Answer:6
Step-by-step explanation:
Answer:
Erik's average speed exceeds the speed limit by 6.91 miles per hour.
Step-by-step explanation:
Let suppose that Erik travels at constant speed. Hence, the speed (
), measured in miles per hour, is determined by following equation of motion:
(1)
Where:
- Distance, measured in miles.
- Time, measured in hours.
Please notice that a hour equals 60 minutes. If we know that
and
, then the speed of Erik is:
![v = \frac{19.2\,mi}{0.267\,h}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B19.2%5C%2Cmi%7D%7B0.267%5C%2Ch%7D)
![v = 71.910\,\frac{mi}{h}](https://tex.z-dn.net/?f=v%20%3D%2071.910%5C%2C%5Cfrac%7Bmi%7D%7Bh%7D)
Which is 6.91 miles per hour above the speed limit.
<u>Answer:</u>
Value of cosθ is ±√7/3 .
<u>Step-by-step explanation:</u>
According to the Question , value of :
![\red{\implies sin\theta = \dfrac{\sqrt2}{3}}](https://tex.z-dn.net/?f=%5Cred%7B%5Cimplies%20sin%5Ctheta%20%3D%20%5Cdfrac%7B%5Csqrt2%7D%7B3%7D%7D%20)
And , we know the identity of sine and cosine as ,
<u>Using</u><u> </u><u>,</u><u> </u><u>this</u><u> </u><u>ident</u><u>ity</u><u> </u><u>we</u><u> </u><u>have</u><u> </u><u>;</u><u> </u>
![\implies sin^2\theta + cos^2\theta = 1 \\\\\implies \bigg( \dfrac{\sqrt2}{3}\bigg)^2 + cos^2\theta = 1 \\\\\implies \dfrac{2}{9} + cos^2\theta = 1 \\\\\implies cos^2\theta = 1 - \dfrac{2}{9} \\\\\implies cos^2\theta = \dfrac{9-2}{9} \\\\\implies cos\theta = \sqrt{\dfrac{7}{9}} \\\\\underline{\boxed{\blue{\bf \implies cos\theta = \pm \dfrac{\sqrt 7 }{3}}}}](https://tex.z-dn.net/?f=%5Cimplies%20sin%5E2%5Ctheta%20%2B%20cos%5E2%5Ctheta%20%3D%201%20%5C%5C%5C%5C%5Cimplies%20%5Cbigg%28%20%5Cdfrac%7B%5Csqrt2%7D%7B3%7D%5Cbigg%29%5E2%20%2B%20cos%5E2%5Ctheta%20%3D%201%20%5C%5C%5C%5C%5Cimplies%20%5Cdfrac%7B2%7D%7B9%7D%20%2B%20cos%5E2%5Ctheta%20%3D%201%20%5C%5C%5C%5C%5Cimplies%20cos%5E2%5Ctheta%20%3D%201%20-%20%5Cdfrac%7B2%7D%7B9%7D%20%5C%5C%5C%5C%5Cimplies%20cos%5E2%5Ctheta%20%3D%20%5Cdfrac%7B9-2%7D%7B9%7D%20%5C%5C%5C%5C%5Cimplies%20cos%5Ctheta%20%3D%20%5Csqrt%7B%5Cdfrac%7B7%7D%7B9%7D%7D%20%5C%5C%5C%5C%5Cunderline%7B%5Cboxed%7B%5Cblue%7B%5Cbf%20%5Cimplies%20cos%5Ctheta%20%3D%20%5Cpm%20%5Cdfrac%7B%5Csqrt%207%20%7D%7B3%7D%7D%7D%7D)
Now , here since θ is in 2nd quadrant and in 2nd quadrant cos is negative . Hence ,the value of cos will be :
Answer:
-4x + y + 6z
Step-by-step explanation:
Combine like terms (Terms with the same variable):
(2x + 5y - z) + (-6x - 4y + 7z)
Add straight across:
2x - 6x = -4x
5y - 4y = y
-z + 7z = 7z - z = 6z
-4x + y + 6z is your answer.
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Answer:
b and d/ a and c
Step-by-step explanation: