We performed the following operations:
![f(x)=\sqrt[3]{x}\mapsto g(x)=2\sqrt[3]{x}=2f(x)](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%5B3%5D%7Bx%7D%5Cmapsto%20g%28x%29%3D2%5Csqrt%5B3%5D%7Bx%7D%3D2f%28x%29)
If you multiply the parent function by a constant, you get a vertical stretch if the constant is greater than 1, a vertical compression if the constant is between 0 and 1. In this case the constant is 2, so we have a vertical stretch.
![g(x)=2\sqrt[3]{x}\mapsto h(x)=-2\sqrt[3]{x}=-g(x)](https://tex.z-dn.net/?f=g%28x%29%3D2%5Csqrt%5B3%5D%7Bx%7D%5Cmapsto%20h%28x%29%3D-2%5Csqrt%5B3%5D%7Bx%7D%3D-g%28x%29)
If you change the sign of a function, you reflect its graph across the x axis.
![h(x)=-2\sqrt[3]{x}\mapsto m(x)=-2\sqrt[3]{x}-1=h(x)-1](https://tex.z-dn.net/?f=h%28x%29%3D-2%5Csqrt%5B3%5D%7Bx%7D%5Cmapsto%20m%28x%29%3D-2%5Csqrt%5B3%5D%7Bx%7D-1%3Dh%28x%29-1)
If you add a constant to a function, you translate its graph vertically. If the constant is positive, you translate upwards, otherwise you translate downwards. In this case, the constant is -1, so you translate 1 unit down.
Answer:
Step-by-step explanation:
A sample of bacteria is decaying according to the half-life model f(t) = Ne -0.226t, where N is the initial sample size and t
is time in hours. At t = 4, there are 25 bacteria remaining. What was the initial sample amount? Round your answer to the
nearest whole number, and do not include units.
Answer:
The rate of change is "-3". Which means the rate at which the tractor uses fuel.
Step-by-step explanation:
The equation describes a line and any line follows the equation:
y = m*x + c
Where "m" is the rate of change and "c" is the shift on the line. Comparing the equation for the fuel and the equation from the line, the rate of change must be "-3". The rate of change in this context describes the speed at which the tractor uses fuel, at a rate of 3 gallons per hour.
Answer:
168/(x² +7x)
Step-by-step explanation:
The height of each window is 14/(x+7), and the width of each window is 12/x. The area of each window is the product of its height ans width:
area = (14/(x+7))(12/x) = 168/(x(x +7))
area = 168/(x² +7x)
_____
<em>Comment on the problem</em>
There is not enough information given to determine suitable values for x. If x is 42, each window is a square 3 3/7 inches on a side.
Answer:
64
in²
Step-by-step explanation:
I did not ever do a problem like this, however this is the beauty of math, you can easily reverse engineer it.
Remember,
A = 
And if we have 4 circles that means the area of one circle is 1/4th the total
So,
A=
Assuming that 16 is the radius squared times 4 lets ignore that squared for now because when going backwards we would get rid of the squared last as that was the first step.
A= 
=
=4
Now lets get it back to by square rooting the 4
A=
=2
The radius of one small circle is 2. Therefore; the diameter would be 4 for each. This in mind we know that two small circles diameters make up the radius of the larger circle we will multiply it by two again.
This gives us a final radius of the bigger circle of 8
Therefore, the area of the bigger circle is 8² which simplifies to 64
And a final answer of
64 in²
Hope this helps :)
