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BaLLatris [955]
3 years ago
5

Use the pi key on a scientific or graphing calculator to compute the percent of error of the approximation of pi, 3.14, to the v

alue pi. Show your steps, and round your answer to the nearest hundredth of a percent.
Mathematics
1 answer:
Kitty [74]3 years ago
4 0
Percent error is calculated as \frac{approximation-theoretical}{theoretical}*100.
The approximation in this case is 3.14, and the theoretical or actual value is pi.

Using the formula, the percent error will be:
\frac{3.14- \pi }{ \pi }*100 = -0.0507%

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Given the set points K+1:(-1,8),(1,0) and (2,5), find the quadratic polynomial interpolate
Sauron [17]

Answer:

The interpolating polynomial is p(x) = 1-4x+3x^2.

Step-by-step explanation:

We want to find a quadratic polynomial p(x) such that p(-1)=8, p(1)=0 and p(2)=5. In order to do this let us write p(x) = a_0+a_1x+a_3x^2.

Now, evaluating the polynomial in the points -1, 1 and 2 we get

\begin{cases} 8 = p(-1) &= a_0-a_1+a_2\\ 0 = p(1) &= a_0+a_1+a_2\\ 5 = p(2) &= a_0+2a_1+4a_2\end{cases}

This relations give us a linear system of equations:

\begin{cases} 8 &= a_0-a_1+a_2\\ 0 &= a_0+a_1+a_2\\ 5&= a_0+2a_1+4a_2\end{cases}

where the a_0, a_1 and a_2 are the unknowns.

The augmented matrix of the system is

\begin{pmatrix}1 & -1 & 1 & 8\\ 1 & 1 & 1 & 0\\ 1 & 2 & 4 & 5\end{pmatrix}

In this matrix it is easy to eliminate the 1's of the first column and get

\begin{pmatrix} 1 & -1 & 1 & 8\\ 0 & 2 & 0 & -8\\ 0 & 3 & 3 & -3\end{pmatrix}

From this matrix we can find the values of each unknown. Notice that the second row gives us 2a_2=-8 that yields a_1=-4.

Then, the third row means 3a_1+3a_2=-3 that gives -12+3a_2=-3. So, a_2=3.

Finally, the first row is a_0-a_1+a_2=8 and substituting is a_0+7=8 that yields a_0=1.

Therefore, the interpolating polynomial is

p(x) = 1-4x+3x^2.

8 0
3 years ago
Cindy is make a display for a project. She plans on 100 stickers that are 2 inch by 2 inch square on a poster board. The poster
gavmur [86]

Answer:

YES

Step-by-step explanation:

the dimensions of the poster board has to be converted to inches to add comparability

1 feet = 12 inches

3 x 12 = 36 inches

width = 2 x 12 = 24 inches

Area = length x breadth

36 x 24 = 864 cm^2

area of sticker = 2 x 2 = 4cm^2

Number of stickers that can be put on the board = 864 / 4 = 216

216 is greater than 100. So the board has enough room for the stickers

8 0
3 years ago
A pizza has a diameter of 10 inches. If the
s344n2d4d5 [400]

Answer:

78.5

Step-by-step explanation:

The formula for area of a circle is pir^2

So we have 5 for r, so r^2 would be 25.

Using 3.14 for pi, we get the answer is 78.5

4 0
2 years ago
Read 2 more answers
the area of a square floor on a scale drawing is 100 square centimeters and the scale of the drawing is cm : 2 ft what is the ar
schepotkina [342]
The actual floor is 200 square feet and the ratio is 100 square centimeters: 200 square feet
7 0
3 years ago
Read 2 more answers
What is the value of (-7)
beks73 [17]

Answer:

i dont know maybe ha got you its

Step-by-step explanation:

i   know maybe go find on the internet not brainly though

7 0
2 years ago
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