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Ronch [10]
4 years ago
11

Find the first 4 terms in the expansion of ( 1 + x 2 ) 8. Use your answer to find the value of ( 1.01 ) 8

Mathematics
1 answer:
anyanavicka [17]4 years ago
7 0

(1+x^2)^8

=(1+8x^2+8*7/(1*2)x^4+8*7*6/(1*2*3)x^6+8*7*6*5/(1*2*3*4)x^8+....)

=1+8x^2+28x^4+56x^6+70x^8+....)

For x<1, higher power terms diminish in value, hence we can approximate powers of numbers.

1.01=(1+0.1^2) => x=0.1 in the above expansion

(1.01)^8

=1+8(0.1^2)+28(0.1^4)+56(0.1^6) [ limited to four terms, as requested]

=1+0.08+0.0028+0.000056 (+0.00000070)

=1.082856 (approximately)

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EQUATION: y=\frac{-3}{4}x-3

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<h2>INSTRUCTIONS:</h2>

FINDING THE Y-INTERCEPT:

Do this simply by finding the number your graph starts at on the Y-Axis (vertical line)! In this case, it's at -3!

FINDING SLOPE:

Remember that slope is rise over run (\frac{rise}{run})

RISE = How far the line goes <em>up </em>and <em>down</em>.

RUN = How far the line goes <em>left </em>or <em>right</em>.

HOW DO I FIND IT? All you have to do is count both rise and run from one point on the line to another! WARNING: The point must hit at a vertex, it cannot be counted if it is in the center of the box, or anywhere that does not touch the edge. I also suggest starting from the <u>Y-Intercept</u> and counting.

GOING LEFT OR DOWN: This is a positive number

GOING RIGHT OR UP: This is a negative number.

(You will see how this applies, below, yayyyy)

CALCULATING OUR NUMERATOR, AKA RISE:

Starting from the y, to get to the next point on the line, you can see we have to go down three. This means our numerator is -3!

CALCULATING OUR DENOMENATOR, AKA RUN:

Starting from where we just stopped, we must continue getting to the next point, and to do that, you can see we have to go to the right four! This means our denomenator is 4!

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3 years ago
A bag contains two steel balls and five brass balls. The total weight of the bag is 13 pounds. If two steel balls are added and
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x = the weight of one steel ball y = the weight of one brass ball 2x + 5y = 13 (2 + 2)x + (5 - 2)y = 12 by solving the above system of equations we find:

x = 1.5 lbs y =2 lbs one steel ball weighs 1.5 lbs.one brass ball weighs 2 lbs.

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