Given quadrilateral QRST - quadrilateral HIJK, QR = 10, QT = 6, and HI = 8, find KH.

Mathematics

2 answers:

Leto [7]2 years ago

5 0

Answer:

B. 24/5

Step-by-step explanation:

Hope this helps

Elis [28]2 years ago

3 0

Answer:

B. 24/5

Step-by-step explanation:

QR = 10

QT = 6

HI = 8

Quadrilateral QRST ~ quadrilateral HIJK, therefore, their corresponding side lengths would be proportional to each other.

This:

QR/HI = QT/HK

Plug in the values

10/8 = 6/HI

Cross multiply

10*HI = 8*6

10*HI = 48

Divide both sides by 10

HI = 48/10

HI = 24/5

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vlada-n [284]

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\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}\\\\
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\\\\\\
\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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