3 years ago

Through: (4, 3), perp. to y = 2x + 3 write the equation please

1 answer:

8 0

Because it’s perpendicular, the slope must be -1/2, which is the opposite of 2. You can put the points into y-3=-1/2(x-4) and simplify if need be.

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Easy question

Leviafan [203]

$\dfrac{\mathrm dy}{\mathrm dt}=ky\iff\dfrac{\mathrm dy}y=k\,\mathrm dt$

Integrating both sides, we get

$\ln|y|=kt+C$
$\implies y=e^{kt+C}=e^{kt}e^C=Ce^{kt}$

When $t=0$ , we have $y=10000$ , so that

$10000=Ce^{0k}\implies C=10000$

When $t=4$ , we have $y=8000$ , which means

$8000=10000e^{4k}\implies k=\dfrac14\ln\dfrac{8000}{10000}\approx-0.0558$