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3 years ago

Please help me I can't do this answer

Mathematics

1 answer:

Tomtit [17]3 years ago

6 0

Answer:

Its option number 2 perhaps, sorry if im wrong

Step-by-step explanation:

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The set of the consecutive odd numbers 1, 3, 5, 7, ... , N has a sum of 400. How many numbers are in the set?

Amanda [17]

Well, we could try adding up odd numbers, and look to see when we reach 400. But I'm hoping to find an easier way.

First of all ... I'm not sure this will help, but let's stop and notice it anyway ...
An odd number of odd numbers (like 1, 3, 5) add up to an odd number, but
an even number of odd numbers (like 1,3,5,7) add up to an even number.
So if the sum is going to be exactly 400, then there will have to be an even
number of items in the set.

Now, let's put down an even number of odd numbers to work with,and see
what we can notice about them:

 1, 3, 5, 7, 9, 11, 13, 15 .

Number of items in the set . . . 8
Sum of all the items in the set . . . 64

Hmmm. That's interesting. 64 happens to be the square of 8 .
Do you think that might be all there is to it ?

Let's check it out:

Even-numbered lists of odd numbers:

1, 3 Items = 2, Sum = 4
1, 3, 5, 7 Items = 4, Sum = 16
1, 3, 5, 7, 9, 11 Items = 6, Sum = 36
1, 3, 5, 7, 9, 11, 13, 15 . . Items = 8, Sum = 64 .

Amazing ! The sum is always the square of the number of items in the set !

For a sum of 400 ... which just happens to be the square of 20,
we just need the first 20 consecutive odd numbers.

I slogged through it on my calculator, and it's true.

I never knew this before. It seems to be something valuable
to keep in my tool-box (and cherish always).

3 0

3 years ago

Write a definite integral that represents the area of the region. (Do not evaluate the integral.) y1 = x2 + 2x + 3 y2 = 2x + 12F

Svet_ta [14]

Answer:

$A = \int\limits^3__-3}{9}-{x^{2}} \, dx = 36$

Step-by-step explanation:

The equations are:

$y = x^{2} + 2x + 3$

$y = 2x + 12$

The two graphs intersect when:

$x^{2} + 2x + 3 = 2x + 12$

$x^{2} = 0$

$x_{1} = 3\\x_{2} = -3$

To find the area under the curve for the first equation:

$A_{1} = \int\limits^3__-3}{x^{2} + 2x + 3} \, dx$

To find the area under the curve for the second equation:

$A_{2} = \int\limits^3__-3}{2x + 12} \, dx$

To find the total area:

$A = A_{2} -A_{1} = \int\limits^3__-3}{2x + 12} \, dx -\int\limits^3__-3}{x^{2} + 2x + 3} \, dx$

Simplifying the equation:

$A = \int\limits^3__-3}{2x + 12}-({x^{2} + 2x + 3}) \, dx = \int\limits^3__-3}{9}-{x^{2}} \, dx$

Note: The reason the area is equal to the area two minus area one is that the line, area 2, is above the region of interest (see image).

3 0

3 years ago

ANSWER ASAP --- NO LINKS-- 25 POINTS

Crazy boy [7]

Evaporation is a type of vaporization that occurs on the surface of a liquid as it changes into the gas phase. The surrounding gas must not be saturated with the evaporating substance. When the molecules of the liquid collide, they transfer energy to each other based on how they collide with each other. Wikipedia

3 0

3 years ago

Simplify the following expression. A. B. C. D.

Dahasolnce [82]

Answer:

Step-by-step explanation:

Let's start by crossing everything out!

12/3 can be crossed out to 4.

a^3/a^2 can be crossed out to a.

b^6/b^4 can be crossed out into b^2.

c^5/c^5 is just 1.

So which the results we got, we can multiply them, so that it is 4ab^2.

4ab^2 is our final answer!

5 0

2 years ago

PLEASE HELP!! THANKS!! WILL GIVE BRAINLIEST!!

marishachu [46]

Answer:

the third from the top option

Step-by-step explanation:

7 0

3 years ago