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3 years ago

What is the distance between the points (7,3) and (-8, O) on a coordinate grid?

Mathematics

1 answer:

Georgia [21]3 years ago

5 0

Answer:15.29 or sqrt of 234

Step-by-step explanation:

Distance Formula

Sqrt of (-8-7)^2 + (0-3)^2

Sqrt of -15^2 + -3^2

Sqrt of 225 +9

Sqrt of 234 or 15.297

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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

One zero of x^3 - 4x = 0 is 0 what are the other zeros of the function

myrzilka [38]

So you have x^3 - 4x = 0. What you can do is pull out an x from both x^3 and - 4x so it looks like this:

$x( {x}^{2} - 4) = 0$

Then you can find a number that makes the part inside the parentheses turn into zero. For beginners, it may be easier to write it out seperately and solve for x.

${x}^{2} - 4 = 0$

We need to solve for x, so the first step is to add 4 to both sides, so we get something like this:

${x}^{2} = 4$

Then, we can square root both sides to get rid of the power on the x, so it looks like this:

$x = \sqrt{4}$

Now, every square root has two answers, a positive and a negative. If we look at the bottom example:

${2}^{2} = 4$

${( - 2)}^{2} = 4$

We can see that both -2 and 2 to the power of two will equal to 4.

So finally, we get:

$x = - 2 \: and \: 2$

These are the other 'Zero's for the original function. If you are not sure of what a 'Zero' is, it is where the function crosses over the x-axis on a graph.

5 0

2 years ago

The sum of a number and 10

adell [148]

Answer:

10 + x

Step-by-step explanation:

Sum means add

Hope this helps you :)

pls give me brainlest ;)

3 0

3 years ago

Which equation represents the line through (0,0) and (3, 4)?

Andreas93 [3]

Answer:

4-0

3-0

=4/3

y-0 =4/3

x-0

3y-0=4x-0

3y=4x

y=4/3x

Step-by-step explanation:

7 0

2 years ago

Is y= 5/2x - 3 and 5x = 2y - 4 parallel or perpendicular or neither?

PIT_PIT [208]

Answer:

Neither

Step-by-step explanation:

Parallel must have the same slope.

Perpendicular must have reciprocal slopes.

These two contain neither.

3 0

3 years ago

What is the distance between the points (7,3) and (-8, O) on a coordinate grid?​

What is the distance between the points (7,3) and (-8, O) on a coordinate grid?