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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 to make x=9-y. This ...
EC
Answered by Edward C. • Maths tutor
6075 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 = x 7 dx du = 2(ln x)/x dx v = 1/8 x 8 = 1/8 x 8 (ln x) 2 - | 1/4(ln x)x 7 dx = 1/8 x 8 (ln x) 2 -1/4 | x 7 (ln x) dx Repeat the integr...
RD
Answered by Rowan D. • Maths tutor
8615 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=(6x 2 +2x+15x+5), thus, 8=6x 2 +17x+5, and therefore, 0=6x 2...
OC
Answered by Oliver C. • Maths tutor
12938 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
AA
Answered by Amer A. • Maths tutor
4284 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 ter...
SW
Answered by Sam W. • Maths tutor
6494 Views