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shutvik [7]
2 years ago
6

NO LINKS OR ASSESSMENT!!!Part 6: Write a rule to describe each transformation.​

Mathematics
1 answer:
Scrat [10]2 years ago
6 0

Answer:

  • (x, y) → (x, y - 3)

Step-by-step explanation:

We observe a vertical shift.

The shift is negative by 3 units.

<u>The rule for this translation is:</u>

  • (x, y) → (x, y - 3)
You might be interested in
y′′ −y = 0, x0 = 0 Seek power series solutions of the given differential equation about the given point x 0; find the recurrence
sukhopar [10]

Let

\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = a_0 + a_1x + a_2x^2 + \cdots

Differentiating twice gives

\displaystyle y'(x) = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n = a_1 + 2a_2x + 3a_3x^2 + \cdots

\displaystyle y''(x) = \sum_{n=2}^\infty n (n-1) a_nx^{n-2} = \sum_{n=0}^\infty (n+2) (n+1) a_{n+2} x^n

When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.

Substitute these into the given differential equation:

\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0

\displaystyle \sum_{n=0}^\infty \bigg((n+2)(n+1) a_{n+2} - a_n\bigg) x^n = 0

Then the coefficients in the power series solution are governed by the recurrence relation,

\begin{cases}a_0 = y(0) \\ a_1 = y'(0) \\\\ a_{n+2} = \dfrac{a_n}{(n+2)(n+1)} & \text{for }n\ge0\end{cases}

Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.

• If n is even, then n = 2k for some integer k ≥ 0. Then

k=0 \implies n=0 \implies a_0 = a_0

k=1 \implies n=2 \implies a_2 = \dfrac{a_0}{2\cdot1}

k=2 \implies n=4 \implies a_4 = \dfrac{a_2}{4\cdot3} = \dfrac{a_0}{4\cdot3\cdot2\cdot1}

k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}

It should be easy enough to see that

a_{n=2k} = \dfrac{a_0}{(2k)!}

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then

k = 0 \implies n=1 \implies a_1 = a_1

k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}

k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}

k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}

so that

a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}

So, the overall series solution is

\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = \sum_{k=0}^\infty \left(a_{2k}x^{2k} + a_{2k+1}x^{2k+1}\right)

\boxed{\displaystyle y(x) = a_0 \sum_{k=0}^\infty \frac{x^{2k}}{(2k)!} + a_1 \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}}

4 0
2 years ago
Which system is equivalent to
sammy [17]

<u>Answer:</u>

D) 6x^2 - 8y^2 = 50

-6x^2 - 2y^2 = 11

<u>Step-by-step explanation:</u>

We are given the following two expressions:

3x^2-4y^2=25

and

-6x^2-2y^2=11

Now if we look at the option D) 6x^2 - 8y^2 = 50&#10; and -6x^2 - 2y^2 = 11, we can observe that the earlier part in the given expression is just a simplification of 6x^2 - 8y^2 = 50.

6x^2 - 8y^2 = 50\\\\2(3x^2-4y^2) = 50\\\\3x^2-4y^2 = \frac{50}{2} \\\\3x^2-4y^2=25

and the later part -6x^2 - 2y^2 = 11 is already the same.

Therefore, the correct answer option is D)  6x^2 - 8y^2 = 50

-6x^2 - 2y^2 = 11.

6 0
3 years ago
Read 2 more answers
Find x. Then find the measure of angles A, B and C.
mafiozo [28]

Answer:

x= 11

A=59

B= 37

C = 84

Step-by-step explanation:

A triangle adds up to 180 °.

So the equation will be a °+ b° + c° = 180°

Next, you combine like terms.

6x + 3x + 9x+4-15-7 = 180\\18x-18=180

Then inverse operation,

18x-18=180\\18x=198\\x=11

After to get a, b, and c you just need to plug in x.

6(11)-7=a\\3(11)+4 = b\\9(11)-15=c

4 0
3 years ago
I need help with this problem. ​
MariettaO [177]

Answer:

the numbers next to a variable is a coefficient, for instance in 2x 2 would be the coefficient.

the constants are the numbers without variables next to them, just numbers

like terms are the term that are similar like 2x and 8x or even 5 and 3

lm not exactly sure what they mean when asking for constant terms.

4 0
2 years ago
Work out the length of X.
vlabodo [156]

Answer:

By Pythagoras theorem

H^2=P^2+B^2

25^2=x^2+24^2

625=x^2 + 576

625-576=x^2

49=x^2

x^2=49

x=√49

x=7cm

Hope this helps uhh

6 0
2 years ago
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