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A cup of coffee is cooling down in a room following the equation x = 15 + 70e^(-t/40). Find the rate at which the temperature is decreasing when the coffee cools to 60°C.

First, we need to find the value of t when x = 6p°C. We are told that after t minutes the temperature, x, will be 60°C; so we can insert 60 into the equation for x: 60 = 15 + 70e^(-t/40) Secondly, we can rea...
NA
Answered by Nathan A. • Maths tutor
12427 Views

Find the value of 2∫1 (6x+1) / (6x2-7x+2) dx, expressing your answer in the form mln(2) + nln(3), where m and n are integers.

This fraction can’t be integrated easily, but if we split it using partial fractions, these will be easier to integrate. To do this, we need to factoise the denominator, as this will follow the method of par...
JM
Answered by Jed M. • Maths tutor
14236 Views

Can you differentiate the following function using two methods:- y = e^(2x+1)

The first method to differentiate this fuction is the basic chain rule method. differentiate 2x+1 and add this to the front of the function. This gives us 2e^(2x+1). the other method to differentiate this fu...
RN
Answered by Rajenth N. • Maths tutor
5825 Views

Simplify the expression: 3x + 2y -7x + c + y

The important thing in this question is the letters. We want to group "like terms" together. This is what makes the expression simpler. I go about this by drawing a different shape around each lett...
ES
Answered by Edward S. • Maths tutor
5978 Views

Core 3 - Modulus: Solve the equation |x-2|=|x+6|.

Modulus , also known as absolute value , takes whatever's between the | straight brackets | and makes it positive. For example, |3|=3, and | - 3|=3. Interestingly, if you have any real number x , then | x |=...
MF
Answered by Michael F. • Maths tutor
32195 Views