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AlekseyPX
3 years ago
7

What is the solution to the equation below?

Mathematics
1 answer:
lara31 [8.8K]3 years ago
8 0

Answer:

x=4096, Option B

Step-by-step explanation:

Given, \log_{8}x=4

Formula needed,

\log_{a}b=\frac{\log b}{\log a}

Therefore,

\log_{8}x=\frac{\log x}{\log 8}

\frac{\log x}{\log 8}=4

{\log x}=4{\log 8}

\log x={\log 8^4}

x=8^4

x=4096

Option B is correct.

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Use appropriate algebra and theorem 7. 2. 1 to find the given inverse laplace transform. (write your answer as a function of t.
ollegr [7]

The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.

According to the statement

we have to find the inverse of the Laplace theorem with the help pf the given theorem in the statement.

So, For this purpose, we know that the

Laplace transformation is a transformation of a function f(x) into the function g(t) that is useful especially in reducing the solution of an ordinary linear differential equation with constant coefficients to the solution of a polynomial equation.

Now, We assume you want to find the inverse transform of s/(s^2 +3s -4).

This can be written in partial fraction form as

\frac{(4/5)}{(s+4)} + \frac{(1/5)}{(s-1)}

which can be found in a table of transforms to be the transform of

\frac{4}{5} e^{-4t} + \frac{1}{5} e^t

There are a number of ways to determine the partial fractions. They all start with factoring the denominator.

s^2 +3x -4 = (s+4)(s-1)

After that, you can postulate the final form and determine the values of the coefficients that make it so.

For example:

\frac{A}{(s+4)}  + \frac{B}{s-1}  = (A+B)s + \frac{(4B-A)}{(s^2 +3x -4)}

This gives rise to two equations:

(A+B) = 1

(4B-A) = 0.

So, The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) ℒ−1 s s2 + 3s − 4.

Learn more about Laplace here

brainly.com/question/11630973

#SPJ4

3 0
2 years ago
Which ordered pair is a solution of 6x+3y=15
victus00 [196]
6•2+3•1=15 is the answer
5 0
3 years ago
The surface area of a melting snowball decreases at a rate of3.8cm2/min. Find the rate at which its diameter decreases when the
Scorpion4ik [409]

Answer:

Step-by-step explanation:

This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.

We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of

S=4\pi r^2

In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that

d = 2r so

\frac{d}{2}=r Now we can have the equation in terms of diameter instead of radius. Rewriting:

S=4\pi(\frac{d}{2})^2 which simplifies to

S=4\pi(\frac{d^2}{4}) and a bit more to

S=\pi d^2 (the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.

\frac{dS}{dt}=\pi*2d\frac{dD}{dt} Now let's look at the problem and see what we are given as far as information.

The rate at which the surface area changes is -3.8, and we are looking for \frac{dD}{dt}, the rate at which the diameter is changing, when the diameter is 13. Filling in:

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7 0
3 years ago
Ill mark brainliest!!
Anastasy [175]

Answer:

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Step-by-step explanation:

So from the question, we need to find the fixed amount for the tv's. So we have to make an equation, and don't forget to add the extended warranties:

11(x + 25) = 935

x will represent a tv, and the 25 is the extended warranty for a tv, since the questions states 11 tv's with warranties is 935, the equation will look like that. Now lets slove:

11(x + 25) = 935

multiply

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subtract 275 from both sides

11x = 660

divide both sides by 11

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3 years ago
The Eiffel Tower in Paris France has 674 steps that go from the ground to second floor there are 328 steps from ground to first
Radda [10]

Answer:

346

Step-by-step explanation:

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