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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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Answer:

(x - 7)^2 + (y - 2)^2 = 5^2

Step-by-step explanation:

Center at (7, 2); radius 5

Adapt (x - h)^2 + (y - k)^2 = r^2 to this situation.  Replace h by 7, k by 2 and r by 5:

(x - 7)^2 + (y - 2)^2 = 5^2

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In 1999, there were 9860 Great Danes registered with the American Kennel Club. The number of registered Labrador Retrievers was
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Answer:

153,997 Labrador Retrievers

Step-by-step explanation:

Let's make an equation for this problem. We know that there were 9,860 Great Danes. The number of Labrador Retrievers was 6,997 more than 15 times the number of registered Great Danes. More than can be changed to a plus sign. 15 times the number of Great Danes is 15 times 9,860. The equation is now 15*9,860 + 6,997.

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3 years ago
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The cost of renting a truck is $40. An additional $0.79 is charged for each mile, m, the truck is driven.
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Step-by-step explanation:

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To make this easier, first draw or imagine a vertical line at x=2

Find where the vertical line and the graph intersects.

Draw or imagine that point of intersection.

Now, draw or imagine a horizontal line that goes through the point of intersection.

That horizontal line tells us the the value of the function by passing through that mark that says "-2"

The function's value at x=2 is -2.

Have an awesome day! :)

Step-by-step explanation:

8 0
2 years ago
2. Write a quadratic function that has -intercepts (- 3, 0) and (4, 0) and passes through the point (5, 8)
Reptile [31]

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<u>Quadratic Function</u>

Standard Form of Quadratic Function

The standard representation of a quadratic function is:

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where a,b, and c are constants.

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We are given the two roots of f: x1=-3 and x2=4, thus:

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Operating:

\boxed{f(x)=x^2-x-12}

5 0
2 years ago
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