Use inductive reasoning to find the next term in the sequence 0, 1, 1, 2, 3, 5, 8 …Answer is 13

Mathematics

1 answer:

expeople1 [14]3 years ago

6 0

Answer:

Step-by-step explanation:

Look carefully: you'll see that each new term is the sum of the previous two terms. The 3rd term is 0 + 1, or 1. The 4th term is 1 + 1, or 2. The 8th term is the sum of 5 and 8, or 13.

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Step-by-step explanation:

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Initially, there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A is used. It is observed that 15 grams

hram777 [196]

Answer:

$X(16)=25.71grams$

Step-by-step explanation:

let $X(t)$ denote grams of $C$ formed in $t$ mins.

For $X grams$ of $C$ we have:

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Amounts of A,B remaining at any given time is expressed as:

$40-\frac{2}{3}Xg$ of A and $50-\frac{1}{3}Xg$ of B

Rate at which C is formed satisfies:

$\frac{dX}{dt} \infty(40-\frac{2}{3}X)(50-\frac{1}{3}X)->\frac{dX}{dt}=k(90-X)\\\therefore \frac{dX}{(90-X)^2}=kdt->\int{\frac{dX}{(90-X)^2}} \, =\int {k} \, dt \\\therefore \frac{1}{90-X}=kt+c->90-X=\frac{1}{kt+c}\\\\X(t)=90-\frac{1}{kt+c}$