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3 years ago

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A manufacturer determines that the cost of making a computer component is $4.191919. Write the repeating decimal cost as a frac

tion and as a mixed number.

1 answer:

tankabanditka [31]3 years ago

3 0

Let $x=4.191919\ldots$ . Then $100x=419.191919\ldots$ . So

$100x-x=99x=415$

$\implies x=\dfrac{415}{99}=4+\dfrac{19}{99}$

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Using a Line to Find a Point-Slope Equation and the Equivalent Function A coordinate grid with a line passing through the points

RoseWind [281]

Answer:

y = x/4 -1/2

Step-by-step explanation:

given coordinates : ( -2, -1 ) and ( 2 , 0 )

gradient = y2 - y1 / x2 - x1

= 0 - -1 / 2 - -2

= 1/4

equation of line:

y - y1 = m( x - x1 )

y - 0 = 1/4 ( x - 2 )

y = x/4 -1/2

the line shown below to confirm:

5 0

2 years ago

Read 2 more answers

Jean runs 8 mi and then rides 11 mi on her bicycle on a biathlon. She rides 9 mph faster than she runs. If the total time for he

Ipatiy [6.2K]

Let Jean's speed while running = x mph

Then Jean's speed while riding will be = x+9 mph

Distance covered by running = 8 miles

Distance covered by riding = 11 miles

Total time taken to complete the race = 1.5 hours

As, $time=\frac{distance}{speed}$

So, time for running= $\frac{8}{x}$

And time for riding= $\frac{11}{x+9}$

Equation becomes:

$\frac{8}{x}+\frac{11}{x+9}=1.5$

Now, multiply every term by 2x(x+9) to clear denominators:

$16(x+9)+22x=3x(x+9)$

Simplifying it we get

$3x^{2}-11x-144=0$

Solve the quadratic equation using formula

$x= \frac{-b+\sqrt{b^{2}-4ac }}{2a}$

putting a=3 , b= -11, c= -144

we get (x - 9)(3x + 16) = 0

where x=9 and x= $\frac{-16}{3}$

Neglect the negative answer as speed cannot be negative, so x = 9 mph

Hence, Jean's running speed is 9 mph and riding speed is x+9 = 9+9 = 18 mph

4 0

3 years ago

If f (n)(0) = (n + 1)! for n = 0, 1, 2, , find the taylor series at a=0 for f.

Pie

Given that $f^{(n)}(0)=(n+1)!$ , we have for $f(x)$ the Taylor series expansion about 0 as

$f(x)=\displaystyle\sum_{n=0}^\infty\frac{(n+1)!}{n!}x^n=\sum_{n=0}^\infty(n+1)x^n$

Replace $n+1$ with $n$ , so that the series is equivalent to

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}$

and notice that

$\displaystyle\frac{\mathrm d}{\mathrm dx}\sum_{n=0}^\infty x^n=\sum_{n=1}^\infty nx^{n-1}$

Recall that for $|x|$ , we have

$\displaystyle\sum_{n=0}^\infty x^n=\frac1{1-x}$

which means

$f(x)=\displaystyle\sum_{n=1}^\infty nx^{n-1}=\frac{\mathrm d}{\mathrm dx}\frac1{1-x}$
$\implies f(x)=\dfrac1{(1-x)^2}$

5 0

3 years ago

If I have (-2, 7) and (6, y) distancia = 10 . How can I find y?

shusha [124]

Answer:

y = 13

Step-by-step explanation:

Calculate the distance d using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 2, 7) and (x₂, y₂ ) = (6, y)

d = $\sqrt{(6+2)^2+(y-7)^2}$ , that is

d = $\sqrt{8^2+(y-7)^2}$ = 10

$\sqrt{64+(y-7)^2}$ = 10 ← square both sides

64 + (y - 7)² = 100 ( subtract 64 from both sides )

(y - 7)² = 36 ← take the square root of both sides

y - 7 = 6 ( add 7 to both sides )

y = 13

7 0

2 years ago

Find perimeter of the figure thanks and round to the nearest hundredth

Gnom [1K]

Answer:

40.56

Step-by-step explanation:

you need the circumference of the cirle aka perimeter of circle so 8(pi) and then because its only half, divided by 2... 12.56

now you hgave circumference so add 12.56 to 28 and there you go. you can round how ever necessary

7 0

3 years ago

Read 2 more answers