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3 years ago

What is the solution to this equation?

Mathematics

1 answer:

quester [9]3 years ago

4 0

Answer:

x = -7/2

Step-by-step explanation:

(1/4) ^ (x+1) = 32

Rewriting 32 as 2^5 and 1/4 and 2^-2

2^-2 ^ (x+1) = 2^5

We know that a^b^c = a^ ( b*c)

2 ^ (-2x-2) = 2 ^ 5

Since the bases are the same, the exponents have to be the same

-2x-2 = 5

Add 2 to each side

-2x = 7

Divide by -2

x = -7/2

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Please help me with the below question.

VMariaS [17]

By letting

$y = \displaystyle \sum_{n=0}^\infty c_n x^{n+r}$

we get derivatives

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

$y'' = \displaystyle \sum_{n=0}^\infty (n+r) (n+r-1) c_n x^{n+r-2}$

a) Substitute these into the differential equation. After a lot of simplification, the equation reduces to

$5r(r-1) c_0 x^{r-1} + \displaystyle \sum_{n=1}^\infty \bigg( (n+r+1) c_n + (n + r + 1) (5n + 5r + 1) c_{n+1} \bigg) x^{n+r} = 0$

Examine the lowest degree term $\left(x^{r-1}\right)$ , which gives rise to the indicial equation,

$5r (r - 1) + r = 0 \implies 5r^2 - 4r = r (5r - 4) = 0$

with roots at r = 0 and r = 4/5.

b) The recurrence for the coefficients $c_k$ is

$(k+r+1) c_k + (k + r + 1) (5k + 5r + 1) c_{k+1} = 0 \implies c_{k+1} = -\dfrac{c_k}{5k+5r+1}$

so that with r = 4/5, the coefficients are governed by

$c_{k+1} = -\dfrac{c_k}{5k+5} \implies \boxed{g(k) = -\dfrac1{5k+5}}$

c) Starting with $c_0=1$ , we find

$c_1 = -\dfrac{c_0}5 = -\dfrac15$

$c_2 = -\dfrac{c_1}{10} = \dfrac1{50}$

so that the first three terms of the solution are

$\displaystyle \sum_{n=0}^2 c_n x^{n + 4/5} = \boxed{x^{4/5} - \dfrac15 x^{9/5} + \frac1{50} x^{13/5}}$

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2 years ago

The position of an object at time t is given by s(t) = 1 - 12t. Find the instantaneous velocity at t = 2 by finding the derivati

yulyashka [42]

The change of displacement with respect to time is defined as speed. Velocity is a vector quantity. The instantaneous velocity at t = 2 is -12.

<h3>What is velocity?</h3>

The change of displacement with respect to time is defined as Velocity. velocity is a vector quantity. It is a time-based component. Its standard unit is m/sec.

Given that the position of an object at time t is given by s(t) = 1 - 12t. Therefore, the velocity of the object can be written as,

V = ds/dt

= d(1 - 12t)/dt

= -12

s'(t) = -12

Now, the instantaneous velocity at t=2 is,

s'(2) = -12

Hence, the instantaneous velocity at t = 2 is -12.

To learn more about Velocity:

brainly.com/question/862972

#SPJ1

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2 years ago

Find the product of 8 and 6

motikmotik

To find the product of 8 and 6 work out 8 multiplied by 6 which is 48

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3 years ago

A large farm has 75 acres of wheat and 62.5 acres with a new job . The farm crew can harvest the wheat from 12 acres and the cor

RSB [31]

Answer:

All the fields will be harvested in 6.25 days

Step-by-step explanation:

because 75 ÷ 12 and 62.5 ÷ 12 is 6.25

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3 years ago

In the interval,<br> [0,2), what are the solutionms of the equation sin x =-1/2?

kotykmax [81]

Answer:

Step-by-step explanation:

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3 years ago