Answer:
See below
Step-by-step explanation:
See attached for reference
The path has been created by bikers is almost a right triangle with sides of 12, 21 and 24 miles and angles of 61, 89 and 30 deg
a) Biker A travels a straight line (hypotenuse of triangle)
It is likely the bikers meet at the bottom point of the triangle
They make almost same displacement from the start point:
24 miles ≈ √12²+21² miles
b) they meet each other
c) 30 deg
d) e) as per picture attached, it is almost right triangle
f) Together they traveled 12+21+24= 57 miles
Answer:
56
Step-by-step explanation:
Given that there are 8 candidates for student government: Hal, Mary, Ann, Frank, Beth, John, Emily, and Tom.
The three candidates that receive the highest number of votes become candidates for a runoff election.
i.e. 3 persons out of 8 to be selected for becoming candidates for a runoff election.
Since order does not matter we use combinations here
3 persons out of 8 can be done in 8C3 ways
= 56
no of 3-candidate combinations possible are 56
Answer:
$4182.7
Step-by-step explanation:= 4000*(1.5%)*3
Year 1= 4000*(100%+1.5%)= 4060
Year 2= 4060*(100%+1.5%)= 4120.9
Year 3= 4120.9*(100%+1.5%)= 4182.7
Answer:
$163.54
Step-by-step explanation:
Volume of rectangular container = 10m^3
Length = 2(width)
Material for the base cost $10 per square meter
Material for the side cost $6 per square meter
Volume = L*B*H
L= 2W
V = (2W).W. H
10 = 2W^2.H
H = 10 /2W^2
H = 5/W^2
Let C(w) = cost function
C(w) = 10(L.W) + 6(2.L.H + 2.W.H)
= 10(2W.W) + 6(2.2W.H + 2.W.H)
= 10(2W^2) + 6(4W.H + 2.W.H)
= 10(2W^2) + 6(4W*5/W^2 + 2.W*5/W^2)
= 20W^2 + 6(20/W + 10/W)
= 20W^2 + 6((10+20)/W)
= 20W^2 + 6(30/W)
C(w) = 20W^2 + 180/W
To find the minimum value, differentiate C with respect to w
C'(w) = 40W - 180/W^2
Put C'(w) = 0
0 = 40W - 180/W^2
40W = 180/W^2
40W^3 = 180
W^3 = 180/40
W^3 = 4.5
W = cube rt(4.5)
W = 1.65m
C = 20(1.65)^2 + 180/1.65
C = 54.45 + 109.09
C= $163.54
Minimum cost = $163.54
To write the coefficients of the 8 terms, either start with a combination of 7 things taken 0 at a time and continue to 7 things taken 7 at a time or use the 7th row of Pascal’s triangle.
For the first term, write x to the 7th power and 3 to the 0 power. Then decrease the power on x and increase the power on y until you reach x to the 0 and y to the 7.
Simplify by evaluating the coefficients and powers 3
Step-by-step explanation:
