Answer:
the square root of 197
Step-by-step explanation:
delta x=14
delta y=1
therefore with the Pythagorean theorem, the hypotenuse/distance is the square root of 197
Answer:
4 miles
Step-by-step explanation:
6 divided by 3 = 2 = one-third of 6
--> multiply by two to get two thirds of six = 4 miles
Answer:
2√3/3
Step-by-step explanation:
Sec(330°)
=1/cos(330°)
=1/√3/2 (since Cos (330°)=√3/2
=1×2/√3
=2/√3×√3/√3
=2√3/3
Answer:
Domain [-5,3)
Range [0,2]
Step-by-step explanation:
Domain is where the function exists for the x's.
The graph starts at x=-5 and ends at x=3. The graph includes what happened at x=-5 but not at x=3. Since there are no breaks in the graph, the graph exists for x values bigger that or equal to -5 but less than 3.
The domain is [-5,3) in interval notation.
Range is very similar except it is for the y values. So the graph starts at y=0 and stops at y=2. It includes something happening at both and there are no breaks between y=0 and y=2.
The range in interval notation is [0,2].
0.373 seconds. First, calculate the initial vertical velocity of the shell. 800sin(30) = 800*0.5 = 400 m/s Now the formula for the distance traveled is d = 400 m/s * T + 0.5A T^2 Substituting known values gives. 150 = 400 m/s * T + 0.5*9.80m/s^2 T^2 150 = 400 m/s * T + 4.9 m/s^2 T^2 Arrange as a quadratic formula 0 = 400 m/s * T + 4.9 m/s^2 T^2 - 150 4.9 m/s^2 T^2 + 400 m/s * T - 150 = 0 Now solve for T using the quadratic formula with a=4.9, b=400, and c=-150 The calculated value is 0.373 seconds. Is this value reasonable? Let's check. The initial downward velocity is 400 m/s. So 150/400 = 0.375 seconds. Since the actual time will be a bit less due to acceleration by gravity and since the total time is so short, there won't be much acceleration due to gravity, the value of 0.373 is quite reasonable.