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Convert the following formula to conjunctive normal form: A ⇒ ( B ∧ C )
A. ( ¬A ∨ B ) ∧ ( ¬A ∨ C )
B. ( A ∧ ¬B ) ∨ ( A ∧ ¬C )
C. ( ¬A ∧ B ) ∨ ( ¬A ∧ C )
D. ( A ∨ ¬B ) ∧ ( A ∨
The Gaussian distribution also known as the Normal distribution, is given by the following
equation:
𝑦(𝑥) = 𝑒𝑥𝑝 −(𝑥−𝜇)^2/2𝜎^2
where parameter 𝝁 is the mean and 𝝈 the standard deviation.
(i) create a 1000 point Gaussian distribution of random numbers
having 𝜇 = 0 and 𝜎 = 1. (20)
(ii) Plot this distribution. (10)
(iii) Prove that the full width–half maximum (FWHM), of the above distribution is given by :
FWHM = 2𝜎√2ln 2 (10)
(iv) Write a program that estimates the FWHM from your data/graph. (10)
(v) Compare the theoretical and the experimental results of FWHM. (5)
(vi) What are the theoretical and experimental values of 𝒚 at FWHM?
abongile, the manager of a construction company is renovating a home and has expenses of R200 000,00 now and another R41 812,00 in six months time.as he finds it difficult to find the cash now, he proposes to settlle all the debt after six months with a single payment. the debt is subject to an interest rate of 9.5% per annum, compounded quarterly. what is the value of the payment that will settle his debt at the end of month six?
The population of City A is 8,000,000 at the end of the year 2020.The
number of immigrants is 25,000n at the end of year n. The population
of city increases at the rate of 8% per year. Use recurrence relation to
determine the population of the city at the end of 2030.
you have 80 linear feet of fencing with which to enclose a circular space for a garden find the largest area that can be enclosed with this much fencing and the diameter of the corresponding garden
The correct expression for a number which is twice as big as the number obtained after p has been divided by 3 is
1. 2(p/3)
2. 2p/6
3. 2 + p/3
4. 2 × 3/p
b) Find whether the following series are convergent or divergent √ 𝟏 /𝟒 + √ 𝟐 /𝟔 + √ 𝟑 /8 + ...
The function 𝑓(𝑥)=2𝑐𝑜𝑠 𝑥−3 is defined for the domain 0≤𝑥≤𝜋/2
a. Find the range of 𝑓(𝑥)
b. Find 𝑓^−1(𝑥).
The function 𝑓(𝑥) is defined as 𝑓(𝑥)=𝑎+𝑏cos𝑥, where 𝑎 and 𝑏 are constants. The range of 𝑓(𝑥) is given by −6≤𝑓(𝑥)≤2.
a. Find the values of 𝑎 and 𝑏
b. Solve the equation 𝑓(𝑥)=0 for 0°≤𝑥≤360°
c. Sketch the graph of 𝑦=𝑓(𝑥) for 0°≤𝑥≤360°
Consider 𝑔(𝑥)=4sin3𝑥
a. Write down the period of 𝑔(𝑥)
b. Write down the number of solutions to the equation 𝑔(𝑥)=3, for 0≤𝑥≤2𝜋
c. Starting with the graph of 𝑦=sin𝑥, state the transformations which can be used to sketch 𝑔(𝑥).
#339914 on Dec 2023