Answer:
The average of rate was of 0.4314 cm/day, which means that on average, during this interval, the plant grew by 0.4314 cm each day.
Step-by-step explanation:
Average rate of change:
The average rate of change of a function f(x), from x = a to x = b, is given by:
![A = \frac{f(b)-f(a)}{b-a}](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D)
In this question:
![f(x) = 12(1.03)^n](https://tex.z-dn.net/?f=f%28x%29%20%3D%2012%281.03%29%5En)
From n = 3 to n = 10
![a = 3, b = 10](https://tex.z-dn.net/?f=a%20%3D%203%2C%20b%20%3D%2010)
![f(b) = f(10) = 12(1.03)^{10} = 16.13](https://tex.z-dn.net/?f=f%28b%29%20%3D%20f%2810%29%20%3D%2012%281.03%29%5E%7B10%7D%20%3D%2016.13)
![f(a) = f(3) = 12(1.03)^{3} = 13.11](https://tex.z-dn.net/?f=f%28a%29%20%3D%20f%283%29%20%3D%2012%281.03%29%5E%7B3%7D%20%3D%2013.11)
Average rate of change:
![A = \frac{f(b)-f(a)}{b-a} = \frac{16.13-13.11}{10-3} = 0.4314](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D%20%3D%20%5Cfrac%7B16.13-13.11%7D%7B10-3%7D%20%3D%200.4314)
The average of rate was of 0.4314 cm/day, which means that on average, during this interval, the plant grew by 0.4314 cm each day.
I don't have a visual I can provide, but the ratio of the areas is the square of the ratio of the perimeters of a 2D figure.
Intuitively, you can imagine that the triangle is simply being "scaled up" by a factor of 7/3, so the base scales up to 7/3 its original length and the height becomes 7/3 its original height.
Therefore, the new ratio is the square of the ratio of the perimeters, which is 9:49.
Answer:
x = 24, y = 19
Step-by-step explanation:
Form the question,
Note: opposite side of a parallelogram are equal.
From the diagram,
2x-8 = x+16
Solve for x.
Collect like terms
2x-x = 16+8
x = 24.
Also,
2y = y+19
Solve for y
Collect like terms
2y-y = 19
y = 19.
Hence, x = 24, y = 19.
The first option is correct
Answer:
![(2x^3)^3=8\cdot x^{9}](https://tex.z-dn.net/?f=%282x%5E3%29%5E3%3D8%5Ccdot%20x%5E%7B9%7D)
Step-by-step explanation:
<u>Properties of Exponents</u>
The property called Power to a Power shows us how to simplify expressions of the type:
![(x^n)^m=x^{n*m}](https://tex.z-dn.net/?f=%28x%5En%29%5Em%3Dx%5E%7Bn%2Am%7D)
Similarily the property called Power of a product simplifies expressions like:
![(x.y)^n=x^n.y^n](https://tex.z-dn.net/?f=%28x.y%29%5En%3Dx%5En.y%5En)
The company mentioned in the question uses the expression
![(2x^3)^3](https://tex.z-dn.net/?f=%282x%5E3%29%5E3)
millimeters per second to calculate the maximum capacity of a photocell with an area of x^3 square millimeters.
First, use the power of a product property:
![(2x^3)^3=2^3\cdot (x^3)^3](https://tex.z-dn.net/?f=%282x%5E3%29%5E3%3D2%5E3%5Ccdot%20%28x%5E3%29%5E3)
Now use the power to a power property:
![(2x^3)^3=2^3\cdot x^{3*3}](https://tex.z-dn.net/?f=%282x%5E3%29%5E3%3D2%5E3%5Ccdot%20x%5E%7B3%2A3%7D)
Operate:
![\mathbf{(2x^3)^3=8\cdot x^{9}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%282x%5E3%29%5E3%3D8%5Ccdot%20x%5E%7B9%7D%7D)