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3 years ago

5.49 to the nearest cent

Mathematics

2 answers:

GrogVix [38]3 years ago

7 0

$5.50 would be the answer.

krok68 [10]3 years ago

7 0

5.50 I think that this is what it would be. Hope it helps!

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What is the equation of the line that goes through the points (1,2) and (2,1)?

Mandarinka [93]

Answer:

y = -x+3

Step-by-step explanation:

We have two points so we can find the slope

m =(y2-y1)/(x2-x1)

(1-2)/(2-1)

-1/1

The slope is -1

We can use the slope intercept form of the equation

y = mx+b where m is the slope and b is the y intercept

y = -x+b

Substitute a point into the equation to find b

2 = -1 +b

Add 1 to each side

2+1 =-1+1 +b

3 =b

y = -x+3

4 0

2 years ago

8 x - 4 (5 - x) = -44

Sphinxa [80]

8 x - 4 (5 - x) = -44

mutiply the bracket by -4

(-4)(5) = -20

(-4)(-x)= 4x

8x-20+4x= -44

8x+4x-20= -44 ( combine like terms )

12x-20= -44

move -20 to the other side

sign changes from -20 to +20

12x-20+20= -44+20

12x= -44+20

12x= -24

divide both sides by 12

12x/12= -24/12

Answer: x= -2

3 0

3 years ago

If you have the fraction 8/25, and you are trying to turn it into a decimal, which of the following would be helpful?

AysviL [449]

In this situation you will need to do 8 divided by 25 which will give the answer 0.32.

8 0

2 years ago

Read 2 more answers

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

sandy had 10 dollars in her collection. she gave 3 to her younger sister. her parents were so impressed that they quadrupled her

pantera1 [17]

(10-3)*4

Hope this helps!

7 0

3 years ago

Read 2 more answers