The answer is D. All you have to do is graph the equation, and you will have the vertex and the roots. By the way, you can rule out B and C because those two do not follow the rules of a quadratic. Also, A and B have the wrong axis of symmetry, because the rocket lands after 10 seconds.
Answer:
Total distance covered by the bird is 6.07 km.
Step-by-step explanation:
When a bird begins to fly distance of the runner from the finish line = 4.1 km
Speed of the bird = 10.2 km per hour
Therefore time taken by the bird to cover 4.1 km = ![\frac{\text{Distance}}{\text{Speed}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%7BDistance%7D%7D%7B%5Ctext%7BSpeed%7D%7D)
= ![\frac{4.1}{10.2}](https://tex.z-dn.net/?f=%5Cfrac%7B4.1%7D%7B10.2%7D)
= 0.402 hours
Distance covered by the runner in 0.402 hours = Speed × time
= 3.4×0.402
= 1.3667 km
Now the distance between the bird at the finish line and the runner = 4.1 - 1.3667 = 2.6332 km
Now the runner and bird are moving towards each other.
When they meet each other they will cover the total distance of 2.6332 km in equal time.
If the bird covers the distance = x km, then the distance covered by the runner = (2.6332 - x) km
Now time taken by the bird = time taken by the runner
![\frac{x}{10.2}=\frac{2.6332-x}{3.4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B10.2%7D%3D%5Cfrac%7B2.6332-x%7D%7B3.4%7D)
3.4x = 26.86 - 10.2x
3.4x + 10.2x = 26.86
13.6x = 26.86
x = ![\frac{26.86}{13.6}](https://tex.z-dn.net/?f=%5Cfrac%7B26.86%7D%7B13.6%7D)
x = 1.97 km
Total distance covered by the bird = 4.1 km + 1.97 km
= 6.07 km
Therefore, total distance covered by the bird is 6.07 km.
Answer:
a = 12 and b = 18
Step-by-step explanation:
Given that,
8,a,b,27 are in geometric sequence.
For a GP, the nth term is given by :
![a_n=ar^{n-1}](https://tex.z-dn.net/?f=a_n%3Dar%5E%7Bn-1%7D)
Put n = 4
![a_4=ar^{4-1}\\\\a_4=ar^3\\\\27=8\times r^3\\\\r^3=\dfrac{27}{8}\\\\r=\dfrac{3}{2}=1.5](https://tex.z-dn.net/?f=a_4%3Dar%5E%7B4-1%7D%5C%5C%5C%5Ca_4%3Dar%5E3%5C%5C%5C%5C27%3D8%5Ctimes%20r%5E3%5C%5C%5C%5Cr%5E3%3D%5Cdfrac%7B27%7D%7B8%7D%5C%5C%5C%5Cr%3D%5Cdfrac%7B3%7D%7B2%7D%3D1.5)
Put n = 2,
![a_2=ar^{2-1}\\\\a=ar\\\\a=8\times 1.5\\\\a=12](https://tex.z-dn.net/?f=a_2%3Dar%5E%7B2-1%7D%5C%5C%5C%5Ca%3Dar%5C%5C%5C%5Ca%3D8%5Ctimes%201.5%5C%5C%5C%5Ca%3D12)
Put n = 3
![a_3=ar^2\\\\=8\times 1.5^2\\\\b =18](https://tex.z-dn.net/?f=a_3%3Dar%5E2%5C%5C%5C%5C%3D8%5Ctimes%201.5%5E2%5C%5C%5C%5Cb%20%3D18)
So, the values of a and b is 12 and 18 respectively.
Answer:38
Step-by-step explanation:
Answer:
answer is 55 is correct
Step-by-step explanation:
answer is 55. is correct