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4 years ago

A pentagon has 5 congruent sides and each angle measures 108°.

Mathematics

2 answers:

Lelu [443]4 years ago

8 0

Regular..............................

Dafna11 [192]4 years ago

6 0

I'd say A because all side are equal.

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Find T5(x) : Taylor polynomial of degree 5 of the function f(x)=cos(x) at a=0 . (You need to enter function.) T5(x)= Find all va

Burka [1]

Answer:

$\bf cos(x)\approx1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{4!}=\\\\=1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{24}$

The polynomial is an approximation with an error less than or equals to 0.002652 for x in the interval

[-1.113826815, 1.113826815]

Step-by-step explanation:

According to Taylor's theorem

$\bf f(x)=f(0)+f'(0)x+f''(0)\displaystyle\frac{x^2}{2}+f^{(3)}(0)\displaystyle\frac{x^3}{3!}+f^{(4)}(0)\displaystyle\frac{x^4}{4!}+f^{(5)}(0)\displaystyle\frac{x^5}{5!}+R_6(x)$

with

$\bf R_6(x)=f^{(6)}(c)\displaystyle\frac{x^6}{6!}$

for some c in the interval (-x, x)

In the particular case f

f(x)=cos(x)

we have

$\bf f'(x)=-sin(x)\\f''(x)=-cos(x)\\f^{(3)}(x)=sin(x)\\f^{(4)}(x)=cos(x)\\f^{(5)}(x)=-sin(x)\\f^{(6)}(x)=-cos(x)$

therefore

$\bf f'(x)=-sin(0)=0\\f''(0)=-cos(0)=-1\\f^{(3)}(0)=sin(0)=0\\f^{(4)}(0)=cos(0)=1\\f^{(5)}(0)=-sin(0)=0$

and the polynomial approximation of T5(x) of cos(x) would be

$\bf cos(x)\approx1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{4!}=\\\\=1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{24}$

In order to find all the values of x for which this approximation is within 0.002652 of the right answer, we notice that

$\bf R_6(x)=-cos(c)\displaystyle\frac{x^6}{6!}$

for some c in (-x,x). So

$\bf |R_6(x)|\leq|\displaystyle\frac{x^6}{6!}|=\displaystyle\frac{|x|^6}{6!}$

and we must find the values of x for which

$\bf \displaystyle\frac{|x|^6}{6!}\leq0.002652$

Working this inequality out, we find

$\bf \displaystyle\frac{|x|^6}{6!}\leq0.002652\Rightarrow |x|^6\leq1.90944\Rightarrow\\\\\Rightarrow |x|\leq\sqrt[6]{1.90944}\Rightarrow |x|\leq1.113826815$

Therefore the polynomial is an approximation with an error less than or equals to 0.002652 for x in the interval

[-1.113826815, 1.113826815]

8 0

3 years ago

Suppose that a simulation with a six-sided number cube provided these results during testing.

lyudmila [28]

Theoretical probability:
1 ... (16 and 2/3) %
2 ... (16 and 2/3) %
3 ... (16 and 2/3) %
4 ... (16 and 2/3) %
5 ... (16 and 2/3) %
6 ... (16 and 2/3) %

Experimental results:
1 ... 18
2 ... 16
3 ... 16
4 ... 17
5 ... 16
6 ... 17

The total number of rolls in the experiment was

(18 + 16 + 16 + 17 + 16 + 17) = 100

so the expected frequency for each outcome was 16-2/3 times,
and the SIMULATION probabilities were

1 ... 18%
2 ... 16%
3 ... 16%
4 ... 17%
5 ... 16%
6 ... 17%

To me, this looks fantastically close. The cube
could hardly be more fair than it actually is.

8 0

3 years ago

(07.03 LC) The steps below show the incomplete solution to find the value of q for the equation 4q − 2q − 4 = −1 + 21: Step 1: 4

Elza [17]

Answer:

3: 2q − 4 = 20

Step-by-step explanation:

Solve for q:

2 q - 4 = 20

Add 4 to both sides:

2 q + (4 - 4) = 4 + 20

4 - 4 = 0:

2 q = 20 + 4

20 + 4 = 24:

2 q = 24

Divide both sides of 2 q = 24 by 2:

(2 q)/2 = 24/2

2/2 = 1:

q = 24/2

The gcd of 24 and 2 is 2, so 24/2 = (2×12)/(2×1) = 2/2×12 = 12:

Answer: q = 12

8 0

3 years ago

Read 2 more answers

If figure 1 has 4 tiles, fig 2 has 10, and fig 3 has 16... What is my rule?

Sever21 [200]

Answer:

Add 6 each time.

Step-by-step explanation:

Figure 1 has 4 tiles.

To go from figure 1 (4 tiles) to figure 2 (10 tiles), you added 6 tiles.

To go from figure 2 (10 tiles) to figure 3 (16 tiles), you added 6 tiles.

∴ the rule is to add 6 tiles each time.

7 0

3 years ago

Multiply 4x(-3x - 5)

Scilla [17]

Using the distributive property the product is -12x-20. To distribute you take the numbers and or variables outside of the paranthesis and multiply it by each one in the parenthesis such that 4x is multiplied by -3x getting -12x and multiplying 4x by -5 and the product is -20x and all together the answer is -12x-20

6 0

3 years ago

Read 2 more answers