Fifteen thousand and four hundred and nine
15,409/16000
X=5! you would set the two equations equal and subtract from both sides until you were left with the answer
Answer:
120.51·cos(377t+4.80°)
Step-by-step explanation:
We can use the identity ...
sin(x) = cos(x -90°)
to transform the second waveform to ...
i₂(t) = 150cos(377t +50°)
Then ...
i(t) = i₁(t) -i₂(t) = 250cos(377t+30°) -150cos(377t+50°)
A suitable calculator finds the difference easily (see attached). It is approximately ...
i(t) = 120.51cos(377t+4.80°)
_____
The graph in the second attachment shows i(t) as calculated directly from the given sine/cosine functions (green) and using the result shown above (purple dotted). The two waveforms are identical.
Answer:
The other distances are 400 ft and 750 ft.
Step-by-step explanation:
a + b + c = 2000
a + b + 850 = 2000
a + b = 1150 Equation 1
a^2 + b^2 = c^2
a^2 + b^2 = 850^2
a^2 + b^2 = 722,500 Equation 2
a + b = 1150
a^2 + b^2 = 722,500
a = 1150 - b
(1150 - b)^2 + b^2 = 722,500
1,322,500 - 2300b + b^2 + b^2 = 722,500
2b^2 - 2300b + 600,000 = 0
b^2 - 1150b + 300,000 = 0
![x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cdfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2%20-%204ac%7D%7D%7B2a%7D%20)
![x = \dfrac{-(-1150) \pm \sqrt{(-1150)^2 - 4(1)(300,000)}}{2(1)}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cdfrac%7B-%28-1150%29%20%5Cpm%20%5Csqrt%7B%28-1150%29%5E2%20-%204%281%29%28300%2C000%29%7D%7D%7B2%281%29%7D%20)
![x = \dfrac{1150 \pm \sqrt{1,322,500 - 1,200,000}}{2}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cdfrac%7B1150%20%5Cpm%20%5Csqrt%7B1%2C322%2C500%20-%201%2C200%2C000%7D%7D%7B2%7D%20)
![x = \dfrac{1150 \pm \sqrt{122,500}}{2}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cdfrac%7B1150%20%5Cpm%20%5Csqrt%7B122%2C500%7D%7D%7B2%7D%20)
![x = \dfrac{1150 \pm 350}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cdfrac%7B1150%20%5Cpm%20350%7D%7B2%7D)
![x = \dfrac{1500}{2}~~~or~~~x = \dfrac{800}{2}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cdfrac%7B1500%7D%7B2%7D~~~or~~~x%20%3D%20%5Cdfrac%7B800%7D%7B2%7D%20)
x = 750 or x = 400
Answer: The other distances are 400 ft and 750 ft.
Y = -2(x + 3)^2 - 4
First expand the parentheses:-
y = -2(x + 3)(x + 3) - 4
y = -2 [(x(x + 3) + 3(x + 3)] - 4
y = -2 ( x^2 + 3x + 3x + 9) - 4
y = -2(x^2 + 6x + 9) - 4
Now distribute the -2 over the parentheses:-
y = -2x^2 - 12x - 18 - 4
y = -2x^2 - 12x - 22 Answer