diff options
Diffstat (limited to 'Basic_Engineering_Mathematics_by_John_Bird/CH27')
14 files changed, 233 insertions, 0 deletions
diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.1/Ex27_1.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.1/Ex27_1.R new file mode 100644 index 00000000..8875da74 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.1/Ex27_1.R @@ -0,0 +1,12 @@ +#page no. 279
+#problem 1
+#formula used: circumference of circle = 2*pi*r
+
+peri_circle = function(r)
+{
+ return(pi*r*2)
+}
+
+#given:
+r = 12 #radius of circle
+print(peri_circle(r))
\ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.10/Ex27_10.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.10/Ex27_10.R new file mode 100644 index 00000000..941ac028 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.10/Ex27_10.R @@ -0,0 +1,22 @@ +#page no. 282
+#problem 10
+#formula used: area of circle = pi*r^2
+# cicumference of circle = 2*pi*r
+
+area_circle = function(r)
+{
+ return(pi*r^2)
+}
+
+radius_cir <- function(cir)
+{
+ r = cir/(2*pi)
+ return(r)
+}
+
+
+#given:
+circ = 60 # circumference of circle
+r = radius_cir(circ)
+area = area_circle(r) #area of circle
+print(area)
\ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.11/Ex27_11.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.11/Ex27_11.R new file mode 100644 index 00000000..f6e125a7 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.11/Ex27_11.R @@ -0,0 +1,10 @@ +#page no. 282
+#problem 11
+#formula used: length of arc = r*theta
+arc_length = function(r,theta)
+{return(r*theta)}
+#given:
+r = 5.5 #radius of circle
+theta = 1.20 # angel subtended at center in radians
+s = arc_length(r,theta) # length of arc
+print(s)
\ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.12/Ex27_12.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.12/Ex27_12.R new file mode 100644 index 00000000..d46f903d --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.12/Ex27_12.R @@ -0,0 +1,21 @@ +#page no. 282
+#problem 12
+#formula used: length of arc = r*theta
+
+arc_radius = function(s,theta)
+{return(s/theta)}
+
+peri_circle = function(r)
+{
+ return(pi*r*2)
+}
+
+#given:
+
+s = 4.75 #arc of length
+theta = 0.91 # angle in radian
+r = arc_radius(s,theta)
+dia = 2*r
+print(dia) # diameter of circle
+
+print(peri_circle(r)) # circumference of circle
\ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.13/Ex27_13.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.13/Ex27_13.R new file mode 100644 index 00000000..b68164b3 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.13/Ex27_13.R @@ -0,0 +1,27 @@ +#page no. 282
+#problem 13
+# formula used: minor arc = r*theta
+# circumference of circle = 2*pi*r
+# major arc = circumference - minor arc
+
+deg2rad <- function(deg) {return((deg * pi) / (180))} #degree to radian
+
+peri_circle = function(r)
+{
+ return(pi*r*2)
+}
+
+arc_length = function(r,theta)
+{return(r*theta)}
+
+#given:
+r = 8.4# radius of circle
+theta = 125 # angle in degree
+rad = deg2rad(theta) #angle in radian
+#part(a)
+minor_arc = arc_length(r,rad)
+print(minor_arc)
+#part(b)
+major_arc = peri_circle(r) - minor_arc
+print(major_arc)
+
diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.15/Ex27_15.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.15/Ex27_15.R new file mode 100644 index 00000000..829e4280 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.15/Ex27_15.R @@ -0,0 +1,20 @@ +#page no. 282
+#problem 15
+#formula used: area of sector = (1/2)*r^2*theta
+
+deg2rad <- function(deg)#degree to radian
+ {
+ return((deg * pi) / (180))
+ }
+
+
+area_sector<- function(theta,r)
+{
+ a = (1/2)*r^2*theta
+}
+#given:
+r = 55 #radius of stadium
+theta = 45 #angle in degree
+rad = deg2rad(theta) #angle in radian
+area = area_sector(rad,r) # maximum area
+print(area)
\ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.16/Ex27_16.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.16/Ex27_16.R new file mode 100644 index 00000000..d4758088 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.16/Ex27_16.R @@ -0,0 +1,13 @@ +#page no. 282
+#problem 15
+#formula used: area of sector = (1/2)*r^2*theta
+angle = function(r,area)
+{theta = (area*2)/r^2}
+rad2deg <- function(rad) {return((rad * 180) / (pi))} #radian to degree
+#given:
+r = 1.8 #radius of garden sprayer distance
+area = 2.5 # area of sector sprayed
+theta = angle(r,area) # angle in radian
+print(theta)
+degree = rad2deg(theta) #angle in degree
+print(degree)
diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.2/Ex27_2.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.2/Ex27_2.R new file mode 100644 index 00000000..02731d8d --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.2/Ex27_2.R @@ -0,0 +1,13 @@ +#page no. 279
+#problem 2
+#formula used: circumference of circle = 2*pi*r
+
+peri_circle = function(r)
+{
+ return(pi*r*2)
+}
+
+#given:
+dia = 75 #diameter of circle
+r = dia/2 #radius of circle
+print(peri_circle(r))
\ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.3/Ex27_3.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.3/Ex27_3.R new file mode 100644 index 00000000..6cc2d87e --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.3/Ex27_3.R @@ -0,0 +1,14 @@ +#page no. 279
+#problem 3
+#formula used: circumference of circle = 2*pi*r
+
+radius_cir <- function(cir)
+{
+ r = cir/(2*pi)
+ return(r)
+}
+
+#given:
+circ = 112
+radius = radius_cir(circ)
+print(radius)
\ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.4/Ex27_4.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.4/Ex27_4.R new file mode 100644 index 00000000..5504b4c6 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.4/Ex27_4.R @@ -0,0 +1,17 @@ +#page no. 279
+#problem 4
+#formula used: pythagoras theorem
+
+hypotenuse <- function(b,p)
+{
+ h = sqrt(b^2+p^2)
+ return(h)
+}
+
+#given:
+ab = 150 # tangent to circle
+ # act as perpendicular height
+ r = 40 #radius of circle(base)
+ ao = hypotenuse(r,ab)
+ print(ao)
+
\ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.5/Ex27_5.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.5/Ex27_5.R new file mode 100644 index 00000000..c3fbbdb9 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.5/Ex27_5.R @@ -0,0 +1,22 @@ +#page no. 280
+#problem 5
+#formula used:
+
+deg2rad <- function(deg) {return((deg * pi) / (180))} #degree to radian
+
+deg2rad_min = function(angle,min) #degree to radian while min are given
+{
+ deg = ((angle*60)+min)/60
+ return(deg2rad(deg))
+}
+#part(a)
+ #given:
+ d1 = 125 # angle in degree
+ print(deg2rad(d1))
+
+
+#part(b)
+ #given:
+ d2_angle = 69 # angle in degree and minutes
+ d2_min = 47 # 69 degree and 47 minutes
+ print(deg2rad_min(d2_angle,d2_min))
\ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.6/Ex27_6.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.6/Ex27_6.R new file mode 100644 index 00000000..7c31e6ad --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.6/Ex27_6.R @@ -0,0 +1,15 @@ +#page no. 281
+#problem 6
+#formula used: degrees to minutes
+rad2deg <- function(rad) #radian to degree
+{return((rad * 180) / (pi))}
+
+ #part(a):
+ #given:
+ rad1 = 0.749
+ print(rad2deg(rad1)) #in degree
+
+ #part(b):
+ #given:
+ rad2 = (3*pi)/4
+ print(rad2deg(rad2)) #in degree
\ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.8/Ex27_8.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.8/Ex27_8.R new file mode 100644 index 00000000..38ca7912 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.8/Ex27_8.R @@ -0,0 +1,13 @@ +#page no. 281
+#problem 8
+#formula used: area of semi circle = area of circle/2
+
+area_circle = function(r)
+{
+ return(pi*r^2)
+}
+
+#given:
+r = 14.63 #radius of semicircle
+area = (1/2)*area_circle(r) #area of semicircle
+print(area)
\ No newline at end of file diff --git a/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.9/Ex27_9.R b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.9/Ex27_9.R new file mode 100644 index 00000000..3a1f1ad7 --- /dev/null +++ b/Basic_Engineering_Mathematics_by_John_Bird/CH27/EX27.9/Ex27_9.R @@ -0,0 +1,14 @@ +#page no. 282
+#problem 9
+#formula used: area of circle = pi*r^2
+
+area_circle = function(r)
+{
+ return(pi*r^2)
+}
+
+#given:
+dia = 35.0 #diameter of circle
+r = dia/2 #radius of circle
+area = area_circle(r) #area of circle
+print(area)
\ No newline at end of file |