Answer:
x = ± ![\sqrt{7}](https://tex.z-dn.net/?f=%5Csqrt%7B7%7D)
Step-by-step explanation:
Given
x² - 7 = 0 ( add 7 to both sides )
x² = 7 ( take the square root of both sides )
x = ± ![\sqrt{7}](https://tex.z-dn.net/?f=%5Csqrt%7B7%7D)
The domain is
![- 10 \leqslant x \leqslant 10](https://tex.z-dn.net/?f=%20-%2010%20%5Cleqslant%20x%20%5Cleqslant%2010)
and the range is
![- 5 \leqslant y \leqslant 5](https://tex.z-dn.net/?f=%20-%205%20%5Cleqslant%20y%20%5Cleqslant%205)
Domain is x values (horizontal axis), while range is y values (vertical axis). On a line like this one, domain is calculated from the left most point to the right most, while range is calculated from the down most to the upmost.
Because this line is a solid line rather than a dotted line, less than or equal to
![\leqslant](https://tex.z-dn.net/?f=%20%5Cleqslant%20)
signs are used rather than just
![<](https://tex.z-dn.net/?f=%20%3C%20)
less than signs.
Answer:
(a) ![0.408m/sec^2](https://tex.z-dn.net/?f=0.408m%2Fsec%5E2)
(b) ![0.134m/sec^2](https://tex.z-dn.net/?f=0.134m%2Fsec%5E2)
(c) ![0.039m/sec^2](https://tex.z-dn.net/?f=0.039m%2Fsec%5E2)
Step-by-step explanation:
We have given velocity as function of t ![v(t)=\frac{85t}{(8t+14)}](https://tex.z-dn.net/?f=v%28t%29%3D%5Cfrac%7B85t%7D%7B%288t%2B14%29%7D)
Acceleration is equation rate if change of velocity with respect to time
So ![a=\frac{dv}{dt}=\frac{(8t+14)85-85t\times 8}{(8t+14)^2}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bdv%7D%7Bdt%7D%3D%5Cfrac%7B%288t%2B14%2985-85t%5Ctimes%208%7D%7B%288t%2B14%29%5E2%7D)
(a) Acceleration at t = 5 sec
![a=\frac{(8\times 5+14)85-85\times 5\times 8}{(8\times 5+14)^2}=0.408m/sec^2](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B%288%5Ctimes%205%2B14%2985-85%5Ctimes%205%5Ctimes%208%7D%7B%288%5Ctimes%205%2B14%29%5E2%7D%3D0.408m%2Fsec%5E2)
(b) Acceleration at t = 10 sec
![a=\frac{(8\times 10+14)85-85\times 10\times 8}{(8\times 10+14)^2}=0.134m/sec^2](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B%288%5Ctimes%2010%2B14%2985-85%5Ctimes%2010%5Ctimes%208%7D%7B%288%5Ctimes%2010%2B14%29%5E2%7D%3D0.134m%2Fsec%5E2)
(c) Acceleration at t = 20 sec
![a=\frac{(8\times 20+14)85-85\times 20\times 8}{(8\times 20+14)^2}=0.039m/sec^2](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B%288%5Ctimes%2020%2B14%2985-85%5Ctimes%2020%5Ctimes%208%7D%7B%288%5Ctimes%2020%2B14%29%5E2%7D%3D0.039m%2Fsec%5E2)
Step-by-step explanation:
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