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3 years ago

5

Find the volume of the pyramid. Round your answer to the nearest hundredth.

1 answer:

dybincka [34]3 years ago

8 0

I would say b hope this help ☺

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A teacher places n seats to form the back row of a classroom layout. Each successive row contains two fewer seats than the prece

Alex_Xolod [135]

Answer:

The number of seat when n is odd $S_n=\frac{n^2+2n+1}{4}$

The number of seat when n is even $S_n=\frac{n^2+2n}{4}$

Step-by-step explanation:

Given that, each successive row contains two fewer seats than the preceding row.

Formula:

The sum n terms of an A.P series is

$S_n=\frac{n}{2}[2a+(n-1)d]$

$=\frac{n}{2}[a+l]$

a = first term of the series.

d= common difference.

n= number of term

l= last term

$n^{th}$ term of a A.P series is

$T_n=a+(n-1)d$

n is odd:

n,n-2,n-4,........,5,3,1

Or we can write 1,3,5,.....,n-4,n-2,n

Here a= 1 and d = second term- first term = 3-1=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=1 and d=2

$n=1+(t-1)2$

⇒(t-1)2=n-1

$\Rightarrow t-1=\frac{n-1}{2}$

$\Rightarrow t = \frac{n-1}{2}+1$

$\Rightarrow t = \frac{n-1+2}{2}$

$\Rightarrow t = \frac{n+1}{2}$

Last term l= n,, the number of term $=\frac{ n+1}2$ , First term = 1

Total number of seat

$S_n=\frac{\frac{n+1}{2}}{2}[1+n}]$

$=\frac{{n+1}}{4}[1+n}]$

$=\frac{(1+n)^2}{4}$

$=\frac{n^2+2n+1}{4}$

n is even:

n,n-2,n-4,.......,4,2

Or we can write

2,4,.......,n-4,n-2,n

Here a= 2 and d = second term- first term = 4-2=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=2 and d=2

$n=2+(t-1)2$

⇒(t-1)2=n-2

$\Rightarrow t-1=\frac{n-2}{2}$

$\Rightarrow t = \frac{n-2}{2}+1$

$\Rightarrow t = \frac{n-2+2}{2}$

$\Rightarrow t = \frac{n}{2}$

Last term l= n, the number of term $=\frac n2$ , First term = 2

Total number of seat

$S_n=\frac{\frac{n}{2}}{2}[2+n}]$

$=\frac{{n}}{4}[2+n}]$

$=\frac{n(2+n)}{4}$

$=\frac{n^2+2n}{4}$

4 0

3 years ago

5(r-10)=-51 what is the value of r

raketka [301]

Use distributive method
5r - 50 = -51
Add 50
5r = -1
Divide by 5
r = -1/5

3 0

3 years ago

Read 2 more answers

2 planes left a airport at noon 1 flew east and the other flew west as twice the speed after 3 hours the planes were 2700 miles

const2013 [10]

Speed =distance ÷time
?=2700÷3
?=900 miles per hour

5 0

3 years ago

Read 2 more answers

Please help me ASAP thank you

DaniilM [7]

Answer:

x=17°

Step-by-step explanation:

163+x=180 (L.P)

x=180-163

x=17°

6 0

3 years ago

Martha Alison and Scott buy 3.8 pounds of clay Martha used 1 /4 of the clay for a sculpture Scott used 2/5 of the remaining amou

Sever21 [200]

They are left with 0.51 pounds of clay.

Step-by-step explanation:

Given,

Amount of clay bought = 3.8 pounds

Amount used by Martha = $\frac{1}{4}\ of\ clay$

Amount used by Martha = $\frac{1}{4}*3.8=0.95\ pounds$

Amount left after Martha's use= Total amount - amount used by Martha

Amount left = 3.8 - 0.95 = 2.85 pounds

Amount used by Scott = $\frac{2}{5}\ of\ amount\ left$

Amount used by Scott = $\frac{2}{5}*2.85=\frac{5.70}{5}$

Amount used by Scott = 1.14 pounds

Amount left after Scott's use = Amount left after Martha's - Amount used by Scott

Amount left after Scott's use = 2.85 - 1.14 = 1.71 pounds

Amount used by Alison = 1.2 pounds

Amount left = Amount left after Scott's use - Amount used by Alison

Amount left = 1.71 - 1.2 = 0.51 pounds

They are left with 0.51 pounds of clay.

Keywords: subtraction, fraction

Learn more about subtraction at:

#LearnwithBrainly

3 0

3 years ago