Answer:
The correct option is 4.
Step-by-step explanation:
The given function is
![f(x)=-0.05x^2+2.5x+5.2](https://tex.z-dn.net/?f=f%28x%29%3D-0.05x%5E2%2B2.5x%2B5.2)
Where f(x) is height of the ball and x is the distance.
It is a polynomial function with degree 2. All polynomial functions are defined for all real numbers, therefore the mathematical domain of the function is all real numbers.
![-\infty](https://tex.z-dn.net/?f=-%5Cinfty%3Cx%3C%5Cinfty)
Factorize the given function.
![f(x)=-0.05(x^2-50x-104)](https://tex.z-dn.net/?f=f%28x%29%3D-0.05%28x%5E2-50x-104%29)
![f(x)=-0.05(x^2-50x-104)](https://tex.z-dn.net/?f=f%28x%29%3D-0.05%28x%5E2-50x-104%29)
![f(x)=-0.05(x^2-52x+2x-104)](https://tex.z-dn.net/?f=f%28x%29%3D-0.05%28x%5E2-52x%2B2x-104%29)
![f(x)=-0.05(x(x-52)+2(x-52))](https://tex.z-dn.net/?f=f%28x%29%3D-0.05%28x%28x-52%29%2B2%28x-52%29%29)
![f(x) = -0.05 (x - 52) (x + 2)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-0.05%20%28x%20-%2052%29%20%28x%20%2B%202%29)
Put f(x)=0 to find the x intercepts.
![0 = -0.05 (x - 52) (x + 2)](https://tex.z-dn.net/?f=0%20%3D%20-0.05%20%28x%20-%2052%29%20%28x%20%2B%202%29)
Equate each factor equal to 0.
![x=52,-2](https://tex.z-dn.net/?f=x%3D52%2C-2)
Therefore at x=52 and -2, the graph of f(x) intersects x-axis. Before x=-2 and after x=52 the values of f(x) is negative. Height cannot be negative, therefore reasonable domain is lie between -2 to 52.
Distance cannot be negative, therefore the reasonable domain must be positive.
![0\leq x\leq 52](https://tex.z-dn.net/?f=0%5Cleq%20x%5Cleq%2052)
Therefore the reasonable domain is
and option 4 is correct.
Answer:
b
Step-by-step explanation:
solve for c by simplifying both sides of the equation then isolate the variable
Answer:
For solving x x= -24+y/4 For solving Y y=−24−4x
Step-by-step explanation:
This is solving for x
Add y to both sides.
−4x=24+y
Divide both sides by -4
and the answer is
x= -24+y/4
THis is solving Y
Add 4x to both sides
−y=24+4x
Multiply both sides by -1
and the answer is
y=−24−4x
Answer:
![\frac{1}{6}=0.16](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D%3D0.16)
Step-by-step explanation:
Given : There are six balls in bag
Basketballs=2
Playground balls =3
Soccer ball =1
To Find : the probability that if you pick one of the balls without looking, it will be a soccer ball
Solution :
Total no. of balls = 6
No. of soccer balls = 1
Probability = favorable outcomes / total outcomes
Since total outcomes = total no. of balls =6
And favorable outcome = no. of soccer balls = 1
Thus , Probability of getting soccer ball = ![\frac{1}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D)
Hence the probability that if you pick one of the balls without looking, it will be a soccer ball:
![\frac{1}{6}=0.16](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7D%3D0.16)
Answer:
255 m
Step-by-step explanation:
From the given question, the surface of the water body is the reference point. And this point is assumed to be 0, so that any distance above it is positive, and any distance below is negative. This is synonymous to the number line system.
Thus,
For the aircraft, its height = +200 m
For the submarine, its depth = -55 m
So that the difference between the submarine and aircraft can be determined as;
200 - (-55)
= 200 + 55
= 255 m
The distance between the submarine and aircraft is 255 m.