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3 years ago

Simplify the expression 13+(x+8)

Mathematics

1 answer:

Fudgin [204]3 years ago

7 0

Answer:x+21

Step-by-step explanation:

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Find the taylor polynomial t3(x) for the function f centered at the number

inysia [295]

Answer:

$t_3(x)=\frac{7\pi}{4}+\frac{7}{2}(x-1)-\frac{7}{4}(x-1)^2+\frac{7}{12}(x-1)^3$

Step-by-step explanation:

We are given that

$f(x)=7tan^{-1}(x)$

a=1

$T_n(x)=\sum_{r=0}^{n}\frac{f^r(a)(x-a)^r}{r!}$

Substitute n=3 and a=1

$t_3(x)=f(1)+f'(1)(x-1)+\frac{f''(1)(x-1)^2}{2!}+\frac{f'''(1)(x-1)^3}{3!}$

$f(x)=7tan^{-1}(x)$

$f(1)=7tan^{-1}(1)=7\times \frac{\pi}{4}=\frac{7\pi}{4}$

Where $tan^{-1}(1)=\frac{\pi}{4}$

$f'(x)=\frac{7}{1+x^2}$

Using the formula

$\frac{d(tan^{-1}(x))}{dx}=\frac{1}{1+x^2}$

$f'(1)=\frac{7}{2}$

$f''(x)=\frac{-14x}{(1+x^2)^2}$

$f''(1)=-\frac{7}{2}$

$f''(x)=-14x(x^2+1)^{-2}$

$f'''(x)=-14((x^2+1)^{-2}-4x^2(x^2+1)^{-3}})$

By using the formula

$(uv)'=u'v+v'u$

$f'''(x)=-14(\frac{x^2+1-4x^2}{(1+x^2)^3}$

$f'''(x)=(-14)\frac{-3x^2+1}{(1+x^2)^3}$

$f'''(1)=-14(\frac{-3(1)+1}{2^3})=\frac{7}{2}$

Substitute the values

$t_3(x)=\frac{7\pi}{4}+\frac{7}{2}(x-1)-\frac{7}{4}(x-1)^2+\frac{7}{2\times 3\times 2\times 1}(x-1)^3$

$t_3(x)=\frac{7\pi}{4}+\frac{7}{2}(x-1)-\frac{7}{4}(x-1)^2+\frac{7}{12}(x-1)^3$

7 0

3 years ago

The probability distribution for a

Luden [163]

Answer:

0.30

Step-by-step explanation:

P(x ≤ -3) = P(x=-3) + P(x=-5)

P(x ≤ -3) = 0.13 + 0.17

P(x ≤ -3) = 0.30

6 0

3 years ago

Is 56 a multiple of 6?

andreyandreev [35.5K]

Good evening ,

_______

Answer:

____________________

Step-by-step explanation:

A number is a multiple of 6 if it can be divided by 6 .

Since 3 don’t divide 56 because 5 + 6=11 and 3 don’t divided 11 ,

Then 6 don’t divide 56

then , 56 isn’t a multiple of 6.

3 0

3 years ago

Determine the measure of an angle whose measure is 14 times that of its complement

mrs_skeptik [129]

Answer:

84°

Step-by-step explanation:

Let the two complementary angles be x and y.

If the measure of an angle is 14 times the other, then x = 14y...... 1

Since the two angles are complementary, their sum will be 90° i.e x+y = 90° ...... 2

Substitute equation 1 into 2

14y+y = 90

15y = 90

y = 90/15

y = 6

Since the angle is x = 14y

x = 14(6)

x = 84°

Hence the measure of the angle is 84°

8 0

3 years ago

How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!

gavmur [86]

Answer: A. they will have too much butter

Step-by-step explanation: to much

6 0

2 years ago