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2 years ago

The 8th term of an arithmetic sequence is 12.5 and the 13th term is 20. What is the 25th term?

1 answer:

7 0

From the 8th to the 13th there are five numbers, and the difference between the 8th and the 13th is 20-12.5=7.5, so the difference between two neighboring number is 7.5÷5=1.5
from the 13th and the 25th there are 12 numbers, so the total difference is 12*1.5=18
so the 25th term is 20+18=38

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MARSVECTORCALC6 3.4.020. My Notes A rectangular box with no top is to have a surface area of 64 m2. Find the dimensions (in m) t

ioda

Answer:

We would have

$l =w =\frac{8\sqrt{3}}{3} \\h = \frac{8\sqrt{3}}{6}$

where " l " is length, " w" is width and "h" is height.

Step-by-step explanation:

Step 1

Remember that

Surface area for a box with no top = $lw+2lh+2wh = 64$

where " l " is length, " w" is width and "h" is height.

Step 2.

Remember as well that

Volume of the box = $l*w*h$

Step 3

We can now use lagrange multipliers. Lets say,

$F(l,w,h) = lwh$

and

$g(l,w,h) = lw+2lh+2wh = 64$

By the lagrange multipliers method we know that

$\nabla F = \lambda \nabla g$

Step 4

Remember that

$\nabla F = (wh,lh,lw)$

and

$\nabla g = (w+2h,l+2h , 2w+2l)$

So basically you will have the system of equations

$wh = \lambda (w+2h)\\lh = \lambda (l+2h)\\lw = \lambda (2w+2l)$

Now, remember that you can multiply the first eqation, by "l" the second equation by "w" and the third one by "h" and you would get

$lwh = l\lambda (w+2h)\\\\lwh = w\lambda (l+2h)\\\\lwh = h\lambda (2w+2l)$

Then you would get

$l\lambda (w+2h) = w\lambda (l+2h) = h\lambda (2w+2l)$

You can get rid of $\lambda$ from these equations and you would get

$lw+2lh = lw+2wh = 2wh+2lh$

And from those equations you would get

$l = w =2h$

Now remember the original equation

$lw+2lh+2wh = 64$

If we plug in what we just got, we would have

$l^{2} + l^{2} + l^2 = 64 \\3l^{2} = 64 \\l = w = \frac{8\sqrt{3} }{3} \\h = \frac{8\sqrt{3} }{6}$

7 0

3 years ago

PLEASE ANSWER IF YOU CAN Cameron did 4 jumping jacks on Wednesday, 9 jumping jacks on Thursday, 19 jumping jacks on Friday, and

Blizzard [7]

Answer:

My answer is 64

Step-by-step explanation:

How I got my answer is that you write the numbers and the difference of the each 2 numbers. When you see the pattern is 5, 10, 20, and it might as well be 25 because you are going to start all over with the pattern

6 0

2 years ago

Read 2 more answers

All of the following describes a balance sheet except which one

nikitadnepr [17]

What is the question here???

5 0

3 years ago

The figures shown are similar

Harlamova29_29 [7]

Hi there!

Based on your options, I think we're going from the big figure to the small figure. 12/8 = 1 1/2

ANSWER:
D - 1.5

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

8 0

3 years ago

1000 coins are tossed find the probability of getting exactly 500 heads.

ipn [44]

Answer:

probability of getting exactly 500 heads= 1

Step-by-step explanation:

If a coin is tossed, the probability of obtaining a head = 0.5

If a coin is tossed, the probability of obtaining a tail= 1- probability of obtaining a head

If a coin is tossed, the probability of obtaining a tail=1-0.5

If a coin is tossed, the probability of obtaining a tail=0.5

So if 1000 coin are tossed, the probability of getting exay 500 heads which is already the half of 1000 is 1

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3 years ago