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3 years ago

6

a shop is having a sale. all items are reduced by 20%.work out the sale price of an item normally priced at £37

1 answer:

Nookie1986 [14]3 years ago

3 0

Answer:

£29.6

Step-by-step explanation:

37/5=7.4

37-7.4=29.6

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Help!!!!!!!!!!!!!!!!!!!!!!!!!!1

Ugo [173]

Answer: D) y= 14/17x - 4/17

3 0

2 years ago

Consider the function f(x)equalscosine left parenthesis x squared right parenthesis. a. Differentiate the Taylor series about 0

dybincka [34]

I suppose you mean

$f(x)=\cos(x^2)$

Recall that

$\cos x=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{x^{2n}}{(2n)!}$

which converges everywhere. Then by substitution,

$\cos(x^2)=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{(x^2)^{2n}}{(2n)!}=\sum_{n=0}^\infty(-1)^n\frac{x^{4n}}{(2n)!}$

which also converges everywhere (and we can confirm this via the ratio test, for instance).

a. Differentiating the Taylor series gives

$f'(x)=\displaystyle4\sum_{n=1}^\infty(-1)^n\frac{nx^{4n-1}}{(2n)!}$

(starting at $n=1$ because the summand is 0 when $n=0$ )

b. Naturally, the differentiated series represents

$f'(x)=-2x\sin(x^2)$

To see this, recalling the series for $\sin x$ , we know

$\sin(x^2)=\displaystyle\sum_{n=0}^\infty(-1)^{n-1}\frac{x^{4n+2}}{(2n+1)!}$

Multiplying by $-2x$ gives

$-x\sin(x^2)=\displaystyle2x\sum_{n=0}^\infty(-1)^n\frac{x^{4n}}{(2n+1)!}$

and from here,

$-2x\sin(x^2)=\displaystyle 2x\sum_{n=0}^\infty(-1)^n\frac{2nx^{4n}}{(2n)(2n+1)!}$

$-2x\sin(x^2)=\displaystyle 4x\sum_{n=0}^\infty(-1)^n\frac{nx^{4n}}{(2n)!}=f'(x)$

c. This series also converges everywhere. By the ratio test, the series converges if

$\displaystyle\lim_{n\to\infty}\left|\frac{(-1)^{n+1}\frac{(n+1)x^{4(n+1)}}{(2(n+1))!}}{(-1)^n\frac{nx^{4n}}{(2n)!}}\right|=|x|\lim_{n\to\infty}\frac{\frac{n+1}{(2n+2)!}}{\frac n{(2n)!}}=|x|\lim_{n\to\infty}\frac{n+1}{n(2n+2)(2n+1)}$

The limit is 0, so any choice of $x$ satisfies the convergence condition.

3 0

3 years ago

Simplify:<br> 2/3 divided by 3 3/4

Nat2105 [25]

Answer:

$\frac{8}{45}$

Step-by-step explanation:

convert mixed number to improper fractions

3 $\frac{3}{4}$ = $\frac{15}{4}$

$\frac{\frac{2}{3} }{\frac{15}{4} }$

apply the fraction rule:

$\frac{2 * 4}{3 * 15}$

multiply the numbers

$\frac{8}{45}$

3 0

1 year ago

At a particular music store, CDs are on sale at $13.00 for the first one purchased and $10.00 for each additional disc purchased

netineya [11]

D=Disc
13+10d=83
10d=83-13
10d=70
D=70/10
D=7
7+1=8
Maria purchased 8 CDs. Hope this helps!

7 0

3 years ago

Read 2 more answers

A high school of 350 students offers biology and chemistry courses. 213 students are enrolled in biology while 155 students are

NNADVOKAT [17]

350 - 213 - 155 + 78 = 60 students not in either

4 0

3 years ago