Answer:
Domain: 
Range: 
Step-by-step explanation:
Given
Required
Determine the domain and the range
Solving for domain:
From the question, we understand that t represent years.
Because years can't be negative;
Then, we can conclude that the domain, t is:
Solving for Range:
We solved domain to be
This implies that the minimum value of t is 
and the maximum is infinity
Substitute 0 for t in
Hence;
The range is
x= A ticket
y=b ticket
x+y=500
10x+60y=6000
-------------------
10x+60y=6000
- x+y=500 (*10) ---> 10x+10y=5000
-------------------
10x+60y=6000
- 10x+10y=5000
-------------------
50y=1000
y=1000/50
y=20
b ticket =20
x+y=500
x+20=500
x=500-20
x=480
a ticket=480
answer is the last option ,
Let us see... ideally we would like to have all equations with the same exponent or the same base so that we can compare the rates. Since the unknown is in the exponent, we have to work with them. In general,
![x^(y/z)= \sqrt[z]{x^y}](https://tex.z-dn.net/?f=x%5E%28y%2Fz%29%3D%20%5Csqrt%5Bz%5D%7Bx%5Ey%7D%20)
.
Applying this to the exponential parts of the functions, we have that the first equation is equal to:
250*(
![\sqrt[5]{1.45} ^t](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B1.45%7D%20%5Et)
)=250*(1.077)^t
The second equation is equal to: 200* (1.064)^t in a similar way.
We have that the base of the first equation is higher, thus the rate of growth is faster in the first case; Choice B is correct.
Answer: 30
Step-by-step explanation:
Given :The weight of a bag of golf balls varies directly as the number of golf balls in the bag.
Let x be the number of golf balls in a bag that weighs 1,110 grams.
Then we have the following direct variation equation,
Multiply 1110 both sides , we get
Hence, there are 30 balls in the bag.
a)
Answer: 0.91 m
Explanation:
We know that,
P.E. = m g h
Where,
P.E = Potential energy
m = Mass of the object
g = acceleration due to gravity (9.8 m/s²)
It is given that, m = 1.5 kg
P.E. = 13.44 J
⇒ 13.44 = 1.5 kg × 9.8 m/s² × h
⇒ h = 0.91 m
Hence, apple sits om 0.91 m tall counter.
b)
Answer: 216 J
Explanation:
P.E. = m g h
Weight, mg = 120 N ( given)
height, h = 1.8 m ( given)
The energy possessed by the suitcase is due to virtue of its position (gravitational potential energy)
P.E. = 120 N × 1.8 m = 216 J
Hence, the energy possessed by the suitcase sitting on the counter is 216 J.
