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3 years ago

Compound interest £2000 for 3 years 5.5% annum

1 answer:

6 0

$\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\£2000\\
r=rate\to 5.5\%\to \frac{5.5}{100}\to &0.055\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{per annum, thus once}
\end{array}\to &1\\
t=years\to &3
\end{cases}
\\\\\\
A=2000\left(1+\frac{0.055}{1}\right)^{1\cdot 3}$

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A rectangle initially has dimensions 6 cm by 7 cm. All sides begin increasing in length at a rate of 1 cm/s. At what rate is the

Morgarella [4.7K]

Answer:

49 cm²/s

Step-by-step explanation:

The problem statement tells you what to do.

Write an equation relating A, b, h:

A = bh . . . . . . the equation for the area of a rectangle

Differentiate with respect to t:

dA/dt = (db/dt)h + b(dh/dt) . . . . . . . product rule

To find the rate of change after 18 seconds, you need to know the dimensions b and h after 18 seconds. Since each dimension was increasing at the rate of 1 cm/s, it is 18 cm more than it was at the beginning:

At 18 seconds,

b = 6 cm + 18 cm = 24 cm;

h = 7 cm + 18 cm = 25 cm.

Of course, db/dt = dh/dt = 1 cm/s. Then the rate of change of area is ...

dA/dt = (1 cm/s)(25 cm) + (24 cm)(1 cm/s)

dA/dt = 49 cm²/s

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You could write a formula for the area as a function of time and differentiate that:

A = (6 +t)(7 +t) = 42 + 13t + t²

Then the derivative is ...

dA/dt = 13 +2t

and when t=18, this is ...

dA/dt = 13 + 2(18) = 49 . . . . cm²/s

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3 years ago

What is the surface area of a cone with a diameter of 28 cm. and height 22 cm in terms of Ï.

Svetlanka [38]

To find the surface area of a cone, use this formula.

pi (r) (r + [square root of h^2 plus r^2] ) substitute

h = height = 22 r = radius = 28/2 = 14 [ ] = sq. root

pi (14) (14 + [ 22^2 + 14^2 ]) solve exponents

pi (14) (14 + [484 + 196]) add

pi (14) (14 + [680]) solve square root

pi (14) (14 + 2[170]) add

pi (14) (40.0768) multiply

pi (561.075) is about 561.1 rounded to nearest tenth

So the answer is C. 561.1pi cm^2

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3 years ago

The position, x, of an object is given by the equation x = A + Bt +Ct2, where t refers to time. What are the dimensions of A, B,

Serjik [45]

Answer: Dimensions of A are of length [L]

Dimensions of B are of $LT^{-1}$

Dimensions of C are of $LT^{-2}$

Step-by-step explanation:

The given equation is

$x(t)=A+Bt+Ct^{2}$

Since the dimension on the L.H.S of the equation is [L] , each of the terms on the right hand side should also have dimension of length[L] to be dimensionally valid

Thus

Dimensions of A = [L]

Dimensions of Bt = [L]

$Bt=[L]\\\\$ $[B][T]=[L]$ $\\\\\therefore [B]=LT^{-1}$