Math Answers

Prove that the length of the chord of a parabola which passes through the focus and which is inclined at 30° to the axis of the parabola is four times the length of the latus rectum.

Prove that the equation of a line through (𝑥₁ , 𝑦₁) and (𝑥₂ , 𝑦₂) can be expressed in the form determinant

x y 1

x₁ y₁ 1

x₂ y₂ 1

= 0

Let 𝑃 be the midpoint of the line segment joining the points 𝐴(𝑎 + 𝑏, 𝑏) and 𝐵(𝑎 − 𝑏, 𝑎 + 𝑏). Find the slope of the line passing through 𝑃 and 𝑄 (𝑏, −𝑎/2) .

Prove that the conic passing through the points of intersection of two rectangular hyperbolas is also a rectangular hyperbola.

(D² − 3DD + 2D²)z = e²x+³y +sin(x-2y)

The pistons in an automobile engine move up and down in the cylinders. If t is in milliseconds, the distance from the top of the piston to the top of the cylinder is given in centimeters by D=7+6 sin (4m)

(a) identify the amplitude, period and frequency of function

(b) Find the largest and the smallest clearance between the piston and the top of the cylinder.

a presidential candidate asks a polling to conduct a nationwide survey to determine the percentage of potential voters who would vote for him over his rival presidential candidate. out of 2 500 respondents in the sample, 945 said they would vote for. What course of action the presidential candidate must do based on the survey results

Let x denote the number of biased die with the following probability mass function p(x) 

X:    1    2   3    4   5     6

P(x):  1/6  1/6  1/5   y   1/5   1/6

a) find the value of y 

b) find the cdf of x

Let x denote the number of biased die with the following probability mass function p(x) 

X:    1    2   3    4   5     6

P(x):  1/6  1/6  1/5   y   1/5   1/6

a) find the value of y 

1.       Solve the exact differential equation (𝗑 − 2𝑒^𝑦)𝑑𝑦 + (𝑦 + 𝗑 sin 𝗑)𝑑𝗑 = 0.

2.     Solve the differential equation 𝗑 𝑑𝑦 + 2𝑦 = 𝗑⁴.