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Use the chain rule to show that, if y = sec(x), then dy/dx = sec(x)tan(x).

First, write y in terms of cos(x). We are familiar with cos(x) and know how to differentiate it. We know that sec(x) = 1/cos(x) = (cos(x)) -1 . Next, find dy/dx in terms of cos(x) and sin(x). Again, we are f...
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Answered by Noah L. • Maths tutor
18146 Views

A right angle triangle has a base of √8 and a height of (√10+3). Show that the area is equal to 2√5+3√2.

The area of a triangle is equal to 1/2 x base x height , so we can write the equation for this question as: Area = 1/2 x √8 x (√10+3) We can then simplify √8 by writing it as its factors; √8 + √4√2 , which e...
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Answered by Elizabeth H. • Maths tutor
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Solve the inequality x^2 > 3(x + 6)

In order to solve this inequality, it is helpful to have all the terms on the left-hand side of the equation. To do this, we can subtract 3(x + 6) from both sides of the equation. This gives us: x^2 - 3(x+6)...
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Answered by Joseph M. • Maths tutor
19239 Views

solve the simultaneous equations 3x+7y=18 and 7x+9y=8

3x+7y=18 (eqn 1) -multiply by 7-> 21x+49y=126 (eqn 1*) 7x+9y=8 (eqn 2) -multiply by 3-> 21x+27y=24 (eqn 2*) (eqn 1*)-(eqn 2*) --> 22y=102 therefor y=51/11 sub in this y value back into (eqn1) -->...
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Answered by Radhika S. • Maths tutor
4038 Views

Solve the following simultaneous equations: (1) 4x+y=7 and (2) 3x+2y=9

This question can be answered by the elimination method. I will choose to eliminate 'y' in this case. Firstly, multiply equation (1) by 2, resulting in 8x+2y=14. Now we can subtract eqaution (2): 3x+2y=9 fro...
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Answered by Alex D. • Maths tutor
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