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What does the Fibonacci sequence mean?
Fibonacci sequence is a sequence where each number is obtained by adding the two preceding numbers, starting from 0 and 1. That is, $T_n=T_{n-1}+T_{n-2}$, $T_1=0$, $T_2=1$.
Fibonacci sequence is a sequence where each number is obtained by adding the two preceding numbers, starting from 0 and 1. That is,
, 
, 
.
See lessCalculus assignment
The derivative of an implicit function, $x^2+y^2=9$ is $2x+2yy'=0\Rightarrow2yy'=-2x\Rightarrow y'=-\dfrac{x}{y}$ From, $x^2+y^2=9$, we have $y^2=9-x^2\Rightarrow y=\sqrt{9-x^2}$. Therefore, $y'=-\dfrac{x}{\sqrt{9-x^2}}$
The derivative of an implicit function,
is 
From,
, we have 
.
Therefore,
See lessScience – Physics
The wavelength ($\lambda$) of a wave with speed, $v$, and frequency, $f$, is given by $\lambda=\dfrac{v}{f}$. Here, $v=12$ m/s and $f=0.25$ s, therefore, $\lambda=\dfrac{12}{0.25}=48$ m.
The wavelength (
) of a wave with speed, 
, and frequency, 
, is given by 
.
Here,
m/s and 
s, therefore, 
m.
See lessOrdinary Annuity
The value of an annuity of $P$ peso paid $t$ times a year at a rate of $r$% compounded $t$ times a year for $n$ years is given by $FV=\dfrac{P\left(1+\frac{r}{t}\right)^{nt}}{\frac{r}{t}}$. Here, $p=10,000$, $t=12$ times a year (monthly), $r=9$% = 0.09, $n=5$ years. Thus, $FV=\dfrac{10000\left(1+\frRead more
The value of an annuity of
peso paid 
times a year at a rate of 
% compounded 
times a year for 
years is given by 
.
Here,
, 
times a year (monthly), 
% = 0.09, 
years.
Thus,
peso.
See lessDecimal to Binary Conversion
To convert a number to binary, we continuously divide the number by 2 and record the remainders. Thus, dividing 23 continuously by 2 gives 2 23 2 11 R 1 2 5 R 1 2 2 R 1 2 1 R 0 0 R 1 Reading the remainders from down up, we have that 23 to binary is 10111.
To convert a number to binary, we continuously divide the number by 2 and record the remainders.
Thus, dividing 23 continuously by 2 gives
Reading the remainders from down up, we have that 23 to binary is 10111.
See lesswhat is one to one fuction?
A function is said to be one-to-one if every element in the codomain is mapped to exactly one element in the domain. That is, no two elements in the domain map to one element in the codomain.
A function is said to be one-to-one if every element in the codomain is mapped to exactly one element in the domain.
That is, no two elements in the domain map to one element in the codomain.
See lessIf a x b = 2a – 3b + ab, then 3 x 5 + 5 x 3 is equal to?
Let x be a binary operation such that a x b = 2a - 3b + ab, then 3 x 5 = 2(3) - 3(5) + (3)(5) = 6 - 15 + 15 = 6, and 5 x 3 = 2(5) - 3(3) + (5)(3) = 10 - 9 + 15 = 16. Therefore, 3 x 5 + 5 x 3 = 6 + 16 = 22.
Let x be a binary operation such that a x b = 2a – 3b + ab, then 3 x 5 = 2(3) – 3(5) + (3)(5) = 6 – 15 + 15 = 6, and 5 x 3 = 2(5) – 3(3) + (5)(3) = 10 – 9 + 15 = 16.
Therefore, 3 x 5 + 5 x 3 = 6 + 16 = 22.
See lessPermutation problem
Any of the 15 contestants can take the 1st position. Any of the remaining 14 contestants (after the first position is selected) can take the 2nd position. And any of the remaining 13 contestants can take the 3rd position. Therefore, the number of ways, the first, second, and third positions can be sRead more
Any of the 15 contestants can take the 1st position. Any of the remaining 14 contestants (after the first position is selected) can take the 2nd position. And any of the remaining 13 contestants can take the 3rd position.
Therefore, the number of ways, the first, second, and third positions can be selected is given by
ways.
See lessmathematics for everyone
The probability that the first student cannot solve the problem is $1-\dfrac{1}{2}=\dfrac{1}{2}$. The probability that the second student cannot solve the problem is $1-\dfrac{1}{3}=\dfrac{2}{3}$. The probability that the third student cannot solve the problem is $1-\dfrac{1}{4}=\dfrac{3}{4}$. The pRead more
The probability that the first student cannot solve the problem is
.
The probability that the second student cannot solve the problem is
.
The probability that the third student cannot solve the problem is
.
The probability that none of the three students can solve the problem is
.
Thus, the probability that the problem is solved is
.
See lessCalculus and Trigonometry
To find the inverse of $f(x)=\ln(2x-3)+2$, first, for simplicity sake, let's substitute $y$ for $f(x)$ to get $y=\ln(2x-3)+2$. Next, subtract 2 from both sides to get $y-2=\ln(2x-3)$. Next, take the exponent of both sides to get $e^{y-2}=e^{\ln(2x-3)}=2x-3$. Next, add 3 to both sides to get $e^{y-2}Read more
To find the inverse of
, first, for simplicity sake, let’s substitute 
for 
to get 
.
Next, subtract 2 from both sides to get
.
Next, take the exponent of both sides to get
.
Next, add 3 to both sides to get
.
Next, divide through by 2 to get
.
Finally, we will substitute
for 
and 
for 
to get 
See less