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Find the values of k for which the equation (2k-3)x^2 - kx + (k-1) = 0

A quadratic equation has two equal roots when its discriminant is equal to 0. Calculating the discriminant of the given equation: D = k² - 4(k-1)(2k-3) = k² - 8k²+20k-12...

Answered by Katerina P. • Maths tutor

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At the supermarket, Ben buys 5 apples and 3 pears, at a total cost of £3.70. Jenny buys 6 apples and 6 pears, costing £5.40. Construct two simultaneous equations to work out the price, in pence, of apples and pears.

Ben: 5 apples and 3 pears costing £3.70, therefore: 5a + 3p = 3.7. Jenny: 6 apples and 6 pears costing £5.40, therefore: 6a + 6p = 5.4. (1) 5a + 3p = 3.7, (2) 6a + 6p = 5.4. Multiply equation (1) by 2: 10...

Answered by Charlotte B. • Maths tutor

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A curve C has the following equation: x^3 + 3y - 4(x^3)*(y^3) a) Show that (1,1) lies on C b) Find dy/dx

a) Substituting the coordinate (1,1) into the left hand side of the equation for C we obtain: (1³) + 3*1 - 4(1³)(1³) = 1 + 3 - 4 = 0 = The right hand side of the equation,...

Answered by Harry W. • Maths tutor

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show that tan(x)/sec2(x) = (1/2)sin(2x)

tan(x)/sec²(x) Sec(x) = 1/cos(x), therefore 1/sec(x) = cos(x). also tan(x) = sin(x)/cos(x).using substitution, tan(x)/sec²(x) = (sin(x)/cos(x)) * cos²(x) = sin(x)cos(x). s...

Answered by Olaitan O. • Maths tutor

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