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Solve algebraically the simultaneous equations 2x+y=5 and 3x+y=7, for x and y.

Assign 2x+y=5 to be 'Equation 1,' and 3x+y=7 to be 'Equation 2.'The steps to solving for x and y are: 1.get rid of one variable (being either x or y) 2.solve for the other variable 3.substitute the now kn...

Answered by Natalie K. • Maths tutor

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A projectile is thrown from the ground at 30 degrees from the horizontal direction with an initial speed of 20m/s. What is the horizontal distance travelled before it hits the ground? Take the acceleration due to gravity as 9.8m/s^2

Draw diagram outlining the symmetric parabolic shape of the projectile's motion. Find vertical component of the initial speed using SOH CAH TOA. sin(30) = opposite/hypotenuse = x/30therefore, x = 30sin(30...

Answered by Raphael D. • Maths tutor

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Calculate the rate of change of y(t) = 1/(4t), when t = 8

Write in differentiable form: 1/4 t^-1Differentiate: - 1/4 t ^-2Evaluate derivative at t =8: 1/256

Answered by Sophie C. • Maths tutor

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A is the point with coordinates (5, 9) B is the point with coordinates (d, 15). The gradient of the line AB is 3. Work out the value of d.

gradient is calculated using the change in y coordinates divided by change in x coordinates. so, (15-9)/(d-5)=3 => 6/(d-5)= 3rearrange this equation to get d on one side (6/3)+5 = d therefore d= 7

Answered by Eve C. • Maths tutor

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Functions question: f(x) = 3x + 2a; g(x) = ax + 6; fg(x) = 12x + b. a and b are constants; Work out the value of b

So this is a functions question which is essentially asking you to combine the first two functions and then equate them with the last one.
fg(x) can be considered as replacing the x in f(x) with g(x)...

Answered by Ritik P. • Maths tutor

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