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Solve the equation: 13y − 5 = 9y + 27.

13y - 5 = 9y + 27 First we must collect all similar terms together on either side of the equation: 13y - 9y = 27 + 5. As you can see, if a term is moved to the other side of the equation, the opposite sign m...
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Answered by Emma R. • Maths tutor
10564 Views

Solve x^2 + x - 2 = 0

(x+2)(x-1)=0 x+2=0x= -2x-1=0x=1
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Answered by Emily W. • Maths tutor
3435 Views

y = arcsec(x), Find dy/dx.

The key to this problem is to apply sec to both sides, and then differentiate implicitly: sec(y)=x; dsec(y)/dx = 1; tan(y)sec(y)dy/dx = 1; dy/dx = 1/(tan(y)sec(y)). Then using the fact that sec(y)=x and tan ...
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Answered by Nicholas Y. • Maths tutor
5393 Views

When solving a trigonometric equation, like sin(x) = -1/3 for 0 ≤ x < 2π, why do I get an answer outside the range? Why are there many correct answers for the value of x?

Drawing the graphs of the trigonometric functions sin, cos &amp; tan, we can see that they all extend along the x-axis to infinity. Indeed, the sin &amp; cos functions move between 1 and -1 on the y-axis, an...
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Answered by Alexandra G. • Maths tutor
10022 Views

How do you solve a simultaneous equation by 'substitution'?

Firstly, demonstrate with an example: Solve: 3x + y = -9 and x 2 + 2x - 3 = yRearrange the first equation to get &quot;y&quot; by itself by moving parts of the equation to the other side e.g. y = - 9 - 3xSub...
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Answered by Sophie H. • Maths tutor
3447 Views