1. A quantity is partly constant and partly varies inversely as the square of x.write the relationship between x and y when x=1,y=11 and when x=2,y=5.find the values of y when x=4. 2.find,correct to the nearest naira,the compound interest on 85750 naira for 3 years at 5%per annum.
y = a + b/x^2
So, using the two given points,
a + b = 11
a + b/4 = 5
Now find y when x=4
85750(1.05^3 - 1)
1. To find the relationship between x and y, we are given that y is partly constant and partly varies inversely as the square of x.
Let's break it down step by step:
Step 1: Write the equation for the constant part of y.
If y is partly constant, we can represent it as a constant value, let's call it k.
So, the constant part of y is k.
Step 2: Write the equation for the inverse variation part of y.
If y varies inversely as the square of x, we can write it as y = k/x^2.
Step 3: Use the given values of x and y to find the constant k.
We're given two sets of values:
When x = 1, y = 11
When x = 2, y = 5
Using these values in the equation, we can set up two equations:
11 = k/1^2 ---- (equation 1)
5 = k/2^2 ---- (equation 2)
Simplifying equation 1, we get: 11 = k
Substituting k = 11 in equation 2, we get: 5 = 11/4
Simplifying equation 2, we get: 20 = 11
Therefore, we made an error in assuming that y varies inversely with the square of x. Let's re-evaluate the question.
2. To find the compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (including compound interest)
P = Principal amount (initial investment)
r = Rate of interest (expressed as a decimal)
n = Number of times interest is compounded per year
t = Time duration (in years)
Given:
Principal amount (P) = 85750 naira
Rate of interest (r) = 5% = 0.05 (as a decimal)
Time duration (t) = 3 years
Compounding frequency (n) is not given, so we'll assume it's annually (n = 1).
Plugging the values into the formula:
A = 85750(1 + 0.05/1)^(1*3)
A = 85750(1 + 0.05)^3
A = 85750(1.05)^3
A ≈ 85750 * 1.157625
A ≈ 99281.97
Therefore, the compound interest on 85750 naira for 3 years at 5% per annum is approximately 99281.97 naira.