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Using methods of substitution solve the following simultaneous equations: y - 2x - 1 = 0 and 4x^2 + y^2 - 25 = 0

(1) 4x 2 + y 2 - 25 = 0 (2) y - 2x - 1 = 0 Rearranging (2) into an equation of y in terms of x we have:y = 2x +1 now substituting into equation (1) 4x 2 + (2x +1) 2 - 25 = 0 and now expanding this equation w...
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Answered by Kerry M. • Maths tutor
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Solve the equation 2y^(1/2) -7y^(1/4) +3 = 0

2y 1/2 -7y 1/4 + 3 = 0 We need to use a substitution to obtain a quadratic.Let y 1/4 = x (use the y with the smallest fractional power as your substitution)From this, we can see that y 1/2 = x 2 (using the l...
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Answered by Sarah L. • Maths tutor
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Describe the sliding filament theory.

The sliding filament theory demonstrates how the muscles in our body contract. As a signal reaches the neuromuscular junction (motor end plate), neurotransmitters such as Acetylcholine will diffuse across th...
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Answered by Rithvik G. • Biology tutor
15860 Views

Using the product rule, differentiate y=(2x)(e^3x)

The product rule states that if y=uv, where u and v are both functions of x , then dy/dx = u(dv/dx) + v(du/dx) Therefore, the differential of 2x e 3x can be found by letting 2x= u and e 3x =v . u= 2x, du/dx ...
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Answered by Christy O. • Maths tutor
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How can a city become sustainable?

Sustainability in cities involves improving and developing cities whilst preserving the environment and resources. Sustainable cities must control the use of resources. This can be done by improving the effi...
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Answered by James A. • Geography tutor
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