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State the interval for which sin x is a decreasing function for 0⁰ ≤ x ≤ 360⁰.

Draw a diagram of the graph y=sin x between the stated interval. Identify the two extrema. Required interval is in between the two points.
Answered by • Maths tutor
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What is the difference between a Supremum and a Maximum of a sequence?

A supremum is a number such that it is larger than all numbers in the given sequence. Although this is true for a maximum, the maximum has an additional property that it must be a member of the sequence so a...
BR
Answered by Ben R. • Maths tutor
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Round 4 and 3/8 to the nearest whole number.

Here we know the lower option will be 4, and that as our numerator is smaller than our denominator, or higher whole number to round to will be 5. Between 4 and 5 the halfway point is 4/8 as 4 is half of eigh...
DD
Answered by Deepali D. • Maths tutor
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Show that the lines y=3x+7 and 2y–6x=8 are parallel. Do not use a graphical method.

y=3x+7 2y-6x=8 2y-6x=82y=8+6xy= 4+3xy=3x+4When both equations equal y they both have a 3 in front of their x meaning that they both have a gradient of 3.
JM
Answered by Jordan M. • Maths tutor
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Curves C1 and C2 have equations y= ln(4x-7)+18 and y= a(x^2 +b)^1/2 respectively, where a and b are positive constants. The point P lies on both curves and has x-coordinate 2. It is given that the gradient of C1 at P is equal to the gradient of C2 at P.

y= ln(4x-7)+18 y= a(x^2 +b)^1/2 At x=2 dy/dx = dy/dx and y =y At x =2 y = ln(8-7) +18 y = ln 1 +18 y =18 At x = 2 18=a(4 +b)^1/2 18/(4+b)^1/2= a y=ln(4x-7)+18dy/dx= 4/(4x-7) At x= 2 dy/dx= 4/8-7= 4 y=a(x^2 +...
JM
Answered by Jordan M. • Maths tutor
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