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3 years ago

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Point W was translated as follows W(-4,7) -> W'(-2,4) a student wrote the algebraic rule to describe the translation as (x,y)

->(x-3,y+2) evaluate the students answer

1 answer:

pishuonlain [190]3 years ago

7 0

Student did it wrong. The translation is: (x,y) → (x+2, y - 3 ).
Explanation:
For x- coordinate: -4 + 2 = -2
For y- coordinate: 7 - 3 = 4

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Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = x/6x^2 +

timama [110]

Looks like your function is

$f(x)=\dfrac x{6x^2+1}$

Rewrite it as

$f(x)=\dfrac x{1-(-6x^2)}$

Recall that for $|x|$ , we have

$\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n$

If we replace $x$ with $-6x^2$ , we get

$f(x)=\displaystyle x\sum_{n=0}^\infty\frac(-6x^2)^n=\sum_{n=0}^\infty (-6)^n x^{2n+1}$

By the ratio test, the series converges if

$\displaystyle\lim_{n\to\infty}\left|\frac{(-6)^{n+1} x^{2(n+1)+1}}{(-6)^n x^{2n+1}}\right|=6|x^2|\lim_{n\to\infty}1=6|x|^2$

Solving for $x$ gives the interval of convergence,

$|x|^2$

We can confirm that the interval is open by checking for convergence at the endpoints; we'd find that the resulting series diverge.

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3 years ago

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If h(x) = 7 + 6f(x) , "where f(5) = 7 and f '(5) = 3", find h'(5).

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Convert the following:<br> 110110two to base ten<br> 25ten to base two<br>

blagie [28]

Answer:

110110 in base 2 when converted in base 10 will be equal to 54
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Step-by-step explanation:

Part 1: 110110two to base ten

For conversion from base 2 to base 10 we multiply each digits of given number with powers of 2

So

$=1*2^5 + 1 * 2^4 + 0 * 2^3 + 1 *2^2 + 1* 2^1 + 0*2^0\\ =1*32+ 1* 16 + 0 + 1*4 + 1*2 +0\\ =32 + 16 +4 + 2\\ = 54$

So 110110two when converted in base 10 will be equal to 54

Part 2: 25ten to base two

For conversion from base 10 to base 2 we will divide the given number with 2 repeatedly and store the remainders until the quotient comes 1. The solution is as follows:

25/2 = 12 remainder 1

12/2 = 6 remainder 0

6/2 = 3 remainder 0

3/2 = 1 remainder 1

Now the remainders will be written in inverse order as:

=1001 base 2

So 25 in base 10 is equal to 1001 base 2

I hope it will help you!

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Answer:

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Step-by-step explanation:

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