Math Answers

The temperature at a point is given by T = xyz. Find the average temperature in the cube

with opposite corners at (0,0,0) and (2,2,2).

Determine the average value of F(x, y, z) = xyz throughout the cubical region D

bounded by the coordinate planes and the planes x = 2, y − 2, z = 2 in the first octant.

ACTIVITY IN BASIC CALCULUS

BASIC RULES IN DERIVATIVE

  Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.

1. f(x) = -₄x⁵ + ______x^-4- 2468

2. f (x) =____x^-3- _____x^1/4 - 12x

3.f(x)= ____ "\\sqrt[4]{x}" ³ - "\\xlongequal{}"

4.f (x) = "\\xlongequal{}" - _____x² + "\\sqrt[4]{x}"

Find the volume of the region bounded above by the plane z = y/2 and below by the

rectangle.

R ∶ 0 ≤ x ≤ 4,0 ≤ y ≤ 2

In the numbers {1,3,5,7,9} construct the following:

• List of possible sample size of 3 that can be taken from this sets of numbers.

• Sampling distribution of the sample means fornthe size of 3 and the standard error.

Consider the set of even single-digit number {0,2,4,6,8}. Construct the sampling distribution of the sample means for the size of 3 and the standard error.

Two of the five (5) foreign automobiles from an overseas shipment have slight paint blemishes. If an agency receives three (3) of these automobiles at random, list the elements of the sample space 𝑆 using the letters B and N for “blemished” and “non-blemished”, respectively. For each sample point, assign a value 𝑥 of the random variable 𝑋 representing the number of automobiles purchased by the agency with paint blemishes. Hint: There are eight (8) elements in the sample space. 

Write applications of Differential Equation in Physics

A couple of FEB’s 3rd year students decided to make some money by offering tutorial class to their juniors in first and second year. The seniors rented a room for RM300 for 3 hours from the faculty, and developed tutorial module for a few courses. The cost of printing the module handouts is RM5 each, and the tutor is paid RM25 per hour, for a total of RM75 for each tutorial session.

a. If students (junior) are charged RM20 per pax to attend the tutorial session, how many of them must enroll for the 3rd year students to break even?

b. If students (junior) are charged RM17 per pax to attend the tutorial session, how many of them must enroll for the 3rd year students to not having a loss?

c. A smaller room is available at the faculty for RM200 for 3 hours. The 3rd year students are considering this possibility. How would this affect the break even point? Use RM20 per pax as tutorial fee.

Find the volume generated if the region enclosed by y = x² and the line y = 2x is revolve about the x-axis. Answer in 2 decimal places.