These are some maths gcse questions pls answer
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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
This can be written in partial fraction form as
which can be found in a table of transforms to be the transform of
There are a number of ways to determine the partial fractions. They all start with factoring the denominator.
After that, you can postulate the final form and determine the values of the coefficients that make it so.
For example:
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
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Let us translate the sentences to mathematics for ease!
A 3-digit number
Ones digit → ( let p represent is )
Hundreds digit is four more than ones digit → ( 4 + p )
Tens digit is twice hundreds digit → 2 ( 4 + p ) = 8 + 2p
Sum of the digits is 12
↓
Hundreds digit + Tens digit + Ones digit = 12
( 4 + p ) + ( 8 + 2p ) + p = 12
Combine like terms
4 + 8 + p + p + 2p = 12
12 + 4p = 12
Take 12 to the opposite side { Do subtraction when you see addition }
12 ( - 12 ) + 4p = 12 - 12
4p = 0
Divide by 4 on either side
p = 0
( 4 + 0 ) + ( 8 + 2 ( 0 ) ) + ( 0 )
The number is 480
Check
Hundreds + Tens + Ones = 12
4 + 8 + 0 = 12
12 = 12
Let us translate the sentences to mathematics for ease!
A 3-digit number
Ones digit → ( let p represent is )
Hundreds digit is four more than ones digit → ( 4 + p )
Tens digit is twice hundreds digit → 2 ( 4 + p ) = 8 + 2p
Sum of the digits is 12
↓
Hundreds digit + Tens digit + Ones digit = 12
( 4 + p ) + ( 8 + 2p ) + p = 12
Combine like terms
4 + 8 + p + p + 2p = 12
12 + 4p = 12
Take 12 to the opposite side { Do subtraction when you see addition }
12 ( - 12 ) + 4p = 12 - 12
4p = 0
Divide by 4 on either side
p = 0
( 4 + 0 ) + ( 8 + 2 ( 0 ) ) + ( 0 )
The number is 480
Check
Hundreds + Tens + Ones = 12
4 + 8 + 0 = 12
12 = 12
Answer:
Option C
10%
Step-by-step explanation:
Given information
Cost of investment=$20000
Selling price=$22000
Profit=Selling price-Cost of investment=22000-20000=2000
Return on investment=profit/cost of investment