Answer:
81%
Step-by-step explanation:
2835 / 3500
0.81 out of 1
81%
Answer:
The magnitude of the vertical component of vector u is ![6\sqrt{2}](https://tex.z-dn.net/?f=6%5Csqrt%7B2%7D)
The magnitude of the horizontal component of vector u is ![6\sqrt{2}](https://tex.z-dn.net/?f=6%5Csqrt%7B2%7D)
Step-by-step explanation:
A vector quantity has, a magnitude and a direction
The horizontal component of vector
is ║u║ cos α
The vertical component of vector
is ║u║ sin α
∵ The magnitude of vector u is 12 ft
∵ The measure of angle α is 135°
- Substitute the magnitude and the angle in the rule of
each component
∴
= 12 cos(135)
∴
= 12 sin(135)
∵ cos(135) = ![-\frac{\sqrt{2}}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D)
∴
= 12 (
)
∴
= ![-6\sqrt{2}](https://tex.z-dn.net/?f=-6%5Csqrt%7B2%7D)
- The magnitude of a number means the number without its sign
∴ The magnitude of the horizontal component of vector u is ![6\sqrt{2}](https://tex.z-dn.net/?f=6%5Csqrt%7B2%7D)
∵ sin(135) = ![\frac{\sqrt{2}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D)
∴
= 12 (
)
∴
= ![6\sqrt{2}](https://tex.z-dn.net/?f=6%5Csqrt%7B2%7D)
∴ The magnitude of the vertical component of vector u is ![6\sqrt{2}](https://tex.z-dn.net/?f=6%5Csqrt%7B2%7D)
Answer:
![\boxed{\text{16 ft}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Ctext%7B16%20ft%7D%7D)
Step-by-step explanation:
h(x) = -2x² + 4x + 16
At the time the ball is thrown,
x = 0
h(0) = -2 × 0² + 4 × 0 + 16 = ![\boxed{ \textbf{16 ft}}](https://tex.z-dn.net/?f=%5Cboxed%7B%20%5Ctextbf%7B16%20ft%7D%7D)
Answer:
![\frac{25}{144}](https://tex.z-dn.net/?f=%5Cfrac%7B25%7D%7B144%7D)
Step-by-step explanation:
We want to know "probability that first is vowel AND second is vowel"
In probability theory, "AND" means Multiplication.
<em>Essentially we want to figure out probability of first drawn to be vowel and multiply that with probability second drawn is vowel as well.</em>
<em />
There are 5 vowels and total 12 letters, so
P (vowel) = 5/12
<u>For the second draw, there are STILL 12 letters and 5 vowels (since the first drawn is REPLACED)</u>. Hence, probability of 2nd vowel is the same. So:
P (vowel for 2nd draw) = 5/12
<em>Now we multiply them to get:
</em>
The height of the door in the actual playhouse would be 4.5 ft