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The curve C has the equation: 2(x^2)y + 2x + 4y – cos (πy) = 17 use implicit differentiation to find dy/dx in terms of x and y

Using the product rule: d/dx(ab)=ab’ + a’b where a and b are variables which have been differentiated with respect to x Derivative: 2(x^2(dy/dx)+2xy) + 2 + 4dy/dx+πsin(πy)dy/dx=0 Expand brackets: 2x^2(dy/dx)...
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Answered by George G. • Maths tutor
6688 Views

A 4 digit number is picked. It's second digit is a prime number, it must be even and it must be greater than 5000. How many possible numbers can be picked?

This involves the product rule for counting. Step 1: Identify the possible numbers for the first digit 5, 6, 7, 8 or 9 (5 in total) Step 2: Identify the possible numbers for the second digit 2, 3, 5 or 7 (4 ...
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Answered by Thomas S. • Maths tutor
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Solve the following inequality and shade the region to which it applies on a graph. 10x(squared) < 64x - 24

Step 1: Simplify the quadratic by dividing by 2. 5x 2 &lt; 32x - 12 Step 2: Move all terms onto one side of the quadratic. 5x 2 - 32x + 12 &lt; 0 Step 3: Factorise the quadratic. (5x - 2)(x - 6) &lt; 0 Step ...
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Answered by Thomas S. • Maths tutor
4057 Views

Factorise 15a^2 + ab - 6b^2

15a 2 +ab-6b 2 =(?a+?b)(?a-?b) factors of 15= 3 and 5 factors of 6= 2 and 3 if we try (3a+2b)(5a-3b) that gives us 15a 2 +10ab-9ab-6b 2 = 15a 2 +ab-6b 2 therefore the answer is (3a+2b)(5a-3b)
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Answered by Aayushi B. • Maths tutor
3491 Views

In one second a mass of 210 kg of air enters at A. The speed of this mass of air increases by 570 m s–1 as it passes through the engine. Calculate the force that the air exerts on the engine.

F = M x A (A= (V-U)/T) F = 210 x 570 F = 119,700 N
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Answered by Sam G. • Physics tutor
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