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Find the set of values for x for which x^2 - 9x <= 36

Rearrange to get x^2 - 9x - 36 &lt;= 0 Solve quadratic (x-12)(x+3) &lt;= 0 Solve for x x = 12, x = -3 Now, we have key points 12 and -3, we need the range of values for x where x^2 - 9x - 36 &lt;= 0. So, we ...
DD
Answered by Daniel D. • Maths tutor
11453 Views

Why does d/dx (tan(x)) = sec^2(x)?

This result comes from using a trig identity and the quotient rule. First, we write tan(x) as sin(x)/cos(x). Then we apply the quotient rule. After doing the standard derivatives, the numerator of our fracti...
TD
Answered by Tutor42661 D. • Maths tutor
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Find dy/dx of the equation (x^3)*(y)+7x = y^3 + (2x)^2 +1 at point (1,1)

Use the product rule d(u.v)/dx = u.(dv/dx) + v(du/dx). Calculate the LHS as such first. (Demonstrate on whiteboard.) Then calculate the RHS. (Demonstrate on whiteboard.) Group the dy/dx terms on one side of ...
SP
Answered by Sophie P. • Maths tutor
5890 Views

Natasha has two bags of fruit. both bags have the same number of fruit in total. 1/3rd of the fruit in bag 1 are apples and 15% of the fruit in bag 2 are apples. There are 20 apples in bag 1, how many apples are in bag 2?

Using the fact that 1/3rd of the fruit in bag 1 are apples and there are 20 apples in total you can work out that there are 60 pieces of fruit in bag 1. This is found by doing 20 x 3 = 60. Then using the fac...
DQ
Answered by Danyal Q. • Maths tutor
3451 Views

Factorise 2e – 4f + ex -2fx

2(e-2f) + x(e-2f) = (2+x)(e-2f)
KT
Answered by Katrina T. • Maths tutor
5374 Views