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2 years ago

The formula for the volume of this rectangular prism is:

Mathematics

1 answer:

juin [17]2 years ago

8 0

Answer:

Step-by-step explanation: Explanation:

and

represent the length, height and width of the prism, then the volume of the rectangular prism is :

............. (1)

Given :

−

;

............... (2)

(

−

)

;

(

)

Let

(

)

be the expression for the length, then the RHS of equation (1) becomes

(

−

)

(

)

(

−

)

(

)

(

−

)

(

)

(

−

)

(

)

(

−

)

−

..... (3)

Comparing this to the LHS of equation (1), we get the following set of equations to solve for

;

−

;

Therefore

(

)

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Answer:

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Step-by-step explanation:

f(x) = 7x + 7

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igor_vitrenko [27]

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Step-by-step explanation: First, swap the sides of the equation so that the one with the variable can be in front.

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3 years ago

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3 years ago

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Prove by mathematical induction that 1+2+3+...+n= n(n+1)/2 please can someone help me with this ASAP. Thanks

Iteru [2.4K]

Let

$P(n):\ 1+2+\ldots+n = \dfrac{n(n+1)}{2}$

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

$P(1):\ 1 = \dfrac{1\cdot 2}{2}=1$

So, the base case is ok. Now, we need to assume $P(n)$ and prove $P(n+1)$ .

$P(n+1)$ states that

$P(n+1):\ 1+2+\ldots+n+(n+1) = \dfrac{(n+1)(n+2)}{2}=\dfrac{n^2+3n+2}{2}$

Since we're assuming $P(n)$ , we can substitute the sum of the first n terms with their expression:

$\underbrace{1+2+\ldots+n}_{P(n)}+n+1 = \dfrac{n(n+1)}{2}+n+1=\dfrac{n(n+1)+2n+2}{2}=\dfrac{n^2+3n+2}{2}$

Which terminates the proof, since we showed that

$P(n+1):\ 1+2+\ldots+n+(n+1) =\dfrac{n^2+3n+2}{2}$

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