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3 years ago

Write an expression that is equivalent to the expression 4n-n+0.5n-2n

Mathematics

1 answer:

FinnZ [79.3K]3 years ago

4 0

Answer:

1.5n

Step-by-step explanation:

The distributive property can be used to simplify expressions like this (collect terms).

= n(4 -1 +.5 -2)

= n(3 +.5 -2)

= n(3.5 -2)

= n(1.5)

= 1.5n

_____

Of course, you can do the addition in any convenient way. Some like to add all the positive and negative terms, then find the difference.

= n((4 +.5) -(1 +2)) = n(4.5 -3) = 1.5n

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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

How many solutions does 2.3y+3.2-y=2.1+1.3y+1.1 have?

jeka57 [31]

1.3y +3.2 = 1.3y +3.2

we notice that both sides of the equation are identical. So substitute y with any value and the equation would still be correct.

y has infinite solutions.

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3 years ago

A trapezoid has an area of 30m^2. if all of its side lengths are tripled, what will its new area be

Norma-Jean [14]

Answer:

270

Step-by-step explanation:

Because we do not know what the side lengths are, as long as they multiply to 30m^2, it's fine

For this question, let's just say the base is 5, and the height is 6. If we triple 5, we get 15, and if we triple 6, we get 18. 15*18=270

Now what if, the sides are not 5 and 6. Will the area still be the same? Let's find out.

10*3=30 so we can say for this answer, the base is 3, and the height is 10.

10 tripled is 30, and 3 tripled is 9. 30*9=270

So as we look at these 2 answers. we can conclude that the new area, no matter the side lengths, will be 270

Hope this helpes!

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4 years ago

joseph is shopping for school supplies he can buy a box of 24 pens for $4.32 or a box of 36 pens for $5.76. which is a better bu

Ugo [173]

I would say it’s better to buy the 36 box pens. 24\4.32=5.6 on the other hand the box of 36 is 36/5.76=6.25

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3 years ago

"3. When we have two sorted lists of numbers in non-descending order, and we need to merge them into one sorted list, we can sim

iren [92.7K]

Answer:

Since we extract n elements in total, the algorithm for the running time for K sorted list is O (n log k+ k) = O (n log k)

Step-by-step explanation:

To understand better how we arrived at the aforementioned algorithm, we take it step by step

a, Construct a min-heap of the minimum elements from each of "k" lists.

The creation of this min-heap will cost O (k) time.

b) Next we run delete Minimum and move the minimum element to the output array.

Each extraction takes O (log k) time.

c) Then insert into the heap the next element from the list from which the element was extracted.

Now, we note that since we extract n elements in total, the running time is

O (n log k+ k) = O (n log k).

So we can conclude that :

Since we extract n elements in total, the algorithm for the running time for K sorted list is O (n log k+ k) = O (n log k)

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3 years ago