Math Answers

Find an equation of the tangent line to the curve 9x³ – y³ = 1 at the point (0, -1).

Find an equation of the tangent line to the curve x⁴ + 2y⁴ = 33 at the point (1,2).

3. a) Define tangent and normal of a curve with figure. Also find the equation of tangent and normal of the ellipse (x ^ 2)/4 + (y ^ 2)/16 = 1 at the point (- 1, 3) .

b) Explain maximum and minimum value of a function with graphically. Evaluate maximum and minimum value of the function f(x) = x ^ 3 - 3x ^ 2 + 3x + 1

Find the equation of a line that passes through the point (2,1) and has a gradient of 2.

Leave your answer in the form y

=

m

x

+

c

∫ ௫ିଵ ௫ యି௫మିଶ௫ 𝑑𝑥 

Factory produces whiteboard markers. The production process can be modelling by normal distribution with a mean length of 11 cm and a standard deviation of 0.25 cm. (a) What is the probability that a randomly selected whiteboard marker has a length longer than 10.5 cm? (2 marks) 100 whiteboard markers are randomly selected for quality checking. (b) What are the mean and standard deviation of the sample mean length? (2 marks) (c) What is the probability that the sample mean length will be between 10.99 cm and 11.01 cm? (2 marks) (d) If 99.8% of the sample means are more than a specific length Y, find Y

Researchers suspect that 18% of all high school students smoke at least one pack of cigarettes a day. At Wilson High School, with an enrollment of 300 students, a study found that 50 students smoked at least one pack of cigarettes a day. At a=0.05, test the claim that 18% of all high school students smoke at least one pack of cigarettes day.

1.       Find the function whose tangent has slope 4x + 1 for each value of x and whose graph passes through the point (1, 2).

Three planets P1, P2, P3 orbit a star in a distant galaxy. The perihelion of a

planet is the point in the orbit of a planet that is closest to the star. The orbital periods

of P1, P2, P3 are 3, 5 and 11 years respectively. The most recent perihelia of these

planets were in the years shown in the table below. What is the next year in which all

three planets achieve perihelion simultaneously?

Prove that 3n+4n+5n is divisible by 12 whenever n is an odd positive integer.