Step-by-step explanation: uhhhh the answers basically explain why. 1 because it's a terminating decimal, 4 because it's a repeating number, and 5 because the square root of 11 is not a perfect square, and is not a repeating or terminating decimal.

7 0

3 years ago

Angle α is in quadrant III, and angle β is in quadrant II. If sin α = –4∕5 and sin β = 1∕2, find cos (α + β).

Minchanka [31]

Answer:

Step-by-step explanation:

Given sin α = –4∕5 and sin β = 1∕2

To get α from sin α = –4∕5,

α = arcsin(-4/5)

α = arcsin (-0.8)

α = -53.13°

If angle α is in quadrant III, then α = 180+53.13 = 233.13° (sin is negative in the 3rd quadrant)

Similarly for sin β = 1∕2

β = arcsin(1/2)

β = arcsin(0.5)

β = 30°

Since β is in quadrant II, β = 180-30 = 150°

To find cos (α + β). where α = 233.13° and β = 30°

cos (α + β)= cos (233.13 + 150)

= cos 383.13°

cos (α + β) = 0.9196

5 0

3 years ago

Alex has 512 cubes, with dimensions in feet (ft), like the one shown. He uses all the cubes to fill a box shaped like a larger r

Alex_Xolod [135]

A) First, find the volume of each cube:

V = s³

= (1/2)³

= 1/8 ft³

We have a total of 64 cubes, therefore the maximum volume will be:

Vmax = 64 · (1/8) = 8 ft³

B) The volume of a rectangular prism is given by:

V = w × l × h

Therefore any combination of w × l × h = Vmax = 8 will be fine.

Examples:

2 × 2 × 2

4 × 2 × 1

5 0

3 years ago