Answer: the speed of the submarine is 5miles per hour
Step-by-step explanation:
The submarine left Hawaii two hours before the aircraft carrier.
Let x = the speed of the submarine
The aircraft carrier traveled at 25 mph for nine hours.
After this time the vessels were 280 miles apart. This means that when they became 280 miles apart, the aircraft carrier has travelled for 9 hours. If the submarine was ahead of the aircraft carrier with 2 hours, that means that the submarine travelled 9 + 2 = 11 hours
Distance travelled = speed × time
Distance travelled by submarine will be 11 × x = 11x miles per hour
Distance travelled by aircraft carrier will be 25 × 9 = 225 miles per hour
If they are 280 miles apart, this would be their total distance. Therefore,
225 + 11x = 280
11x = 280 - 225 = 55
x = 55/11 = 5miles per hour
1. You have the following equation:
2. First, you must apply the Distributive property:
3. Simplify:
3. Add the like terms:
4. Solve for 
:
Therefore, the answer is: 
Answer:
C. 14
Step-by-step explanation:
F(x) = ∫₀²ˣ √(t³−15) dt
Use second fundamental theorem of calculus:
F'(x) = √((2x)³−15) d/dx (2x)
F'(x) = 2 √(8x³−15)
Evaluate at x=2:
F'(2) = 2 √(8×2³−15)
F'(2) = 2 √(64−15)
F'(2) = 2 √49
F'(2) = 14
Answer:
10 gallons
Step-by-step explanation:
Amy's car's maximum capacity to hold gas = 19 gallons
present amount of gas = 9 gallons
As the car's capacity is 19 gallons and present amount in tank is 9 gallons, so we can fill it as much as so that the amount in tank becomes 19 gallons.
let assume she fills x gallons
then x gallons and 9 gallons present earlier should be equal to 19 gallon, as the tank can not hold more than that.
lets write it mathematically
x + 9 = 19
subtracting 9 from both side
x + 9 - 9 = 19 - 9
=> x = 10
Thus, 10 gallons of gas is needed to fill the gas tank.
Answer:
Step by step Explanation:
![\sin \theta = \dfrac{\text{Perpendicular} }{\text{Hypotenuse}} = \dfrac{12}{15}\\\\\\\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}= \dfrac{9}{15}\\\\\text{Now,}\\\\\tan \dfrac{\theta}2 = \dfrac{\sin \tfrac{\theta}2}{\cos \tfrac{\theta}2}\\\\\\~~~~~~~~=\dfrac{2\cos \tfrac{\theta}2 \sin \tfrac{\theta}2 }{2\cos^2 \tfrac{\theta}2}~~~~~~;\left[\text{Multiply by}~ 2\cos\tfrac{\theta}2 \right]](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%20%3D%20%5Cdfrac%7B%5Ctext%7BPerpendicular%7D%20%7D%7B%5Ctext%7BHypotenuse%7D%7D%20%3D%20%5Cdfrac%7B12%7D%7B15%7D%5C%5C%5C%5C%5C%5C%5Ccos%20%5Ctheta%20%3D%20%5Cdfrac%7B%5Ctext%7BBase%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D%3D%20%5Cdfrac%7B9%7D%7B15%7D%5C%5C%5C%5C%5Ctext%7BNow%2C%7D%5C%5C%5C%5C%5Ctan%20%5Cdfrac%7B%5Ctheta%7D2%20%3D%20%5Cdfrac%7B%5Csin%20%5Ctfrac%7B%5Ctheta%7D2%7D%7B%5Ccos%20%5Ctfrac%7B%5Ctheta%7D2%7D%5C%5C%5C%5C%5C%5C~~~~~~~~%3D%5Cdfrac%7B2%5Ccos%20%5Ctfrac%7B%5Ctheta%7D2%20%5Csin%20%5Ctfrac%7B%5Ctheta%7D2%20%7D%7B2%5Ccos%5E2%20%5Ctfrac%7B%5Ctheta%7D2%7D~~~~~~%3B%5Cleft%5B%5Ctext%7BMultiply%20by%7D~%202%5Ccos%5Ctfrac%7B%5Ctheta%7D2%20%5Cright%5D)
![=\dfrac{\sin \theta}{1+ \cos \theta}~~~~~~~~~~~~;[2 \sin x \cos x = \sin 2x ~ \text{and}~ 2\cos^2 x =1+\cos 2x]\\\\\\=\dfrac{\tfrac{12}{15}}{1+ \tfrac{9}{15}}\\\\\\=\dfrac{\tfrac{12}{15}}{\tfrac{24}{15}}\\\\\\=\dfrac{12}{15}\times \dfrac{15}{24}\\\\\\=\dfrac{12}{24}\\\\\\=\dfrac{1}2](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%5Csin%20%5Ctheta%7D%7B1%2B%20%5Ccos%20%5Ctheta%7D~~~~~~~~~~~~%3B%5B2%20%5Csin%20x%20%5Ccos%20x%20%3D%20%5Csin%202x%20~%20%5Ctext%7Band%7D~%202%5Ccos%5E2%20x%20%3D1%2B%5Ccos%202x%5D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B%5Ctfrac%7B12%7D%7B15%7D%7D%7B1%2B%20%5Ctfrac%7B9%7D%7B15%7D%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B%5Ctfrac%7B12%7D%7B15%7D%7D%7B%5Ctfrac%7B24%7D%7B15%7D%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B12%7D%7B15%7D%5Ctimes%20%5Cdfrac%7B15%7D%7B24%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B12%7D%7B24%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D2)
