Larger pets need to be transported in larger portable kennels. Using a graphing calculator and the relationship between the widt
h, length, and height, find the dimensions of a portable kennel whose volume is 7.4 ft3. The dimensions of a portable kennel can be expressed as width x, length x + 0.4, and height x − 0.2? What are the dimensions of a portable kennel with a volume of 7.4 ft3? Use a graphing calculator to solve. Round the dimensions to the nearest tenth.
1 answer:
Answer:
- width: 1.9 ft
- length: 2.3 ft
- height: 1.7 ft
Step-by-step explanation:
The volume of a rectilinear shape is given by ...
V = W·L·H . . . . . where W, L, and H represent width, length, and height
Filling in the given information, we want to find a solution to ...
7.4 = x(x +0.4)(x -0.2)
If we write ...
f(x) = x(x +0.4)(x -0.2)
Then we're looking for the value of x that satisfies ...
f(x) -7.4 = 0
The attached graph shows that value to be 1.897, about 1.9 (feet). Then the desired kennel dimensions are ...
- width: 1.9 ft
- length: 2.3 ft
- height: 1.7 ft
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Answer:
<em>There are approximately 114 rabbits in the year 10</em>
Step-by-step explanation:
<u>Exponential Growth </u>
The natural growth of some magnitudes can be modeled by the equation:
Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
We are given two measurements of the population of rabbits on an island.
In year 1, there are 50 rabbits. This is the point (1,50)
In year 5, there are 72 rabbits. This is the point (5,72)
Substituting in the general model, we have:
Dividing [2] by [1]:
Solving for r:
Calculating:
r=0.095445
From [1], solve for Po:
The model can be written now as:
In year t=10, the population of rabbits is:
P = 113.6
There are approximately 114 rabbits in the year 10