An experimental vehicle was able to travel 3/8 miles on 1/16 gallon of water. At this rate, what was the mileage in miles per ga
1 answer:
Answer:
6 miles per gallon
Step-by-step explanation:
Given : An experimental vehicle was able to travel 3/8 miles on 1/16 gallon of water.
To Find: At this rate, what was the mileage in miles per gallon of water for this vehicle?
Solution:
Since An experimental vehicle was able to travel 3/8 miles on 1/16 gallon of water.
So, the mileage in miles per gallon of water for this vehicle:
Thus the mileage of water for this vehicle is 6 miles per gallon
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Answer: 9 ft
Explanation: Since the velocity is the derivative of position vector and the displacement is the difference between two position vectors, the displacement is computed as a definite integral of velocity for a time interval (from one time to another time).
Because the time interval is t =0 second to t = 3 seconds, the displacement is calculated as
![\text{displacement} = \int_{0}^{3} {v(t) dt} \\ \\ = \int_{0}^{3} {(-t^2 + 6) dt} \\ \\ = \left [ -\frac{t^3}{3} + 6t \right ]_{0}^{3} \\ \\ = \left ( -\frac{(3)^3}{3} + 6(3) \right ) - \left ( -\frac{(0)^3}{3} + 6(0) \right ) \\ \\ \boxed{\text{displacement} = 9}](https://tex.z-dn.net/?f=%5Ctext%7Bdisplacement%7D%20%3D%20%5Cint_%7B0%7D%5E%7B3%7D%20%7Bv%28t%29%20dt%7D%0A%5C%5C%0A%5C%5C%20%3D%20%5Cint_%7B0%7D%5E%7B3%7D%20%7B%28-t%5E2%20%2B%206%29%20dt%7D%0A%5C%5C%0A%5C%5C%20%3D%20%5Cleft%20%5B%20-%5Cfrac%7Bt%5E3%7D%7B3%7D%20%2B%206t%20%5Cright%20%5D_%7B0%7D%5E%7B3%7D%0A%5C%5C%0A%5C%5C%20%3D%20%5Cleft%20%28%20-%5Cfrac%7B%283%29%5E3%7D%7B3%7D%20%2B%206%283%29%20%5Cright%20%29%20-%20%5Cleft%20%28%20-%5Cfrac%7B%280%29%5E3%7D%7B3%7D%20%2B%206%280%29%20%5Cright%20%29%0A%5C%5C%0A%5C%5C%20%5Cboxed%7B%5Ctext%7Bdisplacement%7D%20%3D%209%7D)
Hence, the displacement is 9 ft.
Explanation: Since the velocity is the derivative of position vector and the displacement is the difference between two position vectors, the displacement is computed as a definite integral of velocity for a time interval (from one time to another time).
Because the time interval is t =0 second to t = 3 seconds, the displacement is calculated as
Hence, the displacement is 9 ft.
Answer:
The domain is (-∞ , -3) ∪ (-3, ∞) ⇒ D
Step-by-step explanation:
<em>The domain of the rational fraction is t</em><em>he values of x which make the fraction defined</em><em>. That means </em><em>the domain does not contain the values of x which make the denominator equal to 0</em><em>.</em>
∵ g(x) =
∴ The denominator = x + 3
→ Equate the denominator by 0
∵ x + 3 = 0
→ Subtract 3 from both sides
∴ x + 3 - 3 = 0 - 3
∴ x = -3
→ That means the domain can not have -3 because it makes the denominator
equal to 0
∴ The domain is all values of real numbers except x = -3
∴ The domain = {x : x ∈ R, x ≠ -3}
∴ The domain = (-∞ , -3) ∪ (-3, ∞)
Answer:
cot(x)
Step-by-step explanation:
Recall the Pythagorean Identity