D is partly constant and partly varies with V. when V=40, D=150 and when V=54, D=192.
(i)find the formula connecting D and V
(ii) find D when V =73.
D=av+b
solving for a and b
when v=40,D=150 and when v=54,D=192
150=40a+b.........(1)
192=54a+b.........(2)
Subtract (2) from (1)
42=14a
divide both sides by 14
a=3
Substitute a =3 into (1)
150=40×3+b
150=120+b
b=30.
a) find the relationship
D=av+b
D=3v+b
b) find D when v=73
D=3×73+30
D=249
D = mV + C , ( compare this to your familiar y = mx + b)
when V=40, D=150
150 = 40m + C **
when V=54, D=192
192 = 54m + C ***
subtract ** from ***
42 = 14m
m = 3
sub into ** , 150 = 120 + C
C = 30
so you have D = 3V + 30
sub in your given value of V
D=av+b
Solution for a and b
When v=40,D=150 and when v=54, D=192
150=40a+b..........(1)
192=54a+b..........(2)
Subtract (1) from (2)
(192=54a+b - 150=40a+b)
42=14a+0
Therefore:- 42=14a
Divide both sides by the co-efficient of (a) which is 14
a=3
Substitute a=3 into (1)
150=40×3+b
150=120+b
Collect like terms
b=150-120
b=30
i. The formula connecting D and V
D=av+b
D=3v+b
ii. D when V=73
D=av+b
D=3v+b
D=(3×73)+30
D=219+30
D=249
Divine is right
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x is partly constant and partly various as y, when y=2, x=0 and when y=6, x=20.
Find x when y=3.
Solution.
x=ky + c
0=2k + c ----<1>
20=6k + c ----<2>
Substrate 1 from 2
20 = -4k
Add 4 to both side
20+4 = -4+4k
24=k
Sub.k=24 into <1>
0=2×24+c
0=48+c
C=48
find x when y=3
x = ky + c
x = 24×3+48
x=120//
D=k+mV.
V=40,D=150
150=k+40m
V=54,D=192
192=k+54m(3)-(1):42=14m
m=42/14=3
Substitute for m in (1)
150-k+40(3)
K=150-120=30
So: (i) formulary is D=30+3v
(ii)v=73,d=30+3(73)
=249
2##2₦34479
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D is partly constant and partly varies V,when V=40,D=150 and when V=54,D=192
Find the formula connecting D and V
Find D when V=73
D=av+b solving for a and b when V=40,D=150 and when V=54,D=192 150=40 a+b _(1) 192=549+b_(2) subtract (2)from(1)42=149 Divide both sides by 14 9=3substitute 9=3 into (1) 150=40*3+B150=120+B B=30
The formula connecting D and V is: D = 3V + 30
When V = 73:
D = 3(73) + 30
D = 219 + 30
D = 249.
Find the formula connecting D and V
Let D be partly constant and partly vary with V. When V = 40, D = 150 and when V = 54, D = 192.
To find the formula connecting D and V, we can use the two given points to determine the slope (a) and the y-intercept (b) of the equation:
D = aV + b
We can start by finding the slope or the rate of change of D with respect to V:
a = (D₂ - D₁)/(V₂ - V₁)
a = (192 - 150)/(54 - 40)
a = 42/14
a = 3
Next, we can use one of the points to substitute for D, V, and a to solve for b:
150 = 3(40) + b
150 = 120 + b
b = 150 - 120
b = 30
Therefore, the formula connecting D and V is:
D = 3V + 30.