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lara [203]
3 years ago
11

A muffin recipe calls for 2/5 tablespoons of vanilla extract for 6 muffins. Arthur is making 18 muffins. How much vanilla extrac

t does he need?
Mathematics
1 answer:
Black_prince [1.1K]3 years ago
7 0
6/5, or 1 and 1/5. Since 6 goes into 18, 3 times, you must multiply 2/5 and 3/1.

<u>2</u>  x  <u>3</u>  =  <u>6</u>
5  x  1  =  5
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Let f be defined by the function f(x) = 1/(x^2+9)
riadik2000 [5.3K]

(a)

\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}

Substitute <em>x</em> = 3 tan(<em>t</em> ) and d<em>x</em> = 3 sec²(<em>t </em>) d<em>t</em> :

\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt

=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}

(b) The series

\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}

converges by comparison to the convergent <em>p</em>-series,

\displaystyle\sum_{n=3}^\infty\frac1{n^2}

(c) The series

\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}

converges absolutely, since

\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}

That is, ∑ (-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ converges absolutely because ∑ |(-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ| = ∑ (<em>n</em> ² + 9)/<em>e</em>ⁿ in turn converges by comparison to a geometric series.

5 0
3 years ago
To make grape juice, water is added to a large cylindrical vat of grapes. If the diameter of the vat is 16 feet, what is the are
amid [387]

Answer:

200.96cm^2 base area

Step-by-step explanation:

Eq of circle area  = πr^2

= 3.14 x 8^2

  3.14 x 64

  200.96cm^2

 

.

5 0
3 years ago
Suppose a club publishes a newsletter. Expenses are$.50 for printing and mailing each copy, plus$300 total for research and writ
luda_lava [24]

200 copies must be  sold

n= number od newsletters

0,50*n+300=2,00*n

300=1,5*n

Divide both sides by 1,5

200=n

0,50*200+300=2*200

100+300=400

400=400



5 0
3 years ago
Read 2 more answers
Find 4 + (-1 2/3)and write the answer in its simplest form
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11/3


Mark brainliest please


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C is the least that is beause it is .015  which is smaller than 0.15
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