# 急 ! F5 變分計法 7q02

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12.

(a)

R : resistance

v : speed

R ∝ v³

Then, R = kv³

where k is constant.

When v = vo, R = Ro :

Ro = kvo³

When v = 2vo :

R = k(2vo)³

R = 8kv³

R = 8Ro

New resistance : Original resistance

= 8Ro : Ro

= 8 : 1

(b)

When v = vo(1 + 10%) :

R = k[vo(1 + 10%)]³

R = 1.331kvo³

R = 1.331Ro

% increase in resistance

= [(1.331Ro - Ro)/Ro] x 100%

= 33.1%

13.

W ∝ 1/d²

Then, W = k/d²

where k is constant.

When d = (6400 + 4200), W = 22 :

22 = k/(6400 + 4200)²

k = 22*(10600)²

Hence, W = 22*(10600)²/d²

When d = (6400 + 1500) :

W = 22*(10600)²/(6400 + 1500)²

W = 39.6

When the space shuttle is the nearest to the centre of the Earth,

the weight of the spaceman = 39.6 kg

14.

(a)

(To read the graph, read x-axis as "N" and y-axis as "E".)

(For example, a straight line y = x + 1 should read E = N + 1.)

E is partly constant C and partly varies directly as N.

Then, E = C + kN

where C and k are constant.

When N = 0, E = C

From the graph : When N = 0, E = 600

Then C = 600

(b)

Slope of the graph

= (1000 - 600)/(40 - 0)

= 10

vertical intercept = 600

(Slope-intercept form of a st. line : y = mx + c)

Equation of the graph (slope-intercept form) :

E = 10N + 600

E = 600 + 10N

(c)

E = 600 + 10N

When N = 50 :

E = 600 + 10(50)

E = 1100

Amount that each player pays

= \$1100/50

= \$22

資料來源： fooks