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3 years ago

7. Allan went shopping for stationery. He bought x pens at $1.75 each and y books at

Mathematics

1 answer:

timurjin [86]3 years ago

4 0

Answer:

$4.25

Step-by-step explanation:

x pens=$1.75

y pens =$2.50

Now,

in the terms of x and y ,

Alan spend altogether=1.75 +2.50

=$4.25

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3 years ago

Using the letters in the word INNOVATIVE, find the number of permutations that can be formed using 4 letters at a time. Show you

lyudmila [28]

Answer: 1) 5040 and 2) 165

Step-by-step explanation:

1) Here total number of letters = 10

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= P (10, 4)

= $10_P_4$

= $\frac{10!}{(10-4)!}$

= $\frac{10!}{6!}$

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3 years ago

"(b) use part (a) to find a power series for f(x) = 1 (4 + x)3 ."

Firdavs [7]

Assuming

$f(x)=\dfrac1{(4+x)^3}$

Recall that for $|x|$ ,

$\displaystyle\sum_{n\ge0}x^n=\frac1{1-x}$

Denote the above by $s(x)$ . Then

$s'(x)=\displaystyle\sum_{n\ge1}nx^{n-1}=\frac1{(1-x)^2}$
$s''(x)=\displaystyle\sum_{n\ge2}n(n-1)x^{n-2}=\frac2{(1-x)^3}$

Now,

$\dfrac1{(4+x)^3}=\dfrac1{4^3}\dfrac1{\left(1-\left(-\frac x4\right)\right)^3}=\dfrac1{2^7}\dfrac2{\left(1-\left(-\frac x4\right)\right)^3}$

which means we have

$f(x)=\dfrac1{2^7}s''(x)=\dfrac1{128}\displaystyle\sum_{n\ge2}n(n-1)\left(-\frac x4\right)^{n-2}$

which is valid for $\left|-\dfrac x4\right|$ , or $|x|$ .

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3 years ago

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Troyanec [42]

D 1 is the correct answers

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