4x² + 3x + 5 = 0
x = <u>-3 +/- √(3² - 4(4)(5))</u>
2(4)
x = <u>-3 +/- √(9 - 80)</u>
8
x = <u>-3 +/- √(-71)
</u> 8<u>
</u>x = <u>-3 +/- √(71 × (-1))</u>
8
x = <u>-3 +/- √(71) × √(-1)
</u> 8<u>
</u>x = <u>-3 +/- 8.43i
</u> 8
x = -0.375 +/- 1.05375i
x = -0.375 + 1.05375i x = -0.375 - 1.05375i
<u />
Answer: 5.22 seconds
<u>Step-by-step explanation:</u>
t represents time and y represents the height.
Since we want to know when the ball hits the ground, find t when y = 0
Ball 1 starts at a height of 109 --> h = 109
0 = -16t² + 109
16t² = 109
t = 5.22
Answer:
7.92 cubic units
Step-by-step explanation:
The volume formed is V = ∫πx²dy
Now, since y = x³/4, x = ∛(4y). Also if x = 0, y = 0³/4 = 0 and the curve intersects the line y = 1. So the limits of integration are y = 0 to y = 1
So, V = ∫₀¹πx²dy
= ∫₀¹π[ ∛(4y)]²dy
= π(∛4)²∫₀¹[ ∛(y]²dy
= π(∛4)²∫₀¹y^³/₂dy
= π(∛4)²[y^⁵/₂]₀¹
= π(∛4)²[1^⁵/₂ - 0^⁵/₂]
= π(∛4)²[1 - 0]
= π(∛4)²
= 7.92 cubic units
The velocity is 7.44m/s in a direction to the west
