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A bag contains beads, 60% of which are green. A student claims that the probability of getting two green beads if the beads aren't replaced is 1/3 as 6/10 * 5/9 is 1/3. Is the student right?

They have multiplied the fractions correctly but they are still incorrect. The student has assumed that a bag with 60% green beads contains 10 beads. If the bag had 100 beads and 60 were green, 60% of the be...
AK
Answered by Adithya K. • Maths tutor
3845 Views

Differentiate with respect to x: y=xln(x)

Recall the product rule for differentiation. If y=uv, where u and v are functions defined by functions of x, then we can take the derivative of y as: y'=u'v+v'u ( ) (where ' denotes the derivative) Applying ...
GP
Answered by George P. • Maths tutor
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Integrate ∫_(-1)^1 3/√(x+2) dx using the substitution u x+2

Step 1:Replace any obvious in the integral with the substitution u=x+2 ∫_(-1)^1 3/√u dx Step 2: Differentiate the substitution u=x+2 to find an expression for dx (to differentiate multiply by the power and t...
MY
Answered by Micaela Y. • Maths tutor
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Show that the integral ∫(1-2 sin^2⁡x)/(1+2sinxcosx) dx = (1/2) ln2 between the limits π/4 and 0. [5 marks]

First, we use the trig identities: cos2x=cos^2x-sin^2x, cos^2x+sin^2x=1 and sin2x=2sinxcosx to transform the integral to ∫(cos2x)/(1+sin2x)dx. We know that ∫f'(x)/f(x)dx = ln|f(x)|+c, so we let f(x)=1+sin2x....
AC
Answered by Abby C. • Maths tutor
16647 Views

Write (√(18)+10)/√(2) in the form: p + q√2 [4 marks]

First, simplify √18 by writing it as √(9x2) = √9 x √2 = 3√2. Then, rationalise the denominator by multiplying both top and bottom of the fraction by √2. This gives √2 x √2 = 2 in the denominator, and (3√2+10...
AC
Answered by Abby C. • Maths tutor
21500 Views