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Katarina [22]
3 years ago
9

For the equation given below, evaluate y′ at the point (−2,2) xe^y−4y=2x−4−2e^2

Mathematics
1 answer:
jeka943 years ago
3 0
Implicit differentiation
chain rule is important here

I'll show the steps partially
e^y+xe^yy'-4y'=2
xe^yy'-4y'=2-e^y
y'(xe^y-4)=2-e^y
y'=\dfrac{2-e^y}{xe^y-4}
now evaluate for (-2,2)
x=-2 and y=2
y'=\dfrac{2-e^2}{-2e^2-4}
y'=\dfrac{2-e^2}{-2e^2-4}
y'=\dfrac{e^2-2}{2e^2+4}
that's it, simplest form
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kvv77 [185]

Answer:

120

Step-by-step explanation:

5 0
3 years ago
Determine whether or not 630 is a triangular number. start with the formula t n = n ( n + 1 ) 2 and then use the quadratic formu
ziro4ka [17]
Triangular sequence = n(n + 1)/2

If 630 is a triangular number, then:

n(n + 1)/2  = 630

Then n should be a positive whole number if 630 is a triangular number.

n(n + 1)/2  = 630

n(n + 1)  = 2*630

n(n + 1)  = 1260

n² + n = 1260

n² + n - 1260 = 0

By trial an error note that 1260 = 35 * 36

n² + n - 1260 = 0

Replace n with 36n - 35n

n² + 36n - 35n - 1260 = 0

n(n + 36) - 35(n + 36) = 0

(n + 36)(n - 35) = 0

n + 36 = 0   or   n - 35 = 0

n = 0 - 36,   or  n = 0 + 35

n = -36, or 35

n can not be negative. 

n = 35 is valid.

Since n is a positive whole number, that means 630 is a triangular number.

So the answer is True.
7 0
3 years ago
PLEASE HELP ME FAST!!!! ( It's about y-intercept)
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Step-by-step explanation:

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2. Given that the slope is 6, we plug that value in m, and given that the y-intercept is -7, we plug that value in b:

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algol [13]

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Step-by-step explanation:

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Zinaida [17]
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