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3 years ago

ZABD and ZBDC are complementary. Find the measures of both angles. MZABD =(y - 30), mZBDC = 2yº

Mathematics

1 answer:

frez [133]3 years ago

5 0

9514 1404 393

Answer:

∠ABD = 10°
∠BDC = 80°

Step-by-step explanation:

The sum of complementary angles is 90°.

∠ABD +∠BDC = 90°

(y -30)° +(2y)° = 90°

3y = 120 . . . . . . . . . . . . divide by °, add 30

y = 40 . . . . . . . . . . . divide by 3

∠ABD = (40 -30)° = 10°

∠BDC = 2(40)° = 80°

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Read 2 more answers

For number 6, evaluate the definite integral.

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$\bf \displaystyle \int\limits_{0}^{28}\ \cfrac{1}{\sqrt[3]{(8+2x)^2}}\cdot dx\impliedby \textit{now, let's do some substitution}\\\\
-------------------------------\\\\
u=8+2x\implies \cfrac{du}{dx}=2\implies \cfrac{du}{2}=dx\\\\
-------------------------------\\\\$

$\bf \displaystyle \int\limits_{0}^{28}\ \cfrac{1}{\sqrt[3]{u^2}}\cdot \cfrac{du}{2}\implies \cfrac{1}{2}\int\limits_{0}^{28}\ u^{-\frac{2}{3}}\cdot du\impliedby 
\begin{array}{llll}
\textit{now let's change the bounds}\\
\textit{by using } u(x)
\end{array}\\\\
-------------------------------\\\\
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\\\\\\
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$\bf \\\\
-------------------------------\\\\
\displaystyle \cfrac{1}{2}\int\limits_{8}^{64}\ u^{-\frac{2}{3}}\cdot du\implies \cfrac{1}{2}\cdot \cfrac{u^{\frac{1}{3}}}{\frac{1}{3}}\implies \left. \cfrac{3\sqrt[3]{u}}{2} \right]_8^{64}
\\\\\\
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