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Maths
A Level

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)...

NA
Answered by Nathan A. Maths tutor
11801 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 ...

JM
Answered by Jed M. Maths tutor
13614 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...

RN
Answered by Rajenth N. Maths tutor
5035 Views

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

Modulus, also known as absolute value, takes whatever's between the |straight brackets|...

MF
Answered by Michael F. Maths tutor
31545 Views

Using Trigonometric Identities prove that [(tan^2x)(cosecx)]/sinx=sec^2x

You should begin by identifying all the Trigonometric Identities that may be useful in this problem. Specifically, cosecx=1/sinx tanx=sinx/cosx 1/cosx=secx and possibly tan^2x + 1= sec^2x. I began by c...

MB
Answered by Mary B. Maths tutor
9315 Views

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