Summation of 3n + 2 from n = 1 to n = 14 = (3(1) + 2) + (3(2) + 2) + (3(3) + 2) + . . . + (3(14) + 2) = 5 + 8 + 11 + ... + 44 ia an arithmetic progression with first term (a) = 5, common difference (d) = 3 and last term (l) = 44 and n = 14
Sn = n/2(a + l) = 14/2(5 + 44) = 7(49) = 343
Therefore, the required summation is 343.
Answer:
y=4x+8
Step-by-step explanation:
y=mx+b where m=slope and b=y-intercept
Answer:
Y=2
Step-by-step explanation:
4y+1=8
4×2=8+1=9
You'll do 4×2 which will equal right then plus 1 it'll equal 9.
a)
Lets p = # of fruit pies sold and j = # of bottles of fruit juice sold
Together both classes sold 79 items: p + j = 79
Fruit pie sold sold $1.65 each and bottle of fruit juice sold $1.36 each and together earned $118.17 = 1.65p + 1.36j = 118.17
Now you have two equations
p + j = 79 --> p = 79 - j
1.65p + 1.36j = 118.17
Substitute p = 79 - j into 1.65p + 1.36j = 118.17
1.65(79 - j) + 1.36j = 118.17
130.35 - 1.65j + 1.36j = 118.17
- 0.29j = - 12.18
j = 42
Substitue j = 42 into p = 79 - j
p = 79 - j = 79 - 42 = 37
# of fruit pies sold = 42 and # of bottles of fruit juice sold = 37
b)
Mr. Sanchez's class : $1.65 (37) = $61.05
Mr. Kelly's class: $1.36 (42) = $57.12
Mr. Sanchez's class sold more money than Mr. Kelly's class.
c)
$61.05 - $57.12 = $3.93
Mr. Sanchez's class earned $3.93 more than Mr. Kelly's class
The toal surface area of a cylinder is 2πrh+2πr²
Step-by-step explanation:
The "net" of any geometrical shape refers to the two-dimensional equivalents of the three-dimensional object.
e.g. geometrical net of a cylinder would consist of two circles (one each at top and bottom) and a rectangle extending from bottom to the top in a curvilinear manner.
Hence, the Total surface area (TSA) of the cylinder can be found
by considering cylinder to be made of three parts
- the circle at the bottom
- the circular tube which extends for height "h" of the cylinder
- the circle at the top (considering it is closed cylinder)
The surface area of a circle (for 2-dimensional figures surface area is the same as area since the thickness factor is 1)= πr²
Since there are two circles= surface area (combined)= 2πr²
Moreover, this circle extends to height h. Hence, the combined surface area of the circle extending to height h (int he forms of the tube)= circumference*height= 2πrh
hence TSA= 2πrh+ 2πr²
