$\frac{dN}{dt}=k(725-N)\\separating the variables and integrating\\\int \frac{dN}{725-N}=\int kdt+c\\-log (725-N)=kt+c\\log (725-N)=-kt-c\\(725-N)=e^{-kt-c} =e^{-kt} *e^{-c} =Ce^{-kt} \\when t=0,N=400\\725-400=Ce^{0} =C\\C=325\\when t=3,N=650\\725-650=325e^{-3k} \\\frac{75}{325}=(e^{-k})^3\\\\e^{-k} =(\frac{3}{13}) ^{\frac{1}{3} } \\when t=5\\725-N=325(\frac{3}{13}) ^{\frac{5}{3} } =325*\frac{3}{13}*(\frac{3}{13} )^{\frac{2}{3}}\\N=725-75*(\frac{3}{13} )^{\frac{2}{3} }=725-28=697$

Step-by-step explanation:

6 0

3 years ago

Use the net to find the surface area of the rectangular prism. A) 48 cm2 B) 120 cm2 C) 384 cm2 D) 432 cm2

Marina86 [1]

Formula: length · width

2 big rectangles:96 + 96 = 192
(12 × 8) · 2

2 smaller rectangles: 72 + 72 = 144
(6 × 12) · 2

2 small rectangles: 48 + 48 = 96
(6 × 8) · 2

Add all 3 numbers:

192 + 144 + 96 = 432

Your answer is D. 432 cm²

Hope this helps :)

6 0

3 years ago