All Answers 352881 Answers

convert all to sin and cos and simplify

1/cos^2 = 4sin^2/cos^2

multiply both sides by cos^2, simplipies to sin^2=1/4

arc sin of +/- sqrt 1/4 = pi/6 and (-pi/6 degrees) <- not in 0 to 2pi

going to 2pi we probably will need to add pi to those for the other values

7pi/6 and 5pi/6 and pi/6 from above would be the three answers

1A) reduce what you have to 5sin^2/cos, no fractions, 5 tan sin

1b) always convert everything to sin and cos to make it easy

after doing that and simplifing the top becomes 1/sin^2

the bottom becomes cos^2/sin + sin, common denomenator gives us cos^2+sin^2/sin

hey the top became 1, now we have (1/sin^2)/(1/sin), simplifies into 1/sin or csc with no fractions

2) lets convert those cos to sin

factor a - out then convert using cos (pi/2 - x) = sin

-2(sin^2)x+3sinx -2=0

sinx(-2sinx+3) =2

sinx =2 and sinx = 1/2

#2) y/-x

#3) 7π/4

1

sin^2x sinx = -cos x + cos^2x cosx    ( I will drop the 'x' for easier typing)

                      = -cos ( 1- cos^2)

   sin^2 sin     =   -cos (sin^2)

   sin = - cos

    x = 3pi / 4    and   7pi/4

Let x = cos x   then substitute

6 x^2 +17 x = -5

6x^2 +17x +5=0      Use quadratic formula to find x = -1/3

cos x = -1/3   (?)

Sorry about that.

You got it EP.

Not SURE of this answer, but the POPULATION mean is the average age of ALL of the players and is given as 27.

The SAMPLE mean is the mean of the sample of 12 players....add together the 12 ages and divide by 12 to get the SAMPLE mean

OK....this is kinda long....hang in there and we'll see if I get the same answer as Melody.

The ball's x and y positions are given by

x=xo + vox t = voxt  = .707 v t    (1) (since xo=0  and 45 degrees and there is no x decceleration)

y= yo + voy t - 1/2 a t^2 = .707v t - 1/2 a t^2  (2)

The position of the two ends of the truck bed are given by 

5m + 9 (t)    and  7.5 + 9 (t)

Now...when the ball lands in the truck bed y will = 0, so

y=0= .707v t - 1/2 a t^2     (3)

and the 'x' values for the ball and truck bed will be equal

.707 v t  = 5+ 9 t    substitute THIS value of .707v t in to (3)  and solve for t

0= 5 + 9t - 1/2 (9.8) t^2       results in t = 2.28 sec (using quadratic formula)

THEN the back of the truck bed will be at   5 + 9t = 25.55 m  

              (the front wil be 25.55+2.5=28.05m)

Now solve (1)  for the ball velocity  .707v(2.28)=25.55    results in v = 15.85 m/s

   to land on the BACK of the truck bed.

Repeating some of this for the FRONT of the truck bed:

.707 v (2.28) = 28.05 = 17.4 m/s

Velocity must be   15.85-17.4 m/s     (NOT QUITE THE SAME AS MELODY'S ANSWER)

Ooops.....   GingerAle is correct....I constrained the motion of the truck for the second part (shown in THIS color above) ....here is the CORRECTED version for the second part (it is like the first part)

For the FRONT of the truck bed, we have  .707 v t = 7.5 + 9t

  Substitute THIS value in to equation (3) and solve for t

  0= 7.5 + 9t - 1/2 (9.8)t^2       results in t= 2.459 sec (using quadratic formula)

Then the FRONT of the truck bed will be at 7.5 + 9t = 29.63 m

Now solve (1) for the ball velocity  ,707 v (2.459) = 29.63 m results in  v =17.04 m/s

  to land on the FRONT of the truck bed

SOOOOO Velocity must be between   15.85-17.04 m/s      Taa-Daa ! 

(Thanx everyone for pointing out the errors of my ways....hopefully I will not burn in hell forever)

projectile motion problems figure 2 

A ball is kicked at an angle θ = 45°. It is intended that the ball lands in the back of a moving truck which has a trunk of length L = 2.5 m. If the initial horizontal distance from the back of the truck to the ball, at the instant of the kick, is do = 5 m, and the truck moves directly away from the ball at velocity V = 9 m/s (as shown), what is the maximum and minimum velocity vo so that the ball lands in the trunk. Assume that the initial height of the ball is equal to the height of the ball at the instant it begins to enter the trunk.

You need to check my answer very carefully before you accept it. There is a lot of room for errors . 

That should have been 17.1 m/s  and 18.8 m/s

it is a rectangular prism. How do you find the volume of a rectangular prism?

Google it if you don't know. 

Start by plotting the point in the number plane.

Then you can use pythagoras's theorum to work out the value of the sides in the right angle triangle with the point given. that is  (0,0) (3,-7) (3,0)

You are in the 4th quad so sine will be negative.

Terminating decimal values for k occur when 1+2x is a power of 5, so: \(\sum k=\sum_{p=1}^\infty 5^{-p}=\frac{1}{4}\)

The diagonals of a regular hexagon have two possible lengths. What is the ratio of the shorter length to the longer length? Express your answer as a common fraction in simplest radical form.

EACH of the SIX sides are   3 x 1/2  ft^2

6  *  (3 x 1/2) = 9 sq ft

This is a double post.  See previous.

The correct answer is 'C'

The tank has 5 gallons and needs 4 more gallons to total 9 gallons

4 gallons / (1/4 gal/min) = 16 minutes

You're welcome !   Gotta go .....     Later !

Thank you ElectricPavlov! You're a huge help!

The semi circle area is 1/2 of a circle of radius 2   (the diameter is 4 from the graph)

    area of the full circle would be  pi r^2         

     semi circle area = 1/2 pi r^2 = 1/2 pi (2^2)

Area for a triangle is 1/2 bh     b= 4   h= 5   (from the graph)

       triangle area =  1/2 (4)(5)

Add the reds together for the final answer ....wooohooooo!

Volume of cube = s x s x s

Area of cube = s x s x 6 = 1/6 volume = 1/6 s^3

  sooo    6s^2 = 1/6 s^3       divide by  s^2

              6 = 1/6 s               multiply by 6

              36 = s

Square area =  36 x 36 x 36 = l x l       solve for l = 216 units