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Find the coordinates of the point of intersection of the lines 2x + 3y = 12 and y = 7 - 3x.

We can substitute the equation for y into 2x + 3y = 12.
If y = 7-3x , 2x + 3(7-3x) = 12 2x + 21-9x = 12
Now we can solve for x -7x = =-9x = 9/7
To get y, we must sub x back into y = 7 - ...

Answered by Chrystine A. • Maths tutor

8803 Views

Integrate (1 - x^2)^(-0.5)dx within the limits 0 and 1

The answer is π/2. The key trick to solving this problem is to change variables by using the substitution x = sin(θ). We then need to change the differential and the limits too.

Answered by Cameron W. • Maths tutor

4083 Views

A right-angled triangle has perpendicular sides of length 6cm and 8cm, and a hypoteneuse of 2y cm. Find the length of y.

By Pythagoras' Theorem:(2y)²= 6²+ 8²4y²= 36 +64y² = 9 + 16y² = 25y = ±5However, dimensions can only have a positive value. Therefore ...

Answered by Emmanuel S. • Maths tutor

3227 Views

Solve the simultaneous equations to find x and y: 3y - x = 12 y + 2x = -3

3y - x = 12 (1)y + 2x = -3 (2)multiply equation (2) by 3: 3y + 6x = -9 (3)subtract equation (1) from equation (3): 3y + 6x - 3y + x = -9 -12 7x = -21 x = -3substitute x into equation (2): y -6 = -3 y = 3a...

Answered by Chloe G. • Maths tutor

4293 Views

Differentiate y = x^3− 5x^2 + 3x

the rule for differentiating in terms of x is to multiply by the power then decrease the power by one. So going through the equation x^3 will be multiplied by 3 and go to x^2 so will be 3x^2. Then its imp...

Answered by Georgia D. • Maths tutor

7629 Views