Math Answers

There are two planes:

x+4y-3z+12=0 and 2x+8y-6z+4=0

a) Explain how I know these planes are parallel and distanced?

b) How far apart are these lines?

Maximise 1170x1 + 1110x2

Subject to: 9x1 + 5x2 ≥ 500

7x1 + 9x2 ≥ 300

5x1 + 3x2 ≤ 1500

7x1 + 9x2 ≤ 1900

2x1 + 4x2 ≤ 1000

x1, x2 ≥ 0

-Find graphically the feasible region and the optimal solution.

Find the corresponding area between z = 0 and each of the following: a. z = 0.96 b. z = 2.74 c. z = -1.67

Check the whether the set { 2/7, 2/8, 2/9,..} is countable or not. Also a give example of proper subset of R which is uncountable

Check whether the function, ,f defined below, is uniformly continuous or not:

f(x)=x^(1/2), x∈[1,2]

Prove or disprove the following statement

‘ Every strictly increasing onto function is invertible'

Is every onto strictly decreasing function invertible? Justify your answer.

Evaluate each of the following functions, find the indicated derivative

1. 𝑓(𝑥) = 𝑥^2 − 4𝑥 + 1; 𝑓′(2)

2. 𝑓(𝑥) = 𝑥^3 + 2; 𝑓′(−2)

3. 𝑓(𝑥) = 2𝑥^4 + 3𝑥^3 − 2𝑥 + 7; 𝑓′(0)

4. f(x) = √2x + 7; f'(1)

5. f(x) = 1 + √x^2 + 3x +6; f'(2)

6. f(x) = x/x+4 ; f'(-3)

7. f(x) = x^2 +3/4 - x^2 ; f'(-1)

8. f(x) = √x + 3/x - 4 ;f'(1)

9. f(x) = 3- √ 5x - 9/2x - 1 f'(2)

10. f(x) = 2x^2 + 3 - 1; f'(-1)

All strictly monotonically decreasing sequences are convergent.

True or false with full explanation

Determine whether each of the following statements is a proposition or not. If it is, give its truth value.

p: Mindanao is an island in the Philippines.

q: Find a number which divides your age.

r: My seatmate will get a perfect score in the Logic exam.

s: Welcome to the Philippines!