$\frac{dy}{dx}=x^{2}(y-1)\\\frac{1}{y-1} \text{ } dy=x^{2} \text{ } dx\\\int \frac{1}{y-1} \text{ } dy=\int x^{2} \text{ } dx\\\ln|y-1|=\frac{x^{3}}{3}+C\\$

From the initial condition,

$\ln|3-1|=\frac{0^{3}}{3}+C\\\ln 2=C$

So we have that $\ln |y-1|=\frac{x^{3}}{3}+\ln 2\\e^{\frac{x^{3}}{3}+\ln 2}=y-1\\2e^{\frac{x^{3}}{3}}=y-1\\y=2e^{\frac{x^{3}}{3}}+1$

4 0

2 years ago

Which value of HNK are used to write the function f(x) = x2 + 12x + 6 in vertex form?

anygoal [31]

Answer:

( − 6 , − 30 )

Step-by-step explanation:

Rewrite in vertex form and use this form to find the vertex ( h , k ) .

6 0

3 years ago

In the multiplication sentence below, which number is the<br> product?<br> 7x9 = 63

grin007 [14]

Answer:

Step-by-step explanation:

plz brainliest :)

do you want an explanation?

4 0

2 years ago

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Please help due in 20 minutes!!

Nikitich [7]

Answer:

length is 15.5 and the width is 12.5

Step-by-step explanation:

Length rectangle = 3cm. longer than its width.

Rectangle perimeter = 56 cm.

find its dimensions?

P = 2L +2w

L= w + 3

P= 56

P = 2L +2w

56 = 2(w+3) +2(w)

56 = 2w +6 + 2w

4w= 56 - 6

4w = 50

w = 50/4

w = 12.5

L= 12.5 +3 = 15.5

L= 15.5

Solution:

Length= 15.5 cm

Width = 12.5 cm

i know it looks complex but i hope this helps :)

7 0

3 years ago

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