variation - Ans.fyi 參考答案

variation

[匿名]

2012-02-15 3:16 am

1.It is given that z varies directly as x and inversely as the product of y and w.When x:y=8:3and w =4,z=6
a)Find the value of z when w:x=2:5and y=10
b)Find the value of w when x:y=5:6 and z=4

2.Suppose r varies directly as the square root of v and inversely as the square root of h.Find the percentage change in r in each of the following cases.
a)h decreases by 50% and v increases by100%

3.It is known that the price($P) of a certain kind of precious marble stone varies directly as the cube of its length(l cm).Mr Chan uses$400 to buy a piece of the marble stone and cuts it into two pieces of equa; length.He then sells these two pieces of marble stone.Find Mr Chan's
a)profit or loss b)profit%or loss%

4.The time(t h)taken for a car to cover a certain journey varies inversely as the speed(v km/h) of the car.Suppose a car covers the journey in 2 hours at a speed of 80km/h
a)If the speed of the car increases by 20%,find the percentage change in the time taken for it to cover the same journey.

5.The resistance that a canoe experiences when it travels in water varies directly as the cube of its speed.
a)If the speed of the canoe doubles,find the ratio of the new resistance to the oringinal resistance.

thx a lot!

回答 (1)

Godfrey

2012-02-16 11:48 am

✔ 最佳答案

Let k = proportionality constant and * = multiply

1.
kx k8
z=---- 6 = --------
yw 3(4)

k = 12(6)/8 = 9

(a)
9(5)
z =------- = 2.25
10(2)
(b)
9(5)
4 =-------
6w

w = 1.875

2.
r = k(v)^0.5
------------
h^0.5

r(h^.5)/ (v)^.5 = k

r2(0.5h1)^0.5) r1(h1^0.5)
----------------- = ------------
(2v1)^0.5 v1^0.5

r2(0.5^0.5(h1)^0.5) r1(h1^0.5)
---------------------- = ------------
2^0.5(v1)^0.5 v1^0.5

r2(0.5^0.5 r1
-------------- = ------------
2^0.5 1

r2(0.5) = r1
r2 = 2r1
r increases by 100%

3.
P = kl^3
400 =kl^3
Pnew = 2k(0.5l)^3
Pnew = 2k(0.5)^3(l)^3
Pnew = 0.25k(l)^3
Pnew = 0.25($400) = $100
(a) loss % = $100 - $400 = -$300 (negative indicates loss)
loss = $300
(b) loss % = $300/$400* 100% = 75%

4.
t = k/v, so tv = k
tv = tnew(1.2v)
tnew = tv/1.2v = t/1.2 = 0.833t
% change in time = (0.833t – t)/7 * 100% = -16.67% (decrease in time)
No need to know the exact figures.
or
Distance = speed * time
Distance = 80 km/h * 2 h = 160 km
New time = 160 km/80km/h *1.2 = 2/1.2 h = 16.67 h
% change in time = (1.67 – 2)/2 * 100% = - 16.67% (decrease)

5.
R = kS^3
Rnew = k(2S)^3
Rnew = 8k(S)^3
Ratio Rnew/R = 8k(S)^3/kS^3=8/1
Ratio of the new resistance to the original resistance 8 to 1

👍 0 👎 0