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This question is concerning the completion of the square by using plane geometry
The area of a
The area of a rectangle of sides x and y is : xy
Consider the expression : x
2 + 10x
Such can be considered as the sum of two areas viz square x
2 and a rectangle 10x
Now do the following (sketch essential)
Divide the rectangle into two equal areas viz 5x and 5x
Next to the square place the two rectangles with the side x in common. One to the RHS and the other below.
You will now have a ’nearly complete’ square
a) What is the length of each side of the ’missing square’ in your diagram
b) If you add the area of the missing square to make a big square, what is the area of the complete (big) square
c) By using the areas from your sketch, find the expressions ? and ?? in the following:
x
2 + 10x + (?)2 = (??)2
Consider a population which is normally distributed.If the variance of the population is 9 and n=9,what is the variance of the sampling distribution of sample means
A line up for tickets to a local concert had an average (mean) waiting time of 20 minutes with a standard deviation of 4 minutes.
a. What percentage of the people in line waited for more than 20 minutes?
Obtain the solution of the differential equation
(x^2)y" - 2xy' + 2y = (log (base e) x) ^2, (x>0),
using the method of undetermined coefficients.
Obtain the solution of the differential equation
y"+3y'+2y=e^(2t) using the method of variation of parameters
Choose a quantity to be represented by a variable, then write a mathematical expression for each.
1. The product of three consecutive integers
2.. Jose's age in 10 years
3. The distance traveled by a man driving at the rate of 45 kph
4. The total amount in pesos of 30 coins consisting of 5-peso coins and 10-peso coins
5. The sum of three consecutive odd integers
6. The fraction of work done by a man who can finish a job in three days
7. The total interest after one year if a fraction of P500 000 is invested at 5% annual interest rate and the remaining part is invested at 7.5% annual interest rate
8. A three-digit number whose hundreds digit is twice its tens digit and the tens digit is 3 more than the units digit
9. The percentage of alcohol in a mixture formed by combining 1.5 liter of pure water and x liters of 30% alcohol solution.
10. The total distance traveled by a boat 1 hour and 20 minutes upstream and 40 minutes downstream if the rate of the current is 3 kph.
Compute the minimum distance that a truck slides on a horizontal
asphalt road if it is traveling at 20 m/s. The coefficient of sliding
friction between asphalt and rubber tire is 0.50. The mass of the
truck is 8000 kg.
Life Insurance A 39-year-old woman purchases a $300,000 term life insurance policy for an annual payment of $450. Based on a period life table for the U.S. government, the probability that she will survive the year is 0.999053Find the expected value of the policy for the insurance companyRound to two decimal places for currency problems
In the aggregate expenditures model, the size of the marginal propensity to consume (MPC) is assumed to always be…
a. equal to infinity.
b. zero.
c. greater than ten.
d. an amount greater than zero, but less than one.
e. an amount greater than ten, but more than zero.
300 j of heat added to a system and 250 j of work is added by the system. what is the change in internal energy by the system?
#340153 on Dec 2023