The graph of `sqrt((x+2)^2+y^2)+sqrt(x^2+(y+2)^2)=6` is a(n):

It is 2 o'clock. The hour hand is `10cm` long and the minute hand is `16cm` long. Find the distance, in `cm`, between the tip of the minute hand and the tip of the hour hand.

There are 7 cards and each has a number on the front and a number on the back. The sum of the seven front numbers equals the sum of the seven back numbers. Also, the sum of the two numbers on each card is the same. The fourteen numbers are all unique positive integers. The numbers on the front of the first six cards are: 1, 15, 20, 7, 11 and 16. Find the sum of the two numbers on the seventh card.

Given that `x^2017-2x+1=0` and `xne1` , find the value of `1+x+x^2+x^3+...+x^2016`.

Jim and his wife Jeri attend a party with four other married couples. As they enter, Jim and Jeri shake hands with some of the guests, but not with each other. During the event, each person (except one) shakes hands with some of the guests, but not with their spouse. After the party, Jim asks each guest how many people they shook hands with and got answers 0,1,2,3,4,5,6,7,8. How many people did Jeri shake hands with?

A trapezoid (trapezium) is inscribed in a semicircle of radius 4. Find the maximum possible area of the trapezoid (trapezium).

Pakrit, a primary school teacher, created a new game for the students. The game uses a spinner that has regions labelled `1, 3, 5, 6 and 9`. The areas of the regions are in the ratio `4:5:3:7:1` respectively. A student is to spin the spinner four times and then sum the numbers obtained. FInd the student's expected score.

Evaluate `sum_(k=1)^(100)1/(4k^2-1)`.

Find the maximum gradient of a tangent line to `y=6/(x^2+3)`.

How many values of `x` in the interval `0satisfy`

At a swimming pool, 5 swimmers leave their goggles in the locker room. The instructor finds all of the goggles and randomly returns them to the swimmers.

What is the probability that exactly one swimmer gets the correct googles?

The graph of the equation `x^2-xy-2y^2=0` is

`A` and `B` are the points of intersection of `x^2+y^2-4x-2y-20=0` and `x^2+y^2+10x-4y+13=0` . Find the gradient of `AB`.

In `\triangle ABC` , `AB=14` and `BC=12` . The median from A is perpendicular to the median from C. Find AC.  

Find the number of zeros there are after the last non-zero digit when you evaluate `100^100-100!`.

Find the minimum value of `f(x)=(x-9)^2+(x-5)^2+(x-3)^2+(x-7)^2-(x-8)^2-(x-4)^2`.

There is exactly one ordered pair `(x,y)` where `x` and `y` are positive integers, that satisfies `x^4-y^2=577` . Find `x+y`.

A particle moves along the co-ordinate plane with velocity `v(t)=6sin3t`. Find the total distance travelled by the particle in the first `pi` seconds.

The tangent line of `sqrtx+sqrty=4` at the point `(1,9)` has an x-intercept of...  

Which of the following numbers is prime?

You are inflating a large spherical balloon at the rate of `17cm^3/sec`. Find the rate its radius is increasing at the moment the radius is `20cm`.

Find the `x-`coordinates for the points of inflection of `X~N(3,2)`.

Find the value of `lim_(x->o)((1-cosx)/(xsinx))`.

In `\triangle ABC`, `A, B and C` are at `(0,0), (2,2) and (4,1)` respectively. Find `sin(ABC)`.

Find the maximum domain for the function `f(x)=(1)/(4sqrt(sqrt(x)-x)-2)`.

Find the mean average value of the roots of the equation `2x^10-80x^9+4x-7=0`.

A camera is positioned `100m` at right angles to a straight road along which a car is traveling at `120m/sec`. The camera turns so that it is always pointed at the car. In radians per second, find the speed that the camera is turning as the car passes closest to the camera.

How many sequences x₁,x₂,x₃,x₄,x₅ satisfy x_1<x_2<x_3<x_4<x₅ if each x_i is chosen from 1,2,3,...,9?

Given that `f(n)=log_2(3)xxlog_3(4)xx...xxlog_(n-1)(n)`, find `sum_(k=2)^10f(2^k)`.

In `/_\ ABC`, we are given `/_ABC=150^circ`. `B` is a point on `bar(AD)` and `C` is a point on `bar(AE)` such that `bar(AB)=bar(BC)=bar(CD)=bar(DE)`. Find `/_ADE`.

`f(x)=ax+b`, where `a` and `b` are real numbers and `f(f(f(x)))=8x+28`. Find `a+b`.

Evaluate  `(-sqrt(3)+i)^9`.

Find the area bounded by the graph of  `3x^2y-8xy=2xy^2`.

If the roots of  `P(x)=x^3+2ax^2-x-10a` are all real integers, find the three roots.