4 years ago

Find the surface area of a rectangular prism that is 16inches long, 12inches wide, and 5 inches high

Mathematics

2 answers:

8090 [49]4 years ago

3 0

664 is the answer to this problem

defon4 years ago

3 0

664 is the answer that you need

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The sum of 30 times (1/3)^(n-1) from 1 to infinity

sergeinik [125]

Let

$S_n=\displaystyle1+\frac13+\frac1{3^2}+\cdots+\frac1{3^n}$

Then

$\dfrac13S_n=\displaystyle\frac13+\frac1{3^2}+\frac1{3^3}+\cdots+\frac1{3^{n+1}}$

and

$S_n-\dfrac13S_n=\dfrac23S_n=1-\dfrac1{3^{n+1}}\implies S_n=\dfrac32-\dfrac1{2\cdot3^n}$

and as $n\to\infty$ , we end up with

$\displaystyle\lim_{n\to\infty}S_n=\lim_{n\to\infty}\sum_{i=1}^{n+1}\frac1{3^{i-1}}=\lim_{n\to\infty}\left(\frac32-\frac1{2\cdot3^n}\right)=\frac32$

So we have

$\displaystyle\sum_{n=1}^\infty30\left(\frac13\right)^{n-1}=30\cdot\frac32=45$

8 0

3 years ago

Which civilization was known to use geometry to construct canals for the transportation of water?

Alina [70]

The correct answer should be D. Babylonians.

6 0

3 years ago

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The value of the x-intercept for the graph of 4x-5y=40 is

Alik [6]

$\hbox{x-intercept - y=0}: \\
4x-5 \times 0=40 \\
4x=40 \\
x=\frac{40}{4} \\
\boxed{x=10}$

8 0

3 years ago

Solve for p.<br><br> 12p − 9p − –7p − 8 = –18

Zielflug [23.3K]

Answer:

p=-1

Step-by-step explanation:

12p - 9p --7p -8 =-18

19p-9p-8=-18

10p - 8 = -18

10p = -10

p=-1

5 0

3 years ago

Find the nth term of each of the sequences.<br> (a) 16, 19, 22, 25, 28, ...<br> (b) 1,3,9,27,81,...

juin [17]

Answer:

a) 16, 19, 22, 25, 28, 31, 34, 37, 40

b) 1, 3, 9, 27, 81, 243, 729, 2187

<h3>Explanation:</h3>

a) Add 3 on every number.

b) Multiply every number by 3.

6 0

3 years ago