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3 years ago

4 equivalent expressins to 42+18

Mathematics

1 answer:

maria [59]3 years ago

8 0

1. 30 + 30
2. 20 + 40
3. 12 * 5
4. 300/5

(Bonus)
5. 10 + 50

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Find x on this special right triangle, 45 is not an option!!!!

zloy xaker [14]

let the line between 2 tria be y

sin 60/8√2 = sin 90/y

y=13.06

sin 45/13.06 = sin 90/x

x=18.46

7 0

3 years ago

Read 2 more answers

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

Find n so that the number sentence below is true:

adell [148]

Answer: n=6

Step-by-step explanation:

2^3 x 4^3 = 2^3 x 2^n = 2^9

(2×2×2) ×(4×4×4) = (2x2x2) ×2^n=(2x2x2x2x2x2x2x2x2)

8 x 64 = 8x 2^n = 512

512= 8x 2^n = 512

divide all through by 8 so that 2^n can stand alone

512/8 = (8x 2^n)/8 = 512/8

64 = 2^n = 64

express 64 as a base of 2

2^6 = 2^n = 2^6

since they all have same base, cancel out the base.

therefore,

6=n=6

n = 6

6 0

3 years ago

One ounce of a yogurt contains of 1.2 grams of sugar. How many grams of sugar are in 14.25 ounces of yogurt?

mel-nik [20]

Answer:

17.1 grams of sugar

Step-by-step explanation:

Just multiply them

3 0

3 years ago

Identify and label each of the mathematical properties below.

vazorg [7]

Answer:

1. Commutative

2. Associative

3. Identity

4.Distributive

5. Identity

6. Associative

7. Commutative

8. Identity

9. Identity

5 0

3 years ago