Let the curve C be the intersection of the cylinder
and the plane
The projection of C on to the x-y plane is the ellipse
To see clearly that this is an ellipse, le us divide through by 16, to get
or
,
We can write the following parametric equations,
for
Since C lies on the plane,
it must satisfy its equation.
Let us make z the subject first,
This implies that,
We can now write the vector equation of C, to obtain,
The length of the curve of the intersection of the cylinder and the plane is now given by,
But
Therefore the length of the curve of the intersection intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.
Answer: the value of her investment after 4 years is £8934.3
Step-by-step explanation:
The formula for determining compound interest is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount invested.
t represents the duration of the investment in years.
From the information given,
P = 8000
r = 2.8% = 2.8/100 = 0.028
n = 1 because it was compounded once in a year.
t = 4 years
Therefore,
A = 8000(1+0.028/1)^1 × 4
A = 8000(1+0.028)^4
A = 8000(1.028)^4
A = £8934.3 to the the nearest penny
Answer:
22, -6
Step-by-step explanation:
q-8=14 or 8-q=14
q=22 or q= -6
