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Vikki [24]
2 years ago
11

3. Jalen is a lifeguard at a public swimming pool and is planning to string

Mathematics
1 answer:
m_a_m_a [10]2 years ago
7 0

Answer:

Flag = 55.90m

Step-by-step explanation:

Given

Length = 50m

Width = 25m

Required

Determine the length of the flag

Because the flag crosses through opposite diagonals of the pool. Its length is the length of the diagonal of the pool.

This is calculated using Pythagoras theorem.

Flag^2 = Length^2 + Width^2

Substitute values for Length and Width

Flag^2 = 50^2 + 25^2

Flag^2 = 2500 + 625

Flag^2 = 3125

Take positive square root of both sides

Flag = \sqrt{3125

Flag = 55.90m

<em>Hence, the length of the flag is approximately 55.90m</em>

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The first three terms of an arithmetic progression are m,12 and n . Find the value of m+n​
Vera_Pavlovna [14]
<h3>Answer:  24</h3>

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

Explanation:

There are a few approaches. Here's one way to solve.

Let d be the common difference between the terms.

We add d to each term of this arithmetic sequence to get the next term.

  • First term = m
  • Second term = 12 = m+d
  • Third term = n = (m+d)+d = m+2d

Focusing on the second equation, we can solve for d like so

m+d = 12

d = 12-m

This is then plugged into the third equation

n = m+2d

n = m+2(12-m)

n = m+24-2m

n = 24-m

Therefore,

m+n = m+(24-m) = 24

It turns out that it doesn't matter what m and n are because m+n is always equal to 24 in this case.

-----------------

A more concrete example:

Let's say m = 2. We won't set up n just yet but we'll be able to compute it fairly soon.

Since m = 2, this means d = 12-m = 12-2 = 10. This is the gap between adjacent or neighboring terms.

If d = 10, then the third term must be n = 12+d = 12+10 = 22

We can then see that m+n = 2+22 = 24

-----------------

I'll do another example:

m = 5

d = 12-m = 12-5 = 7

n = 12+d = 7 = 19

m+n = 5+19 = 24

Whenever in doubt, or if you get stuck, it helps to come up with actual numeric values to hopefully clear things up.

-----------------

An alternative way to get the answer:

Let's try to determine what m+n is actually saying. We have 12 right in the middle of the first term (m) and third term (n). Because the gap between the numbers is the same (that being d), we know that 12 is the midpoint of m and n. It might help to draw out a number line to see what's going on.

The midpoint of m and n is (m+n)/2

Set this equal to 12 and isolate the "m+n"

(firstTerm+thirdTerm)/2 = second term

(m+n)/2 = 12

m+n = 2*12

m+n = 24

So in general, if the first three terms of the arithmetic sequence are m, k, n, then m+n = 2k.

3 0
3 years ago
Holly bought blank CD's and spent $34.57.What is that amount rounded to the nearest dollar?.
Tamiku [17]

Answer:

$35

Step-by-step explanation:

Rounding to the nearest dollar which would be 4 so in that case you would use the 5 in .57 and because 5 is a large number it would make the 4 into a five thus making it $35. Hope this helped :)

3 0
3 years ago
Find the volume of the prism
weqwewe [10]
Using the formula V = bh

5 0
3 years ago
Fill in the table of values so that this is a proportional relationship with k=3/2
Zigmanuir [339]

Step-by-step explanation:

the table is non-existent

3 0
3 years ago
Use ABC to find the value of sin A. <br> a. 12/37<br> b. 37/12<br> c. 35/37<br> d. 12/35
FromTheMoon [43]

Answer:

  a.  12/37

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

  Sin = Opposite/Hypotenuse

  sin(A) = BC/AB = 12/37

4 0
3 years ago
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