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How do you find the point or points of intersection of a straight line and a circle?

Given the equation of the straight line is: x+y=9 and the equation of the circle is: (x-2)²+(y-3)²=16 , find the point or points of intersection? The equation x+y=9 can be rearranged...

Answered by Edward C. • Maths tutor

5475 Views

Integrate | x^7 (ln x)^2 dx ( | used in place of sigma throughout question)

Start the integration by parts process

|udv = uv - |vdu

u = (ln x)² dv = x⁷ dx

du = 2(ln x)/x dx v = 1/8 x⁸

...

Answered by Rowan D. • Maths tutor

8266 Views

The area of a rectangle is 8cm^2. It has a length of (3x+1)cm and a width of (2x+5)cm. Work out the value of x.

We know that the equation of the area of a rectangle is width times by length. Therefore:

8=(3x+1)(2x+5)

If we multiply out the brackets we get:

8=(6x²+2x+15x+5), thus, 8=6...

Answered by Oliver C. • Maths tutor

12542 Views

Finding the length of the side opposite a known angle while having the hypotenuse length known

Sin x is equal to the length of the opposite side divided by the length of the hypotenuse. So, the length of the opposite side is Sin x multiplied by the length of the hypotenuse

Answered by Amer A. • Maths tutor

4034 Views

In a geometric series, the first and fourth terms are 2048 and 256 respectively. Calculate r, the common ratio of the terms. The sum of the first n terms is 4092. Calculate the value of n.

A geometric series S always follows the same pattern: S = a + ar + ar^2 + ar^3 ... Here i've labelled the first term a, and the common ratio r. The next term in a geometric series is always the preceding ...

Answered by Sam W. • Maths tutor

6208 Views