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3 years ago

SOMEONE PLEASE HELP EQUATION AND ANSWERS ARE ATTACHED IMAGES.

Mathematics

1 answer:

yulyashka [42]3 years ago

8 0

The value of a is 1/64.

Notice how the denominator in the fractions (right column) keep multiplying by 2.

32 * 2 = 64. So the answer is 1/64

You might be interested in

X, Y and Z form the vertices of a triangle. XY = 12.4m, XZ = 10.4m and YZ = 8.7m. Find the angle ∠ YXZ rounded to 1 DP.

sweet-ann [11.9K]

Answer:

43.8°

Step-by-step explanation:

Applying,

Cosine rule,

From the diagram attached,

x² = y²+z²-2yxcos∅.................... Equation 1

where ∅ = ∠YXZ

Given: x = 8.7 m, y = 10.4 m, z = 12.4 m

Substitute these values into equation 1

8.7² = 10.4²+12.4²-[2×10.4×12.4cos∅]

75.69 = (108.16+153.76)-(257.92cos∅)

75.69 = 261.92-257.92cos∅

collect like terms

257.92cos∅ = 261.92-75.69

257.92cos∅ = 186.23

Divide both sides by the coefficient of cos∅

cos∅ = 186.23/257.92

cos∅ = 0.722

Find the cos⁻¹ of both side.

∅ = cos⁻¹(0.7220)

∅ = 43.78°

∅ = 43.8°

6 0

3 years ago

1) Use power series to find the series solution to the differential equation y'+2y = 0 PLEASE SHOW ALL YOUR WORK, OR RISK LOSING

iogann1982 [59]

$y=\displaystyle\sum_{n=0}^\infty a_nx^n$

then

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

The ODE in terms of these series is

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

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

$\implies\begin{cases}a_0=y(0)\\(n+1)a_{n+1}=-2a_n&\text{for }n\ge0\end{cases}$

We can solve the recurrence exactly by substitution:

$a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0$

$\implies a_n=\dfrac{(-2)^n}{n!}a_0$

So the ODE has solution

$y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}$

which you may recognize as the power series of the exponential function. Then

$\boxed{y(x)=a_0e^{-2x}}$

7 0

3 years ago

Factor the polynomial 8x² − 24x − 224 completely. help now!

IgorLugansk [536]

Answer:

8 ( x − 7 ) ( x + 4 )

Step-by-step explanation:

7 0

3 years ago

What is the slope and y-intercept of the liner function y = -2/3x+3?

IrinaVladis [17]

Answer: (-2/3 , 3) is the answer

6 0

3 years ago

Find the minimum sample size needed to be 99% confident that the sample's variance is within 30% of the population's variance.

liq [111]

The Minimum sample size table is attached below

Answer:

$X=173$

Step-by-step explanation:

From the question we are told that:

Confidence Interval $CI=99\%$

Variance $\sigma^2=30\%$

Generally going through the table the

Minimum sample size is

$X=173$

7 0

2 years ago