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laila [671]
3 years ago
6

Find the repeating decimal between -2 1/3 and -2 1/5.

Mathematics
1 answer:
Andrew [12]3 years ago
6 0

let's first off, make the mixed fractions to improper fractions and then <u>multiply one by the other's denominator</u>, that way both fractions have the same denominator, so let's start,

\bf \stackrel{mixed}{2\frac{1}{3}}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}}~\hfill \stackrel{mixed}{2\frac{1}{5}}\implies \cfrac{2\cdot 5+1}{5}\implies \stackrel{improper}{\cfrac{11}{5}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{multiplying one by the other's denominator}}{\cfrac{7}{3}\cdot \cfrac{5}{5}\implies \boxed{\cfrac{35}{15}}\qquad \qquad \cfrac{11}{5}\cdot \cfrac{3}{3}\implies \boxed{\cfrac{33}{15}}} \\\\[-0.35em] ~\dotfill

\bf \boxed{-\cfrac{35}{15}}\rule[0.35em]{9em}{0.25pt}~~\underset{\underset{\textit{\large -2.66666666...}}{\uparrow} }{-\cfrac{34}{15}}~~\rule[0.35em]{9em}{0.25pt}\boxed{-\cfrac{33}{15}}

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The table shows the cost of downloading songs.
Sonbull [250]

Answer:


Step-by-step explanation:

rate of change=cost per song

so the first option


3 0
3 years ago
Given isosceles right triangle CDE with m∠D = 90, sin C = sin D
Butoxors [25]

Answer:True

Step-by-step explanation:

Given

\angle D=90^{\circ}

For isosceles triangle , CD=DE (x=y)

from figure,

\sin C=\dfrac{y}{H}\\\\\sin D=\dfrac{x}{H}\\\\\text{CD=DE}\\\\\therefore \sin C=\sin D=\dfrac{x}{H}=\dfrac{y}{H}

Thus, the given statement is true

7 0
3 years ago
Solve these recurrence relations together with the initial conditions given. a) an= an−1+6an−2 for n ≥ 2, a0= 3, a1= 6 b) an= 7a
8_murik_8 [283]

Answer:

  • a) 3/5·((-2)^n + 4·3^n)
  • b) 3·2^n - 5^n
  • c) 3·2^n + 4^n
  • d) 4 - 3 n
  • e) 2 + 3·(-1)^n
  • f) (-3)^n·(3 - 2n)
  • g) ((-2 - √19)^n·(-6 + √19) + (-2 + √19)^n·(6 + √19))/√19

Step-by-step explanation:

These homogeneous recurrence relations of degree 2 have one of two solutions. Problems a, b, c, e, g have one solution; problems d and f have a slightly different solution. The solution method is similar, up to a point.

If there is a solution of the form a[n]=r^n, then it will satisfy ...

  r^n=c_1\cdot r^{n-1}+c_2\cdot r^{n-2}

Rearranging and dividing by r^{n-2}, we get the quadratic ...

  r^2-c_1r-c_2=0

The quadratic formula tells us values of r that satisfy this are ...

  r=\dfrac{c_1\pm\sqrt{c_1^2+4c_2}}{2}

We can call these values of r by the names r₁ and r₂.

Then, for some coefficients p and q, the solution to the recurrence relation is ...

  a[n]=pr_1^n+qr_2^n

We can find p and q by solving the initial condition equations:

\left[\begin{array}{cc}1&1\\r_1&r_2\end{array}\right] \left[\begin{array}{c}p\\q\end{array}\right] =\left[\begin{array}{c}a[0]\\a[1]\end{array}\right]

These have the solution ...

p=\dfrac{a[0]r_2-a[1]}{r_2-r_1}\\\\q=\dfrac{a[1]-a[0]r_1}{r_2-r_1}

_____

Using these formulas on the first recurrence relation, we get ...

a)

c_1=1,\ c_2=6,\ a[0]=3,\ a[1]=6\\\\r_1=\dfrac{1+\sqrt{1^2+4\cdot 6}}{2}=3,\ r_2=\dfrac{1-\sqrt{1^2+4\cdot 6}}{2}=-2\\\\p=\dfrac{3(-2)-6}{-5}=\dfrac{12}{5},\ q=\dfrac{6-3(3)}{-5}=\dfrac{3}{5}\\\\a[n]=\dfrac{3}{5}(-2)^n+\dfrac{12}{5}3^n

__

The rest of (b), (c), (e), (g) are solved in exactly the same way. A spreadsheet or graphing calculator can ease the process of finding the roots and coefficients for the given recurrence constants. (It's a matter of plugging in the numbers and doing the arithmetic.)

_____

For problems (d) and (f), the quadratic has one root with multiplicity 2. So, the formulas for p and q don't work and we must do something different. The generic solution in this case is ...

  a[n]=(p+qn)r^n

The initial condition equations are now ...

\left[\begin{array}{cc}1&0\\r&r\end{array}\right] \left[\begin{array}{c}p\\q\end{array}\right] =\left[\begin{array}{c}a[0]\\a[1]\end{array}\right]

and the solutions for p and q are ...

p=a[0]\\\\q=\dfrac{a[1]-a[0]r}{r}

__

Using these formulas on problem (d), we get ...

d)

c_1=2,\ c_2=-1,\ a[0]=4,\ a[1]=1\\\\r=\dfrac{2+\sqrt{2^2+4(-1)}}{2}=1\\\\p=4,\ q=\dfrac{1-4(1)}{1}=-3\\\\a[n]=4-3n

__

And for problem (f), we get ...

f)

c_1=-6,\ c_2=-9,\ a[0]=3,\ a[1]=-3\\\\r=\dfrac{-6+\sqrt{6^2+4(-9)}}{2}=-3\\\\p=3,\ q=\dfrac{-3-3(-3)}{-3}=-2\\\\a[n]=(3-2n)(-3)^n

_____

<em>Comment on problem g</em>

Yes, the bases of the exponential terms are conjugate irrational numbers. When the terms are evaluated, they do resolve to rational numbers.

6 0
2 years ago
Three friends were helping to push a car. If all three are pushing equally hard and the net force is 600N, how hard is each one
slavikrds [6]

Answer:

One person is pushing the car in the net force of 200N

Step-by-step explanation:

600 divided by 3 (600 N in total, and 3 person pushing.)

5 0
2 years ago
0.1067 as a fraction
aev [14]

Answer:

1067/10000

Step-by-step explanation:

simple

4 0
2 years ago
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