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Elan Coil [88]
2 years ago
15

Water covers approximately 11,800 mi- of

Mathematics
1 answer:
babymother [125]2 years ago
7 0

0.18x = 11,800

x = 11,800/0.18

x = 65,555.56 = 66,000 square miles

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I need help with #61 to #64 ASAP please and thank you …. Could someone please help me with it… I need to get it done ASAP
aivan3 [116]

Problem 61

The nth triangular number is

T(n) = n(n+1)/2

I'll rewrite this into

T(n) = 0.5n(n+1)

The triangular number right after this is

T(n+1) = 0.5(n+1)(n+2)

I replaced every n with n+1 and simplified

Let's see what we get when we add up the two expressions

T(n) + T(n+1)

0.5n(n+1) + 0.5(n+1)(n+2)

0.5n^2+0.5n + 0.5(n^2+3n+2)

0.5n^2 + 0.5n + 0.5n^2 + 1.5n + 1

n^2+2n+1

(n+1)^2

This shows that the sum of any two consecutive triangular numbers results in a square number

Here's a few examples

  • 0+1 = 1
  • 1+3 = 4
  • 3+6 = 9
  • 6+10 = 16
  • 10+15 = 25

Note each sum is a perfect square, which visually would plot out a square figure.

For quick reference, the set of the first few triangular numbers is {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,...}

<h3>Answer: Square number</h3>

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

Problem 64

Let's say we go with n = 5.

This means,

T(n) = 0.5n(n+1)

T(n-1) = 0.5(n-1)(n-1+1)

T(n-1) = 0.5n(n-1)

T(5-1) = 0.5*5(5-1)

T(4) = 10

This says that when n = 5, the 4th triangular number is 10

Triple that result and add on n = 5

3*T(4) + n = 3*10+5 = 35

This result is beyond obvious which category of figurate number it belongs to. It's not a triangular number since it's not in the form n(n+1)/2. It's not a square number either.

Through a bit of trial and error, you should find it's a pentagonal number

Pentagonal numbers are of the form n(3n-1)/2

If you plugged n = 5 into that, it leads to 35

n(3n-1)/2 = 5*(3*5-1)/2 = 5*14/2 = 70/2 = 35

The diagram shown below represents the first few pentagonal numbers. The number of blue dots corresponds to the pentagonal number itself. Note the equal spacing when dealing with dots on each segment (eg: some interior blue dots are midpoints, others are quarter points, etc.)

<h3>Answer: Pentagonal number</h3>

8 0
2 years ago
Which is the largest interval over which the function shown in the table is decreasing
jeka57 [31]
Okay the answer is b
8 0
3 years ago
Jessica drew a circle divided into 8 equal parts. She shaded 6 of the parts. What fraction is equivalent to the part of the circ
barxatty [35]
The colored 6 out of 8 or 6/8, which can be simplified as 3/4!

Hope this helps!
5 0
3 years ago
Read 2 more answers
Given that log3(z - 1) - logz z = 1+ 3 log3 y, express z in terms of y.
fgiga [73]

Answer:

  z = 1 + 9y³

Step-by-step explanation:

It looks like you have ...

  \log_3{(z-1)}-\log_z{(z)}=1+3\log_3{(y)}\\\\\log_3{(z-1)}-1=1+\log_3{(y^3)}\\\\\log_3{(z-1)}=2+\log_3{(y^3)}\qquad\text{add 1}\\\\z-1=(3^2)(y^3)\qquad\text{take antilog}\\\\\boxed{z=1+9y^3}\qquad\text{add 1}

6 0
3 years ago
Yuan needs to take a taxi to get to the movies. The taxi charges $4.00 for the first mile, and then $2.75 for each mile after th
Murrr4er [49]
Well okay so $19.13 - $4.00 = $15.13  $15.13 / $2.75 = 5.50181818 so that is 5.5 the 5.5 + 1 = 6.5  


THE ANSWER IS 6.5 MILES
8 0
3 years ago
Read 2 more answers
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