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Ronch [10]
3 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]3 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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The surface area of sphere T is 452.16 units squared. The surface area of sphere X is 1808.64 units squared. how many times larg
Art [367]

Answer:

the radius of sphere X is 2 times larger than the radius of sphere T

Step-by-step explanation:

Given

Surface area of sphere, T =452.16

Surface area of sphere, X= 1808.64

how many times larger is the radius of sphere X than the radius of sphere T?

Finding radius of both spheres:

Surface area of sphere is given as

A=4πr^2

Now putting value of Ta=452.16 in above formula

452.16=4πrt^2

rt^2=452.16/4π

rt^2=35.98

Taking square root on both sides

rt=5.99

Now putting value of Xa=1808.64 in above formula

1808.64=4πrx^2

rx^2=1808.64/4π

rx^2=143.92

Taking square root on both sides

rx=11.99

Comparing radius of sphere X and the radius of sphere T

rx/rt=11.99/5.99

      = 2.00

rx=2(rt)

Hence the radius of sphere X is 2 times larger than the radius of sphere T!

3 0
3 years ago
Read 2 more answers
(x + 5) + (x² − 6x + 20)
ratelena [41]

Answer:

x^3-6x^2-10x+100

Step-by-step explanation:

Step 1: Distribute x to (x²-6x+20).

x(x²-6x+20)=x^3-6x^2+20x

Step 2: Distribute 5 to (x²-6x+20).

5(x² − 6x + 20)=5x²-30x+100

Step 3: Combine x^3-6x^2+20x and 5x²-30x+100.

x^3-6x^2-10x+100

hope it helps you <3

8 0
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Answer:

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Step-by-step explanation:

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3 years ago
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