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3 years ago

Find the mean and range 26 19 23 39 31 34 23 25

1 answer:

4 0

I got 27.5 for the mean
mean: you add up all the #'s and divide them my their quantity( in other words by how many numbers there are)
In your case you have 8 numbers, you add them and divide them by 8!

Hope it helps ;)

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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

If the two legs of an isosceles right triangle measure 7 in which of the following represents the length of its hypotenuse

anyanavicka [17]

Answer:

Hypotenuse would be 14

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

A small business produces and sells balls. The fixed costs are $20 and each ball costs $4.32 to produce. Each ball sells for $8.

Gemiola [76]

Part 1:

Fixed Cost, f = $20

number of balls = n

Cost of each ball, c = 4.32

Price of each ball, p = 8.32

Equation for total cost:

Total Cost of balls will come by adding the cost of all balls and the fixed cost

Total Cost = number of balls made × Cost of each ball + fixed cost

C = 4.32n + 20

Equation for revenue:

Revenue = Number of balls made × price of each ball

R = 8.32n

Part 2:

Use the graphing method to determine how many balls must be sold to break even

Breakeven means Revenue = total Cost

This happens at a point (5,41.6) where n = 5 is the number of balls sold

and C = 41.6 is the total cost

When 5 balls are sold there will be breakeven

R = 4n - 20

C = 4.32n + 20

Red line represent Cost

Black line represent Revenue

5 0

3 years ago

What is the answer to 72% of 14?

SSSSS [86.1K]

14/100 = 0.14
0.14x72 = 10.08

7 0

3 years ago

Identify the outlier of the set:

Finger [1]

Help the math of mine plz

3 0

3 years ago