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3 years ago

10

Jenny predicted that she would sell 12 bracelets, but she actually sold 16 bracelets. Which expression would find the percent er

ror? Use the table below to help answer the question

1 answer:

lawyer [7]3 years ago

7 0

Answer:

Start Fraction 4 over 16 End Fraction (100)

Step-by-step explanation:

Your Welcome;)

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Use trigonometric substitution to evaluate the integral 13 + 12x − x2 dx . First, write the expression under the radical in an a

SCORPION-xisa [38]

I don't see a square root sign anywhere, so I'll assume the integral is

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx$

First complete the square:

$13+12x-x^2=49-(6-x)^2=7^2-(6-x)^2$

Now in the integral, substitute

$6-x=7\sin t\implies\mathrm dx=-7\cos t\,\mathrm dt$

so that

$t=\sin^{-1}\left(\dfrac{6-x}7\right)$

Under this change of variables, we have

$7^2-(6-x)^2=7^2-7^2\sin^2t=7^2(1-\sin^2t)=7^2\cos^2t$

so that

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx=-7\int\sqrt{7^2\cos^2t}\,\cos t\,\mathrm dt=-49\int|\cos t|\cos t\,\mathrm dt$

Under the right conditions, namely that cos(<em>t</em>) > 0, we can further reduce the integrand to

$|\cos t|\cos t=\cos^2t=\dfrac{1+\cos(2t)}2$

$\displaystyle-49\int|\cos t|\cos t\,\mathrm dt=-\frac{49}2\int(1+\cos(2t))\,\mathrm dt=-\frac{49}2\left(t+\frac12\sin(2t)\right)+C$

Expand the sine term as

$\dfrac12\sin(2t)}=\sin t\cos t$

Then

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \sin t=\dfrac{6-x}7$

$t=\sin^{-1}\left(\dfrac{6-x}7\right)\implies \cos t=\sqrt{7^2-(6-x)^2}=\sqrt{13+12x-x^2}$

So the integral is

$\displaystyle-\frac{49}2\left(\sin^{-1}\left(\dfrac{6-x}7\right)+\dfrac{6-x}7\sqrt{13+12x-x^2}\right)+C$

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3 years ago

Joe has 4/5 as much money as bob. Tim has $50 more than joe. Rita has $150, which is $35 more than bob. How much money does tim

lesantik [10]

Rita = $150

Bob = $150 - $35 = $115 Bob has $115

Joe = $115 divided by 5 = $23 $23 x 4 = $92 Joe Has $92

Tim = Has $50 more then joe, $92 + $50 = $142 Tim has $142

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3 years ago

There are 45 M&Ms in a standard size bag. At 360 calories per bag,

Artyom0805 [142]

Answer:

about 8 calories per M&M

Step-by-step explanation:

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2 years ago

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Shtirlitz [24]

Answer:

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3 years ago

Kathi's order at the diner cost $12.75. She had<br> to pay 6% tax on the bill. How much is her tax?

Talja [164]

$\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 12.75}}{\left( \cfrac{6}{100} \right)12.75}\implies 0.765~~\approx 0.77~~\textit{about 77 cents}$

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2 years ago