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3 years ago

10

A decorative steel frame is shown below it is made of a circular section and and 6 stems the length of each stem is 45 cm work o

ut the total length of Steel used in the frame

1 answer:

lutik1710 [3]3 years ago

5 0

Answer:

552.78

Step-by-step explanation:

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1. f (x) = 5x + 10. If x = 10, then what is the value of f(x)?

UkoKoshka [18]

Answer:

B: 60

Step-by-step explanation:

f(x)= 5x+10, if x=10

f(10)=5(10)+10

5(10)+10=60

f(10)=60

3 0

3 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

The figure below is a square. Find the length of side x in simplest radical form with a

Leokris [45]

Answer:

$\frac{\sqrt{2} }{2}$

Step-by-step explanation:

45 - 45 - 90 Triangles

When one leg = x, the hypotenuse = x $\sqrt{2}$

So, if the hypotenuse is 1, then divide by $\sqrt{2}$ to get the leg.

$\frac{1}{\sqrt{2} }$ rationalize denominator.

$\frac{1}{\sqrt{2}}$ × $\frac{\sqrt{2}}{\sqrt{2} }$ = $\frac{\sqrt{2}}{\sqrt{2} \sqrt{2} }$ = $\frac{\sqrt{2} }{\sqrt{4}}$ = $\frac{\sqrt{2}}{2}$

3 0

3 years ago

Which of the following data sets represents a positive correlation?<br><br><br><br> A<br> B<br> C

dmitriy555 [2]

B as you can see the points go upwards as they go across :) Hope this helps!

8 0

3 years ago

Read 2 more answers

I need help cause uh i’m dumb

ozzi

Answer:

$650

Step-by-step explanation:

<u>9100-4500</u> = <u>4550</u>

14-7 7

= <u>650</u>

1

=$650

8 0

3 years ago