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mixer [17]
3 years ago
15

What is the LCD of 3/10 and 7/15??

Mathematics
2 answers:
Maurinko [17]3 years ago
8 0
Least Common Denominator of 10 and 15 is 30.So 30 might be the denominator.Hope this helped.
Nitella [24]3 years ago
3 0
30 would be a great answer

Hope it helps!.!.!.!.!.!.!
You might be interested in
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
3 years ago
Can you help me? Look at the last question I posted as an example.
ivolga24 [154]

Step-by-step explanation:

1. (-3/2, 1)

2. (6,-3)

3. (8/3, 2)

4. <u>(</u><u>2</u><u>,</u><u>-4</u><u>)</u>

<u>5</u><u>.</u><u>(</u><u>-3</u><u>,</u><u>-1</u><u>)</u>

<u>6</u><u>.</u><u> </u><u>(</u><u>0</u><u>,</u><u>3</u><u>/</u><u>2</u><u>)</u>

<u>7</u><u>.</u><u> </u><u>(</u><u>4</u><u>,</u><u> </u><u>-2</u><u>)</u>

<u>8</u><u>.</u><u>(</u><u>8</u><u>,</u><u>2</u><u>)</u>

<u>9</u><u>.</u><u> </u><u>(</u><u>0</u><u>,</u><u>0</u><u>)</u>

8 0
3 years ago
Read 2 more answers
What is the vertex of y=-3x^2+6x+15? Help is much appreciated.
DENIUS [597]

Answer:

<u>(1, 18)</u>

Step-by-step explanation:

Rewrite the equation in vertex form by completing the square for -3x^2 + 6x + 15. This = -3(x - 1)^2 + 18.

Set y equal to the new right side.

y = -3(x - 1)

Use the vertex form, y = a(x - h)^2 + k, to determine the values of a, h, and k.

a = -3

h = 1

k = 18

Vertex = (h, k) / (1, 18)

5 0
3 years ago
PLEASE help me with this question! This is really urgent! No nonsense answers please.
algol [13]

Answer:

The last answer choice: Jalon can score 10 times as many points in the next level as in the level he has reached.

Step-by-step explanation:

For every level increase the number of points is multiplied by 10.  So after reaching the first level, Jalon will have 10 points.  After the second level, 100 points.  After the thierd level, 1000 points.  After the fourth level, 10000 points, and so on like that.

5 0
3 years ago
Fabio drinks 2 quarts of water each day. How many cups of water does Fabio drink each day? (1 quarts = 4 cups
Westkost [7]

If Fabio drinks 2 quarts of water each day, he would drink 8 cups of water in accordance with direct proportion.

<h3>What is a proportion?</h3>

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, a direct proportion can be represented by the following equation:

y = kx

Where:

  • y and x are the variables.
  • k represents the constant of proportionality.

By applying direct proportion, we have:

1 quarts = 4 cups

2 quarts = X cups

Cross-multiplying, we have:

X = 4 × 2

X = 8 cups.

In conclusion, the quantity of water which Fabio drinks each day is equal to 8 cups.

Read more on direct proportion here: brainly.com/question/1266676

#SPJ1

5 0
1 year ago
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