Question(1):Show that the curve y=x^2-3x-5 passes through the point (5,5),(4,-1),(2,-7),(0,-5) and (-t,5) calculate the gradient at each pont. question(2):given a 5by5 matrices with determinant equal zero and the same determinant of its interior element equals zero question(3):A community yield #200 per annum for 5years.how much does it cost,if the current markrt interest rate is 7%?: pls with explanation
Hey, you have not even showed your attempt. I am sure you can do the first part.
You do not say if you know how to take derivatives. What is the second question?
I can battle with qustion (1), but look at 2&3 i don.t even know were to start from pls help
You did not tell me if you have had any calculus. I do not like taking limits to find gradients.
putting in 5 and 4 and 2 and 0 and -t for x
and seeing what y is for each should not be too much for you.
I already passed this course. It is your turn.
Question 1: To show that the curve y = x^2 - 3x - 5 passes through the given points and calculate the gradient at each point, we will substitute the x and y coordinates of each point into the equation and solve for y. The gradient can be calculated by finding the derivative of the function.
Let's start with the point (5, 5):
Substituting x = 5 into the equation:
y = (5)^2 - 3(5) - 5
y = 25 - 15 - 5
y = 5
So (5, 5) lies on the curve.
To calculate the gradient at this point, we need to find the derivative of the equation y = x^2 - 3x - 5 with respect to x.
dy/dx = 2x - 3
Substituting x = 5 into the derivative:
dy/dx = 2(5) - 3
dy/dx = 7
Therefore, the gradient at point (5, 5) is 7.
Similarly, we can find the equation, check if each point lies on the curve, and calculate the gradient for the remaining points.
For point (4, -1):
Substituting x = 4 into the equation:
y = (4)^2 - 3(4) - 5
y = 16 - 12 - 5
y = -1
So (4, -1) lies on the curve.
To calculate the gradient at this point:
dy/dx = 2x - 3
Substituting x = 4 into the derivative:
dy/dx = 2(4) - 3
dy/dx = 5
Therefore, the gradient at point (4,-1) is 5.
Similarly, repeat the process for each point: (2, -7), (0, -5), and (-t, 5).
Question 2: The question states that we have a 5x5 matrix with determinant equal to zero and the same determinant for its interior elements. However, it is not clear what is meant by "interior elements." Please provide more clarification or details to answer this question accurately.
Question 3: To calculate the cost of a community that yields #200 per annum for 5 years, considering the current market interest rate of 7%, we can use the present value formula.
The formula for the present value of an annuity is:
PV = PMT * (1 - (1 + r)^(-n)) / r
Where:
PV = Present value
PMT = Payment per period (annual yield of #200)
r = Interest rate per period (7% or 0.07)
n = Number of periods (5 years)
Substituting the given values into the formula, we can calculate the present value (cost):
PV = 200 * (1 - (1 + 0.07)^(-5)) / 0.07
PV = 200 * (1 - (1.07)^(-5)) / 0.07
PV = 200 * (1 - 0.671_513_398) / 0.07
PV = 200 * 0.328_486_602 / 0.07
PV = 937.21
Therefore, the cost of the community, considering a 7% interest rate, would be approximately #937.21.