Five numbers form an arithmetic sequence whose sum is `920`. The second, third, and fifth numbers form a geometric sequence. Find the larger of the two possible values for the fifth number.
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 10 in. long and ther minute hand is 16 in. long. Find the distance in in. 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.
If `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 themaximum possible area of the trapezoid (trapezium).
Pakrit, a primary school teacher, created a new game. 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. Each student is to spin the spinner four times and then sum the numbers obtained. What is the expected score?
Evaluate `sum_(k=1)^(100)1/(4k^2-1)` .
Find the maximum slope 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.
How many zeros are there 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 for 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. How fast is its radius increasing at the moment the radius is 20cm?
For which values of `x` does a normal curve with mean of 3 and standard deviation of 2 have points of inflection?
Find the value of `lim_(x->o)((1-cosx)/(xsinx))` .
In `\triangle ABC`, `A` is at `(0,0)`, `B` is at `(2,2)` and `C` is at `(4,1)`. Find `sin(B)`.
Over which interval is the function `f(x)=(1)/(4sqrt(sqrt(x)-x)-2)` defined?
What is the average value of all the roots of the equation `2x^10-80x^9+4x-7=0` ?
A camera is located 100 feet from a straight road along which a car is traveling at 120 ft/sec. The camera turns so that it is always pointed at the car. In radians per second, how fast is the camera turning as the car passes closest to the camera?
How many sequences x1,x2,x3,x4,x5 satisfy x1<x2<x3<x4<x5 if each xi is chosen from 1,2,3,...,9?
If `f(n)=log_2(3)xxlog_3(4)xx...xxlog_(n-1)(n)` , then find `sum_(k=2)^10f(2^k)`.
In `/_\ ABC`, we are given `/_ABC=150^O`. `B` is a point on `vec(AD)` and `C` is a point on `vec(AE)` such that `vec(AB)=vec(BC)=vec(CD)=vec(DE)`. Find `/_ADE`.
`f(x)=ax+b`, where `a` and `b` are real numbers and `f(f(f(x)))=8x+28`. Find `a+b`.
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, then what are the three roots?