Answer:
Step-by-step explanation:
<u>Given:</u>
- Investment P = £4900
- Interest rate r = 1.5% or r = 0.015
- Time t = 4 years
- Number of compounds per year n = 1
<u>Find the future amount:</u>
I believe it would be uniform
Answer:
Step-by-step explanation:
If θ is the angle between two vectors u and v, then cosθ = (u·v) / [llull llvll]
u·v = (8)(9) + (7)(7) = 121
llull = √[(8)2 + (9)2] = √145 llvll = √[(7)2+(7)2] = 7√2
So, cosθ = 121/ [7√290]
= 1.015052094
θ = Cos-1(1.015052094) ≈ 3.3
If the length, breadth and height of the box is denoted by a, b and h respectively, then V=a×b×h =32, and so h=32/ab. Now we have to maximize the surface area (lateral and the bottom) A = (2ah+2bh)+ab =2h(a+b)+ab = [64(a+b)/ab]+ab =64[(1/b)+(1/a)]+ab.
We treat A as a function of the variables and b and equating its partial derivatives with respect to a and b to 0. This gives {-64/(a^2)}+b=0, which means b=64/a^2. Since A(a,b) is symmetric in a and b, partial differentiation with respect to b gives a=64/b^2, ==>a=64[(a^2)/64}^2 =(a^4)/64. From this we get a=0 or a^3=64, which has the only real solution a=4. From the above relations or by symmetry, we get b=0 or b=4. For a=0 or b=0, the value of V is 0 and so are inadmissible. For a=4=b, we get h=32/ab =32/16 = 2.
Therefore the box has length and breadth as 4 ft each and a height of 2 ft.
Answer:
20 ; $135 ; service charge for 3 hours spent is $135
Step-by-step explanation:
Given that :
Service fee equation model :
C(h)= 75 + 20h
C = total cost of the service call
h = number of hours the plumber spends working on the problem
The charge per hour is the gradient or slope of the linear equation. From the equation, the slope is of the equation is related to bx from. The general form of a linear equation where b = gradient or slope(charge per hour) and x = number of hours
bx = 20h
b = 20
Charge per hour = 20
C(3) = 75 + 20(3)
75 + 60 = 135
This means that total service call charge for a plumber who spends three hours fixing a problem is $135
