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sashaice [31]
3 years ago
12

Last

Mathematics
1 answer:
igor_vitrenko [27]3 years ago
4 0

Answer:63826.34

Step-by-step explanation:

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Find the sum 38+39+40+41...+114+115
Tasya [4]

It seems like you want to find the sum of 38 to 115:

\displaystyle \large{38 + 39 + 40 + 41 + ... + 114 + 115}

If we notice, this is arithmetic series or the sum of arithmetic sequences.

To find the sum of the sequences, there are three types of formulas but I will demonstrate only one and the best for this problem.

\displaystyle \large{S_n =  \frac{n(a_1+a_n) }{2} }

This formula only applies to the sequences that have the common difference = 1.

Given that a1 = first term of sequence/series, n = number of terms and a_n = last term

We know the first term which is 38 and the last term is 115. The problem here is the number of sequences.

To find the n, you can use the following formula.

\displaystyle \large{n = (a_n - a_1) + 1}

Substitute an = 115 and a1 = 38 in the formula of finding n.

\displaystyle \large{n = (115 - 38) + 1} \\  \displaystyle \large{n = (77) + 1} \\  \displaystyle \large{n = 78}

Therefore the number of sequences is 78.

Then we substitute an = 115, a1 = 38 and n = 78 in the sum formula.

\displaystyle \large{S_{78} =  \frac{78(38+115) }{2} } \\  \displaystyle \large{S_{78} =  \frac{39(38+115) }{1} } \\ \displaystyle  \large{S_{78} = 39(153) } \\  \displaystyle  \large \boxed{S_{78} = 5967}

Hence, the sum is 5967.

4 0
2 years ago
The electromagnetic waves with the shortest wavelengths and the highest frequency are called
Arada [10]
D.) Gamma rays have shortest wavelengths and highest frequency

So, option D is your answer!

Hope this helps!
8 0
3 years ago
Determine which variable is the independent variable and which variable is the dependent variable. Write an equation,
VMariaS [17]

Answer: w =40m

dependent variable = w

independent variable = m.

Step-by-step explanation:

Hi, to answer this question we have to write an equation:

The number of words typed (w) will be equal to the product of the number of words typed per minute (40) and the number of minutes (m)

w =40m

The dependent variable is w , and the independent variable is m.

Because the output value of w depends of the input value of m.

3 0
3 years ago
Read 2 more answers
The product of a number squared and three<br> what is the number written out?
Andru [333]

Answer:

xto the power of three

Step-by-step explanation:

6 0
3 years ago
What is the intermediate step in the form (x + a)2 = b as a result of completing the
nadezda [96]

Answer:

y=(x-1)^2 -1

Step-by-step explanation:

If you put it in the form (x-a)^2=b

The answer will be (x-1)^2=1

4 0
3 years ago
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