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3 years ago

What is the value of X in 1.2÷0.3= X÷0.4

Mathematics

2 answers:

sashaice [31]3 years ago

8 0

$1.2 \div .3 = 4$
$4 = x \div .4$
multiply both sides by .4 to isolate the x variable.

$4 \times .4 = x$

x = 1.6

Anna007 [38]3 years ago

8 0

X=1.6 because you have to divide 0.3 on each side then calculate the math and equal to x=1.6

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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

3 years ago

A baker decorates 42 cupcakes in 30 minutes. She decorates cupcakes at a constant rate. How many cupcakes can the baker decorate

jolli1 [7]

Divide 42 by 30 and that should be your correct answer.

hope this helps.

8 0

3 years ago

Read 2 more answers

Please help i need it !!!

Sedbober [7]

Answer:

x=7

Step-by-step explanation:

3 0

3 years ago

Whats the value of e? -(4e+7)=1

LekaFEV [45]

Answer:

-2

Step-by-step explanation:

-(4e+7)=1

-4e-7=1

-4e=1+7

-4e=8 divided both side by -4

e=-2

4 0

3 years ago

The length of the longer leg of a right triangle is 6 inches more than twice the length of the shorter leg. The length of the hy

Studentka2010 [4]

9514 1404 393

Answer:

15 in, 36 in, 39 in

Step-by-step explanation:

The Pythagorean theorem tells us that for short side x, the relation is ...

(2x +9)² = (2x +6)² +x²

4x² +36x +81 = 4x² +24x +36 +x²

x² -12x -45 = 0 . . . . . subtract the left-side expression

(x -15)(x +3) = 0 . . . . factor

x = 15 . . . . . . . . . . . the positive value of x that makes a factor zero

The side lengths of the triangle are 15 inches, 36 inches, and 39 inches.

6 0

3 years ago