A cylinder has a volume of 320n cubic inches and a height of 5 inches.

Find the 59th term of the following arithmetic sequence. 15, 23, 31, 39

m_a_m_a [10]

$15~~,~~\stackrel{15+8}{23}~~,~~\stackrel{23+8}{31}~~,~~\stackrel{31+8}{39}~~,~~...~\hspace{10em}\stackrel{common~difference}{d=8} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\stackrel{\textit{term position}}{59}\\ a_1=\stackrel{\textit{first term}}{15}\\ d=\stackrel{\textit{common difference}}{8} \end{cases} \\\\\\ a_{59}=15+(59-1)8\implies a_{59}=15+472-8\implies a_{59}=479$

4 0

3 years ago

A particle is moving on a straight line in such a way that its velocity v is given by v ( t ) = 2 t + 1 for 0 ≤ t ≤ 5 where t is

Lady_Fox [76]

Answer:

The total distance traveled by the particle is S = 30.

Step-by-step explanation:

Given that velocity,

v(t) = 2t + 1

To find the total distance travel, we integrate the velocity function, v(t), to obtain the distance function s(t), and evaluate the resulting distance at the interval given. That is at t = 0 to t = 5.

Integrating v(t) with respect to t, we have

s(t) = t² + t + C.

At t = 5

s(5) = 5² + 5 + C

= 25 + 5 + C

= 30 + C

At t = 0

S(0) = 0 + 0 + C

= C

The required distance is now

S(5) - S(0)

= 30 + C - C

= 30.

8 0

3 years ago

Read 2 more answers

Help fast!!!!!!!!!!!!!

miv72 [106K]

Answer:

Refer the photos above and have a good day

4 0

2 years ago

Find the value of x. a.17 b.12 c.40 d.18 e.none are correct

Natali5045456 [20]

Answer:

b.12

Step-by-step explanation:

Key skills needed: Interior Angle Measure Theorem, Equation Creation

1) First, we need to classify this shape. It has 7 sides, which means that we can use the Interior angle Theorem to find out the sum of all the interior angle measures

The theorem is: $S = (n - 2)180$