Answer:
The straight line has got coordinates,they are (0;-3) and (6;0)
The trigonometric equation <span> (sin Θ − cos Θ)^2 − (sin Θ + cos Θ)^3 can be simplified by:
</span>Using x for Θ:
<span>(sinx - cosx)^2 - (sinx + cosx)^2 </span>
<span>= (sin^2 x - 2sinxcosx + cos^2 x) - (sin^2 x + 2sinxcosx + cos^2 x) </span>
<span>= - 2 sinx cosx - 2 sinx cosx </span>
<span>= - 4 sinx cosx </span>
<span>= - 2sin(2x)
</span>
I hope it has come to your help.
The answer is 4 inches. This is because the scale is 1 inch=3 feet. And when doing 12ft divided by 3ft you get 4. The 4 then represents 4 inches. Hope it helps :)
Answer: 54000 cube cm
Step-by-step explanation:
Let h be the height of the box kite,
Also the length of one face = 30 cm,
Hence, the total area of the kite box that is covered by the fabric
= 4 × Area of one face
= 4 × 30 × h
= 120 h
According to the question,
120 h = 7200
h = 60 cm
Hence, the height of the box = 60 cm,
The volume inside the kite = The base area of the box × Its height
= 30² × 60
= 900 × 60
= 54000 cm³
When the ball reaches the ground, its height is 0.
We set the height function equal to zero and solve for t, the time.
h = -16t^2 + 250
-16t^2 + 250 = 0
16t^2 - 250 = 0
![(4t + \sqrt{250})(4t - \sqrt{250}) = 0](https://tex.z-dn.net/?f=%20%284t%20%2B%20%5Csqrt%7B250%7D%29%284t%20-%20%5Csqrt%7B250%7D%29%20%3D%200%20)
![4t + \sqrt{250} = 0](https://tex.z-dn.net/?f=%204t%20%2B%20%5Csqrt%7B250%7D%20%3D%200%20)
or
![4t - \sqrt{250} = 0](https://tex.z-dn.net/?f=%204t%20-%20%5Csqrt%7B250%7D%20%3D%200%20)
![4t = -\sqrt{250}](https://tex.z-dn.net/?f=%204t%20%3D%20-%5Csqrt%7B250%7D%20)
or
![4t = \sqrt{250}](https://tex.z-dn.net/?f=%204t%20%3D%20%5Csqrt%7B250%7D%20)
![t = -\dfrac{\sqrt{250}}{4}](https://tex.z-dn.net/?f=%20t%20%3D%20-%5Cdfrac%7B%5Csqrt%7B250%7D%7D%7B4%7D%20)
or
![t = \dfrac{\sqrt{250}}{4}](https://tex.z-dn.net/?f=%20t%20%3D%20%5Cdfrac%7B%5Csqrt%7B250%7D%7D%7B4%7D%20)
We discard the negative solution since time must be positive.
The positive solution is
![t = \dfrac{\sqrt{250}}{4} \approx 4.0](https://tex.z-dn.net/?f=%20t%20%3D%20%5Cdfrac%7B%5Csqrt%7B250%7D%7D%7B4%7D%20%5Capprox%204.0%20)
Answer: 4.0 seconds