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2 years ago

1 2 3 4 .... 1002 what is the sum of the sequence

1 answer:

3 0

<span>As far as i know it is related to Gauss.
Write the sequences forward and backward first.

1 +2 +3 +.....+1002
1002+1001+1000+.....+1
--------------------------------------... Adding them
1003+1003+......(1002 times)
=1002x1003
But this contains the series twice.
So, the sum is = 1002x1003/2=501x1003=502503. answer</span>

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A machine at a bottling company fills water bottles. the number of bottles filled is proportional to the amount of time the mach

Whitepunk [10]

In the table shown below:

Let N be the number of bottles filled,

Let T be the time in hours.

Given that the number of bottles filled is proportional to the amount of time the machine runs, we have

$\begin{gathered} N\propto T \\ \text{Introducing a proportionality constant, we have } \\ N\text{ = kT} \\ \Rightarrow k\text{ = }\frac{N}{T} \\ \end{gathered}$

Let's evaluate the value of k for each day.

Thus, on monday,

$\begin{gathered} N\text{ = 9900} \\ T\text{ = 5.5} \\ \text{thus,} \\ k\text{ = }\frac{9900}{5.5} \\ \Rightarrow k\text{ = 1800} \end{gathered}$

Tuesday:

$\begin{gathered} N\text{ = }11160 \\ T\text{ = }6.2 \\ \text{thus,} \\ k\text{ = }\frac{11160}{6.2} \\ \Rightarrow k\text{ = 1800} \end{gathered}$

Wednesday:

$\begin{gathered} N\text{ = }12330 \\ T\text{ = }6.25 \\ \text{thus,} \\ k\text{ = }\frac{12330}{6.25} \\ \Rightarrow k\text{ = 1972.8} \end{gathered}$

Thursday:

$\begin{gathered} N\text{ = }10440 \\ T\text{ = }5.80 \\ \text{thus,} \\ k\text{ = }\frac{10440}{5.8} \\ \Rightarrow k=1800 \end{gathered}$

It is observed that all exept wednesday have the same value of k.

Thus, the amount of time required for the number of bottles filled on wednesday is evaluated as

$\begin{gathered} N\text{ = }12330 \\ k\text{ = 1800} \\ T\text{ = ?} \\ \text{but} \\ k\text{ = }\frac{N}{T} \\ 1800\text{ = }\frac{12330}{T} \\ \Rightarrow T\text{ = }\frac{\text{12330}}{1800} \\ T\text{ = 6.85} \end{gathered}$

Hence, the incorrect day is Wednesday. The amount of time for that many bottles should be 6.85 hours.

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11 months ago

What is the difference between a question asking you to factor a quadratic equation completely and a question asking you to solv

saveliy_v [14]

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2 years ago

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point a has the coordinates(2,5) point B has the coordinates (6,17) how long is segment ab in simplified radical form

IRISSAK [1]

Answer:

$4\sqrt{10}$

Step-by-step explanation:

We have been given that point A has the coordinates(2,5) point B has the coordinates (6,17).

To find the length of segment AB we will use distance formula.

$\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Upon substituting coordinates of point A and point B in distance formula we will get,

$\text{Distance between point A and point B}=\sqrt{(6-2)^2+(17-5)^2}$

$\text{Distance between point A and point B}=\sqrt{(4)^2+(12)^2}$

$\text{Distance between point A and point B}=\sqrt{16+144}$

$\text{Distance between point A and point B}=\sqrt{160}$

$\text{Distance between point A and point B}=4\sqrt{10}$

Therefore, the length of segment AB is $4\sqrt{10}$ .

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2 years ago

Convert y+7=4(x-3) standard form

True [87]

Answer:

-4x+y = -5

Step-by-step explanation:

Y+7=4(x-3)

Y+7=4x-12

+7. +7

Y=4x-5

-4x+y=-5

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OLEGan [10]

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2 years ago

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