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hoa [83]
3 years ago
13

A rectangular prism has a length of 3/4 cubic inch and a width of 1/2 inch. The volume is 21/32 cubic inch. Find the height of t

he prism. Write your answer as a mixed number in simplest form.
Mathematics
2 answers:
Oliga [24]3 years ago
7 0
21 / 32 = (3/4) * (1/2) * height

21 / 32 = (3 / 8) * height

21 / 32 * (3 / 8) = height =

63 / 256 inches



Paraphin [41]3 years ago
3 0

Answer:

\texttt{Height of the prism}=1\frac{3}{4}

Step-by-step explanation:

Volume of rectangular prism = Length x Width x Height

\texttt{Volume of rectangular prism =}\frac{21}{32}\\\\\texttt{Length =}\frac{3}{4}\\\\\texttt{Breadth =}\frac{1}{2}

Substituting

      \frac{21}{32}=\frac{3}{4}\times \frac{1}{2}\times h\\\\h=\frac{7}{4}=\frac{4+3}{4}=1\frac{3}{4}

    \texttt{Height of the prism}=1\frac{3}{4}

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frutty [35]
<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

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then we have:

2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2

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i.e.

<u>To prove:</u>  2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

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( Since, the result was true for n=k )

Hence, we have:

2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2

Also, we know that:

-2

(

Since, for n=k+1 being a positive integer we have:

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2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

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Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

2^n\leq 2^{n+1}-2^{n-1}-1  where n is a positive integer.

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