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Sunny_sXe [5.5K]
3 years ago
14

To the nearest whole degree ,what angle measure has a tangent of 8.9352

Mathematics
1 answer:
denis23 [38]3 years ago
5 0
The answer to the nearest whole degree is 84 degrees.
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The variable a  cannot be zero because that would make -9a = zero  and   8 divided by zero is indeterminate.
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If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs do not classify the relationship as a function.

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

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