The distance travelled by an object at time t is given by: d = stwhere d is the distance, s is the speed and t is the time.
Given that the cheetah travels a maximum of 70mph, the distance travelled by the cheetah travelling at 70mph at time t is given by d = 70t
There are 60 mins in one hour, so the distance given in miles per minutes is d = 70/60t = 1.167 miles per minutes.
Part B:
Given that t = 10 minutes, the distance covered by the cheetah in 10 minutes is d = 1.167 x 10 = 11.67 miles.
Part C:
If the cheetah sprinted at maximum speed for 8 minutes and then slowed to 40 mph for the next 8 minutes, then the number of minutes the cheetah have traveled in the first 8 minutes is given by
d = 1.167 x 8 = 9.33 miles.
Part D:
If the cheetah sprinted at maximum speed for 8 minutes and then slowed to 40 mph for the next 8 minutes, then the number of minutes the cheetah have traveled in the second 8 minutes is given by
d = 40/60 x 8 = 5.33 miles
Part E:
The distance the cheetah traveled in the first 8 minutes more than in the second 8 minutes is given by
9.33 miles - 5.33 miles = 4 miles.
Part F:
The ratio of the distance travelled in the first 8 minutes to the distance travelled in the next minutes is given by
9.33 : 5.33 = 1.75 : 1.
Therefore, the distance traveled by the cheetah during the first 8 minutes is 1.75 times greater than the distance traveled during the second 8 minutes.
Answer:
5
Step-by-step explanation:
To solve with calculus, distance is the integral of speed:
d = ∫ |v| dt
d = ∫₀⁴ |t − 3| dt
d = -∫₀³ (t − 3) dt + ∫₃⁴ (t − 3) dt
d = ∫₀³ (3 − t) dt + ∫₃⁴ (t − 3) dt
d = (3t − ½ t²) |₀³ + (½ t² − 3t) |₃⁴
d = [ (9 − 9/2 ) − (0 − 0) ] + [ (8 − 12) − (9/2 − 9) ]
d = 9/2 + 1/2
d = 5
You can also find this geometrically. Graph y = |x − 3|, then find the area under the curve. You will find it's the area of two triangles.
d = ½ (3)(3) + ½ (1)(1)
d = 5
It's important to note that distance is not the same thing as displacement. Displacement is the difference between where you start and where you stop. Distance is length of the path you take.
Answer:
![\frac{\sqrt{41}}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B41%7D%7D%7B4%7D)
Step-by-step explanation:
sec(theta) is defined as: ![sec(\theta)=\frac{1}{cos(\theta)} = \frac{hypotenuse}{adjacent}](https://tex.z-dn.net/?f=sec%28%5Ctheta%29%3D%5Cfrac%7B1%7D%7Bcos%28%5Ctheta%29%7D%20%3D%20%5Cfrac%7Bhypotenuse%7D%7Badjacent%7D)
In the diagram you provided the hypotenuse of the triangle is sqrt(41) and the opposite side is 5, using these two sides, we can solve for the adjacent side by using the Pythagorean Theorem: ![a^2+b^2=c^2](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E2)
So this gives us the equation where a=adjacent side:
![a^2+25=41](https://tex.z-dn.net/?f=a%5E2%2B25%3D41)
Subtract 25 from both sides
![a^2=16](https://tex.z-dn.net/?f=a%5E2%3D16)
Take the square root of both sides
![a=4](https://tex.z-dn.net/?f=a%3D4)
So now plug this into the definition of sec(theta) and you get:
. This is in most simplified form since 41, has no factors besides 41 and 1.
Answer:
Step-by-step explanation:
(Vertical angles)
(Linear pair angles)
In
By interior angle sum postulate of a triangle
Answer:
she spent $137.41
Step-by-step explanation:
175 - 37.59 = $137.41