Sum to product formula for cosine function is
cos(u) - cos (v) = -2sin((u+v)/2).sin((u-v)/2)
substitute u = 165 and v = 75 in above equation (assume all angles are in degrees)
cos165 - cos75
= -2sin((165+75)/2).sin((165-75)/2)
= -2sin(240/2).sin(90/2)
=...

initial height, h0 = 97 ft
initial speed, u=201 ft/s
g = 32.174 ft/s2
A)
h = h0 + ut + 0.5at2
substitute acceleration, a = -g (gravitational acceleration in the opposite direction of initial velocity)
h = h0 + ut - 0.5gt2
Substitute values...

Let probability of A winning the race = PA
Let probability of B winning the race = PB
Let probability of C winning the race = PC
Given:
PA = PB
PA = 2PC
PB = 2PC
We know that probability that either A, B, or C wins is 1
PA+PB+PC = 1
Substitute...

Sum to Product formula for Sine function is
sin(u) + sin (v) = 2sin ((u+v)/2).cos ((u-v)/2)
Substitute u = 11.pi/12 and v = 7.pi/12 in above equation.
sin 11pi/12 + sin 7pi/12
=2sin((11pi/12+7pi/12)/2).cos((11pi/12-7pi/12)/2)
=2sin((18pi/12)/2).cos((4pi/12)/2)
=2sin((3pi/2)/2)...

Lateral surface area of a cone, A = pi x r x l where r=base radius and l = slant height
given r = 3 and A = 219.9.
Substitute these values in above equation for lateral surface area of a cone.
A = pi x r x l
219.9 = 3.1416 x 3 x l ....Divide both sides by (3.1416 x 3)
l=219...

1) Yes.
xy = 3 is a rectangular hyperbola.
This hyperbola lies in first and third quadrant.
Its asymptotes are x-axis (y = 0) and y-axis (x = 0).
Center: (0,0)
Transverse axis of symmetry: y=x
Domain: set of all real numbers except x=0
Vertices: (sqrt(3), sqrt(3))...

Let number of adults attending the dance = a
Let number of students attending the dance = s
Given
a/s = 1/10 ....multiply both the sides by 10 s
s = 10a ........(1)
There were 477 more students than adults
s = a + 477 ........(2)
Substitute...

3x + 4y + z = 7..........(1)
2y + z = 3..........(2)
-5x + 3y + 8z = -31.....(3)
Let us first eliminate z from equations (1) and (3) to get equations (4) and (7) with two variables.
(1) - (2) gives...

grade 6 students received the following scores on a recent math test. find the median of data set: 97,59,64,65,52,50,15,62,55,60,90? (answer)

Median is the middle value after arranging the data in ascending or descending order. If there are even number of values in a data set, then we take the average of the middle two values.
Let us arrange the data in ascending order first.
15, 50, 52, 55, 59, 60, 62, 64, 65, 90,...

Let us first simplify the equation.
(1-cox5x)/(1-cos7x) .... multiply numerator and denominator by (1+cos5x)(1+cos7x)
=[(1-cos5x)(1+cos5x)(1+cos7x)]/[(1-cos7x)(1+cos7x)(1+cos5x)]......remember that (a+b)(a-b)=a2-b2
=[(1-cos25x)(1+cos7x)]/[(1-cos27x)(1+cos5x)] ...

1) use perfect square formula a2+2ab+b2=(a+b)2
16y2 + 24y + 9 = (4y)2 + 2.4y.3 + 32 = (4y+3)2
2) use difference of squares formula a2 - b2 = (a+b)(a-b)
49x2 - 100y2 = (7x)2 - (10y)2 = (7x-10y)(7x+10y)
3) use sum of cubes formula, a3 + b3 =...

a) Easiest way to solve this problem is to remember that a2 - b2 = (a+b) (a-b) and recognize the pattern from the problem
100x2-1 = (10x)2 - (1)2 = (10x+1)(10x-1)
b) If you do not remember the formula for a2 - b2, then you will need to solve the problem by using usual factoring method...

Let the moving point P be (x, y)
remember that slope m of line joining points (x1, y1) and (x2, y2) is m = (y1-y2)/(x1-x2)
slope of line joining point P(x, y) to A(1, 3) is (y-3)/(x-1)
slope of line joining point P(x, y) to B(3, 1) is (y-1)/(x-3)
We have been told that, slope of...

This polynomial is not prime since it has the factors.
1) Fastest and easiest way to solve this problem is to remember the formula for (a+b)2 and observe the pattern.
We know that, a2+2ab+b2 =(a+b)2
16x2 - 24xy + 9y2 = (4x)2 - 2.4x.3y + (3y)2
=(4x-3y)2
2) If...

P(x)=P=x2+14x+54
Function y=ax2+bx+c is a parabola with vertex at x= -b/2a. It opens up if a>0 and it opens down if a <0.
So function P(x)=P=x2+14x+54 is a parabola with a=1, b=14, c=54. Since a=1 >0, it opens up.
Its vertex is at
x = -b/2a = -14/2...

f(x) = - |x+2|, substitute x = -8 to get
f(-8) = - |-8 +2|
f(-8) = - |-6|, absolute value of a negative number is a positive number
f(-8) = -6

^
...

Ratio of height to new height = height:new height = 147/30.5 = 4.82
This is a ratio problem and not a proportion problem.
Ratio is the answer obtained by dividing two similar quantities (quantities with same units). We use symbol
: to specify ratio.
Equality of two ratios is...

Radical expression contains a square root (√) of some expression. It undefined when value inside radical (called discriminant) is negative.
Square root is not defined for negative values of discriminant. It is defined only for all values of discriminant that are greater than or equal to zero...

Let me restate this cryptic question.
2.4 million lb (pounds) of almonds are sold when the selling price is $5.50 per lb.
4.8 million lb (pounds) of almonds are sold when the selling price is $4.50 per lb.
What linear function expresses the amount of almonds sold as a function of the...