#### Exercícios - Aula 2: Funções Matemáticas - Monitoria 2010


getwd()
setwd ("C:/Users/Barbara/Documents/Mestrado/Monitoria/aula funcoes")


##########	Biomassa de Árvores	##########

e<- exp(-1.7953)
e
d<- 15^2.2974
d
modelo1<-e*d
modelo1      #### biomassa modelo 1 = 83.61095
help(log)
ln.b<- -2.6464+1.9960*log(15,base=exp(1))+0.7558*log(12,base=exp(1))
ln.b
b<-exp(4.63691)
b           ####biomassa modelo 2 = 103.2249
## Os modelos resultaram em estimativas bastante distintas.

a<-exp(1)
a
?exp

##########	Sequências	##########

  
rep ("a",6)		####“a” “a” “a” “a” “a” “a”

rep (c(1,2,3),each=3)	####1 1 1 2 2 2 3 3 3

rep (1:3, c(3,2,1))	#### 1 1 1 2 2 3

rep (c((1:5),(4:1)), length=9)	####1 2 3 4 5 4 3 2 1
sequencia<-c(seq(from=1,to=5),seq(from=4,to=1))
sequencia

seq (1,99,by=2)		####Números ímpares de 1 a 99

?rep
rep(1:4, 2)
rep(1:4, each = 2)       # not the same.
rep(1:4, c(2,2,2,2))     # same as second.
rep(1:4, c(2,1,2,1))
rep(1:4, each = 2, len = 4)    # first 4 only.
rep(1:4, each = 2, len = 10)   # 8 integers plus two recycled 1's.
rep(1:4, each = 2, times = 3)  

?seq
seq(0, 1, length.out=11)
seq(stats::rnorm(20))
seq(1, 9, by = 2) # match
seq(1, 9, by = pi)# stay below
seq(1, 6, by = 3)
seq(1.575, 5.125, by=0.05)
seq(17) # same as 1:17

##########	Conta de Luz	##########

consumo<-c(9839,10149,10486,10746,11264,11684,12082,12599,13004,13350,13717,14052)
consumo.diff<-diff(consumo)
consumo.diff
range (consumo.diff) ### min= 260; máx= 518
mean (consumo.diff)  ### media= 383
median (consumo.diff)### mediana=367
var(consumo.diff)	   ### variancia=6476,2

##order(consumo.diff)  ###mediana=367
##sort(consumo.diff)

##########	Área Basal	##########

### A=pi*r^2

dap<-13.5
area<- pi*(dap/2)^2
area	### 143.1388 cm2

(8/2)^2

area2 <- (pi*(7/2)^2)+(pi*(9/2)^2)+(pi*(12/2)^2)
area2	### 251.1991cm2

##########	Variância na Unha	##########

### var= SOMA[(x-media)^2]
### dp= raiz da var

pesos <- c(78.4, 79.8, 76.0, 75.3, 77.4, 78.6, 77.9, 78.8, 79.2, 75.2, 75.0, 79.4)
media<- mean (pesos)
media
length(pesos)
media.rep<-rep (media,12)
media.rep
dife<- (pesos-media)^2
dife
v<-sum (dife)	###var=34.21667

desvio <- sqrt (v)	#### desvio=5.849501
desvio

##########	Teste t	##########

probt<-2*pt(2.2,19,lower.tail=FALSE)
probt  #### o teste é significativo, pois a probabilidade encontrada foi de 0.0403811<0.5.
probt1.9<-2*pt(1.9,19,lower.tail=FALSE)
probt1.9  ### para t=1.9 o teste não é significativo, pois a probabilidade encontrada foi de 0.0727184>0.5.