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Increase 35 by 20%:

An increase by 20% is the same as multiplying by 1.2Therefore, 35 x 1.2 = 42
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Answered by Sam H. • Maths tutor
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Differentiate: f(x)=2(sin(2x))^2 with respect to x, and evaluate as a single trigonometric function.

f(x) = 2sin 2 (2x)Therefore, using the chain rule: f'(x)=2 x 2cos(2x) x 2sin(2x)(The 2 at the front arises from the constant 2, at the start of f(x), the 2cos(2x) comes from differentiating sin 2 (2x), then ...
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Answered by Sam H. • Maths tutor
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Given a right-angled triangle with an angle of 35 degrees and an Opposite side of 12cm, calculate the length of the hypotenuse to 3 significant figures.

First, determine which of SOH-CAH-TOA you need to use. As this question involves the Hypotenuse and the Opposite side, use Sine. As such, write out the equation as: sin(35) = 12/x. (Let x represent the Hypot...
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Answered by Eloise S. • Maths tutor
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Solve for x to 3dp: x^2 + 6x + 2 = 0

We cannot factorise this so we shall use the quadratic formula instead.We need to substitute in the values for a, b, and c.ax 2 + bx + c = 0x 2 + 6x + 2 = 0a = 1, b=6, c=2Once substituted in, we get 2 values...
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Answered by Rikesh S. • Maths tutor
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Solve for x: x^2 + 6x + 8 = 0

First of all we must factorise this:x 2 + 6x + 8 = 0(x+4)(x+2) = 0Now we make each bracket = 0 and solve for x.x+4 = 0 x+2 = 0 x = -4 x = -2
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Answered by Rikesh S. • Maths tutor
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