The jet could fly 2,000 miles in 8 hours and the rate of speed is 250miles per hour.
Answer:
<h2>
y = 16/25x³</h2>
Step-by-step explanation:
If y is inversely proportional to a^3, this is expressed as;
y∝1/a³
y = k/a³ where k is the proportionality constant
Given a=2, y=10, then 10 = k/2³
k = 10*2³
k = 80
Substituting k = 80 back into the formula;
y = 80/a³ ............. 1
Similarly, if a is directly proportional to x, then a ∝ x i.e a = kx
If x=4, a=20 then;
20 = 4k
k = 20/4
k = 5
Substituting k = 5 back into the formula;
a = 5x ....... 2
Substitute equation 2 into 1;
y = 80/a³
y = 80/(5x)³
y = 80/125x³
y = 16/25x³
<em>Hence the formula for y in terms of x is y = 16/25x³</em>
<em></em>
Answer:
100
Step-by-step explanation:
20 times 100 equals 2000
Answer:
<em />
<em />
![f(15) = 62826](https://tex.z-dn.net/?f=f%2815%29%20%3D%2062826)
Step-by-step explanation:
Given
In 1990; Income= $39000
In 2010; Income= $70768
Solving (a): An equation in form of f(x) = ax + b
First, we need to determine the slope, a
![a = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
Taking y as income and x as year index.
When x = 0; y = 39000
When x = 20; y = 70768
Substitute these values in the above formula
![a = \frac{70768 - 39000}{20 - 0}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B70768%20-%2039000%7D%7B20%20-%200%7D)
![a = \frac{31768}{20}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B31768%7D%7B20%7D)
![a = 1588.4](https://tex.z-dn.net/?f=a%20%3D%201588.4)
Next, is to determine the formula using:
![y - y_1 = a(x - x_1)](https://tex.z-dn.net/?f=y%20-%20y_1%20%3D%20a%28x%20-%20x_1%29)
<em>Considering :When x = 0; y = 39000, we have</em>
<em />
<em />
<em />
<em />
<em>Make y the subject of formula</em>
<em />
<em />
<em />
<em>Express y as a function of x</em>
<em />
<em />
Solving (b): Income in 2005
<em>In 2005, x = 15</em>
So:
becomes
![f(15) = 1588.4 * 15 + 39000](https://tex.z-dn.net/?f=f%2815%29%20%3D%201588.4%20%2A%2015%20%2B%2039000)
![f(15) = 62826](https://tex.z-dn.net/?f=f%2815%29%20%3D%2062826)