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allochka39001 [22]
3 years ago
15

The sum of 6 consecutive integers is 519. What is the third number in this sequence?

Mathematics
2 answers:
egoroff_w [7]3 years ago
5 0
<span>let x be the first integer, then
:
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) = 519
:
6x + 15 = 519
:
6x = 504
:
x = 84</span>
Lana71 [14]3 years ago
5 0
<span>6 consecutive integers
x, x+1, x+2, x+3, x+4, x+5

</span><span>sum of 6 consecutive integers is 519
</span>x+ x+1+ x+2+ x+3+ x+4+ x+5 = 519
<span>6x + 15 = 519
6x = 504
x  = 84

</span><span>84 +1 = 85
84 +2 = 86
84 +3 = 87
84 +4 = 88
84 +5 = 89
</span><span>
answer:</span> third number in this sequence = 86<span>

</span>
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padilas [110]

First picture:

You got the first two right (good job!), so I'll just tackle the third one. If you have to compute f(x-4), it means that you have to substitute x-4 in place of x. Differently from the first two points, this will generate a new function, rather than a specific value:

f(x) = \sqrt{x+4}+2 \implies f(x-4) = \sqrt{(x-4)+4}+2 = \sqrt{x}+2

Second picture:

Given the point (x,y) highlighted in the picture, you can deduce that the base is 2x units long (since it spans from (-x,0) to (x,0)) and the height is y units long (because it spans from (x,0) to (x,y)). So, the area of the rectangle is the multiplication between base and height:

A = 2xy

But we know that y=f(x)=\sqrt{36-x^2}, so we have

A = 2x\sqrt{36-x^2}

The domain of this function is given by the domain of the square root: we want its argument to be non, negative, so we have

36-x^2 \geq 0 \iff x^2 \leq 36 \iff -6 \leq x \leq 6

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0 \leq x \leq 6

You can only see the answer 0 < x < 6 because, if you choose x=0 or x=6, the rectangle degenerates to a segment, and your exercise doesn't like this scenario, apparently

4 0
3 years ago
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lora16 [44]
I have attached the graph of y = -x + 1.5

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6 0
3 years ago
Answer this world problem for me
inn [45]
Let's solve this problem step-by-step.

STEP-BY-STEP SOLUTION:

In order to find the answer, we need to do as follows:

Average no. of people per km^2 = total no. of people ÷ total no. of people

Average no. of people per km^2 = 1, 080, 264, 388 ÷ 2, 973, 190

Average no. of people per km^2 = 363.335134317

Now we need to round the answer to the nearest whole number. In this case, we will be rounding down as displayed below:

Average no. of people per km^2 = 363 people

ANSWER:

Therefore, the answer is:

There are an average of 363 people per km^2 of land in India.

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7 0
3 years ago
The circumference of a circle is 3.14 inches.<br> What is the area of the circle?
SVETLANKA909090 [29]

Answer:

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6 0
3 years ago
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Lyrx [107]

Answer: Like terms are -7 and 2. Simplified version would be 7d-5.

Step-by-step explanation:

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7 0
3 years ago
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