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NARA [144]
3 years ago
11

Consider the curve x+xy+2y^2=6. the slope of the line tangent to the curve at the point (2,1) is?

Mathematics
2 answers:
oksian1 [2.3K]3 years ago
7 0
<span>The derivative of your function is:  
1 + (1*dy/dx + y) - 4y(dy/dx) = 0
2 + dy/dx + y - 4y(dy/dx) = 0
(2 + y) + dy/dx (1 - 4y) = 0
(dy/dx) = -(2 + y)/(1 - 4y)
 
and at point (2,1),
dy/dx = -(2 + 1)/(1 - 4*1)
          = -3 / -3
          = 1
 
Slope of tangent line = 1</span>
viktelen [127]3 years ago
5 0
The derivative is actually (-y-1)/(4y+x)
then you plug in the points (2,1) ==>
(-1-1)/(4*1+2) which equals -1/3
then you just plug in your info into a point-slope formula and get:
y-1=-1/3(x-2) which can then be reduced
You might be interested in
Factor this polynomial completely x2 + 3x – 18 A. (x-2)(x + 9) B. (x+3)(x-6) оо C. (x - 3)(x+6) D. (x - 3)(x-6)​
Umnica [9.8K]

Answer:

C. (x-3)(x+6)

Step-by-step explanation:

I think the equation meant x^2+3x-18?

Anyways, to factor these kinds of quadratic, keep into consideration:

ax^2+bx+c=(x+w)(x+v)

ONLY if:

w+v=b\\wv=c

Start off by finding factors of c, which in this case, -18:

±(1, 2, 3, 6, 9, 18)

If one of the numbers is negative then the other number must be positive.

Find which two factors will sum up to b, which in this case, is 3.

1+(-18)\neq 3\\2+(-9)\neq 3\\3+(-6)\neq 3\\6+(-3)=3\\9+(-2)\neq 3\\18+(-1)\neq 3\\

The only two factors that work are 6 and -3.

Replace them into the factored form:

(x+w)(x+v)\\(x+6)(x-3)\\(x-3)(x+6)

3 0
2 years ago
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lesya [120]
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Alina [70]
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miv72 [106K]
Slope = ⅓
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How is the expression (5 + y) ⋅8 described by its factors and terms?
ICE Princess25 [194]
Answer: Choice D
It has two factors and the factor (5+y) has two terms

=========================================================
Explanation:

(5+y)*8 is in the form P*Q where
P = 5+y
Q = 8
So we have two factors multiplied together. A factor is simply a number that helps multiply to a larger one. Another example: 14 has the factors 7 and 2 because 7*2 = 14

The factor 5+y has two terms which are 5 and y. The terms are separated by a plus sign. If you had something like 5-y, then you can write it as 5+(-y) and you'd still have two terms.
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3 years ago
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