Component of force in horizontal direction = 16*cos(60) = 16*0.5 = 8N acceleration = F/m = 8/1.5 = 5.33 m/s2

16(3x - 2)2 - 81y2   16(9x2 - 6x + 4) - 81y2 144x2 - 96x + 64 - 81y2 144x2 - 81y2 - 96x + 64 :)

Length segment BC = √((-1-5)2 + (6-2)2) = √52 =

Length of the segment = √((y2 - y1)2 + (x2 - x1)2) Plug the values y1 = 2, y2 = -6, x1 = 3, x2 = -3   Length of segment = √((-6-2)2 + (-3-3)2) = √(64+81) = √145 = 12.04

X intercept is the point where graph intercepts x axis i.e. y=0   f(x) = y = 0 0 = 6x + 12.6  solve for x 6x = -12.6 x= -12.6/6 = -2.1 :)

√2∠105 = √2 cos105  + √2sin105i = -0.36 + 1.63i   :)

V = Π r2h   V = 3.14  x 1.32  x 4.83 = 25.6 cubic inch   :)

V = 4/3  x 3.14  x 4.83   V = 463 cubic inch   :)

72 + b2 = 252   b2 = 252 - 72   b2 = 625 - 49   b2 = 576   b= √576 = 24   :)

(-3.5  x  4x)   + (3.5x3) = -14x + 10.5

Let speed of wind be "w" mph plane speed with the wind = 200+ w  mph plane speed into the wind = 200 - w   mph   Time to travel 500 miles with wind = 500/(200+w) hours Time to travel 500 miles into the wind = 500/(200-w) hours   so   500/(200...

Sale tax rate = 25/550  x 100 = 4.55% :)

Total ingredients have been reduced by a factor of 280/400= 0.7 All the ingredients should also be reduced by the same factor Chicken - 190 x 0.7 = 133 kg Eggs - 115 x 0.7 = 80.5 kg Sugar - 95 x 0.7 = 66.5 kg :)

Stopping distance is directly proportional to square of speed. So if speed is doubled stopping distance will be 22=4 times = 4x110 = 440ft. :)

Density of water is 1 Kg per liter   So 823000 kg of water = 823000 liter of water   1 gallon = 3.74 liter of water   823000 liters of water = 823000/3.74 gallons = 220053.5 gallons of water

Let width be x so length = 2x -65   perimeter = 2x + 2(2x-65) = 830 solve for x   2x + 4x - 130 = 830 6x = 960 x = 960/6 = 160   so width = 160 and length = 2x160 -65 = 255 :)

Let one number be x so other number must be x-3/4   x + x - 3/4 = 9  1/4 = 37/4   solve for x   2x = 37/4 + 3/4 = 40/4   x = 40/(2x4) = 40/8 = 5   so one number is 5 and other number is 5-3/4 = 4  1/4 :)...

Let amount Kevin kept for himself = x   x + x/2  + x/4 = 735000   solve for x   7x/4 = 735000 x=420000   Kevin got = \$420,000 Daughter got = 420000/2 = \$210,000 Father got = 420000/4 = \$105,000

Top soil required = 50 x 40 x 0.5 = 1000 cubic feet = 1000/27 cubic yard   Option 1 Bags required = 1000/3 = 333.33 ~ 334 bags cost = 334 x 2.25 = \$751.50   Option 2   Cost = (18 x 1000/27) +50 = \$716.67   Option 1 is less expensive...

Let amount invested in 6% account = X So amount invested in 9% account = X + 2000   Interest earned by 6% account = X x 6/100 x 1 = 6x /100 Interest earned by 9% account = (X+2000) x 9/100 x 1 = 9x/100 + 180   as per question   6x/100...