What is the slope of the line passing through the points (1,−5) and (4,1)?

Mathematics

1 answer:

Assoli18 [71]3 years ago

8 0

Answer:

the slope is 2

Step-by-step explanation:

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Please help differentiate this!!!!!!!!!

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$\bf h=20ln(3t+2)+30\\\\
-------------------------------\\\\
\boxed{a}\\\\
\stackrel{0~years}{t=0}\qquad h=20ln[3(0)+2]+30\implies h=20ln(2)+30
\\\\\\
h\approx 43.86
\\\\\\
\boxed{b}\\\\
\stackrel{1~meter}{h=100}\qquad 100=20ln(3t+2)+30\implies 70=20ln(3t+2)
\\\\\\
\cfrac{70}{20}=ln(3t+2)\implies \stackrel{\textit{log cancellation rule}}{e^{\frac{7}{2}}=e^{ln(3t+2)}}\implies e^{\frac{7}{2}}=3t+2
\\\\\\
e^{\frac{7}{2}}-2=3t\implies \cfrac{e^{\frac{7}{2}}-2}{3}=t\implies 10.371817\approx t$

$\bf \boxed{c}\\\\
\cfrac{dh}{dt}=20\left(\cfrac{1}{3t+2}\cdot 3 \right)+0\implies \cfrac{dh}{dt}=20\left(\cfrac{3}{3t+2} \right)\\\\\\ \cfrac{dh}{dt}=\cfrac{60}{3t+2}
\\\\\\
\left. \cfrac{dh}{dt} \right|_{3}\implies \cfrac{60}{3(3)+2}\implies \cfrac{60}{11}
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\left. \cfrac{dh}{dt} \right|_{10}\implies \cfrac{60}{3(10)+2}\implies \cfrac{15}{8}$

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