago
4 0

Answer:

Step-by-step explanation:

Here is an other way:

z=f(x,y)=x²-xy+y²-7=0

\dfrac{\partial f(x,y)}{\partial x} =2x-y\\\\\dfrac{\partial f(x,y)}{\partial y} =-x+2y\\\\\\\dfrac{dy}{dx} =-\dfrac{\dfrac{\partial f(x,y)}{\partial x} }{\dfrac{\partial f(x,y)}{\partial y}} =-\dfrac{2x-y}{-x+2y} \\\\(-1;2)\\Slope=-\dfrac{2*(-1)-2}{1+2*2} =\dfrac{4}{5} \\\\y-2=\frac{4}{5} (x+1)\\\\\\\boxed{y=\dfrac{4x}{5} +\dfrac{14}{5} }

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3 years ago
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Find all solutions for a triangle with C=17deg, a=10, c=11. Round to the nearest tenth
ExtremeBDS [4]

Answer: Angle A = 15.42°, angle B = 147.58°, and side b = 20.17 units.

Step-by-step explanation: Please refer to the attached diagram for details.

A triangle with angles ABC has been sketched from the information given, and we have the missing dimensions as, angles A and B and side b. Since we have an angle with a corresponding side, and another side has been given, we shall apply the Sine Rule which states that;

a/SinA = b/SinB = c/SinC

We can start with the known values as follows

a/SinA = c/SinC

10/SinA = 11/Sin 17

By cross multiplication we now have

(10 x Sin 17)/11 = SinA

(10 x 0.2924)/11 = SinA

2.924/11 = SinA

0.2658 = SinA

By use of calculator or a table of values,

A = 15.42°

Having calculated angle A as 15.42 and having known angle C as 17, angle B can be derived as,

A + B + C = 180° {Sum of angles in a triangle equals 180}

15.42 + B + 17 = 180

32.42 + B = 180

Subtract 32.42 from both sides of the equation

B = 147.58°

And now to calculate the missing side c, we still apply the Sine Rule

b/SinB = c/SinC

b = (c x SinB)/SinC

b = (11 x 0.5361)/0.2924

b = 5.8971/0.2924

b = 20.168

Approximately, b = 20.17

Therefore, the missing angles and side is calculated as

Angle A = 15.42°, angle B = 147.58° and length of side b = 20.17 units

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3 years ago
How can you break a table into two part
AveGali [126]
With a saw?





explanation:
6 0
3 years ago
If cos=3/5, then tan=
Juliette [100K]
This is a 3-4-5 triangle.

Remember, 
SOH-CAH-TOA

S(ine) =  O(pposite)/H(ypotenuse)
C(osine) = A(djacent)/H(ypotenuse)
T(angent) = O(pposite)/A(djacent)

In Cosine, the adjacent = 3, and the Hypotenuse = 5

Hypotenuse is the longest side. 

3,4,5 is the triangle that fits inside, therefore, the Opposite is 4, and Adjacent is 3

T(angent) = O(pposite)/A(djacent)

Plug in the numbers

T = 4/3

tan = 4/3 is your answer

hope this helps
6 0
3 years ago
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