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3 years ago

Find the sum of the first 35 terms of the following series, to the nearest integer. 3, 11, 19...

Mathematics

1 answer:

Tems11 [23]3 years ago

4 0

<h3>Answer: 4865</h3>

=======================================================

Explanation:

The sequence {3,11,19,...} is arithmetic since we are adding 8 to each term to get the next one

3+8 = 11
11+8 = 19

etc. This means the common difference is d = 8.

The first term is a = 3

Let's use this formula

S = n*(2*a + d(n - 1) )/2

so we can find the sum of the first n terms. In this case, n = 35

So,

S = n*(2*a + d(n - 1) )/2

S = 35*(2*3 + 8(35 - 1) )/2

S = 35*(6 + 8(34))/2

S = 35*(6 + 272)/2

S = 35*(278)/2

S = 35*139

S = 4865

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During a bike challenge riders have to collect various colored ribbons each half mile they collect a red ribbon each 8th mile th

soldi70 [24.7K]

Answer:

Green and Blue ribbon

Step-by-step explanation:

Given

They collect

Red Ribbon = ½ mile

Green Ribbon = ⅛ mile

Blue Ribbon = ¼ mile

To find?

Which colors of ribbons will be collected at the ¾ mile mark.

The interpretation of the question is to test which of the above fractions can divide ¾ without a remainder; in other words, multiples of ¾.

Testing each fraction.

Red Ribbon = ½

¾ ÷ ½

= ¾ * 2

= 3/2

= 1.5 or 1 Remainder 1

This is not an exact multiple of ¾. So, the red ribbon won't be passed here.

Green Ribbon = ⅛

¾ ÷ ⅛

= ¾ * 8

= 24/8

= 3

This is an exact multiple of ¾. So, the green ribbon will be collected.

Testing the last ribbon

Blue = ¼

¾ ÷ ¼

= ¾ * 4

= 3

This is an exact multiple of ¾. So, the blue ribbon will be collected.

Hence, the green and blue ribbons will be collected at ¾ mile mark

3 0

3 years ago

Find The art length of a sector with an area of 8 square units.

frez [133]

$\bf \textit{area of a sector of a circle}\\\\
A=\cfrac{\theta \pi r^2}{360}\quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
A=8\\
r=4
\end{cases}\implies 8=\cfrac{\theta \pi 4^2}{360}\implies \cfrac{8\cdot 360}{4^2\pi }=\theta 
\\\\\\
\cfrac{2880}{16\pi }=\theta \implies \boxed{\cfrac{180}{\pi }=\theta }\\\\
-------------------------------\\\\$

$\bf \textit{arc's length}\\\\
s=\cfrac{\theta \pi r}{180}\quad 
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
\theta =\frac{180}{\pi }\\
r=4
\end{cases}\implies s=\cfrac{\frac{180}{\underline{\pi} }\underline{\pi} \cdot 4}{180}\implies s=\cfrac{\underline{180}\cdot 4}{\underline{180}}
\\\\\\
\boxed{s=4}$

if you do a quick calculation on what that angle is, you'll notice that it is exactly 1 radian, and an angle of 1 radian, has an arc that is the same length as its radius.

that's pretty much what one-radian stands for, an angle, whose arc is the same length as its radius.

6 0

3 years ago

Half a number plus 2.5 times that number equals 18. What is the number?

Sholpan [36]

Answer:

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Step-by-step explanation:

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