Answer:
decay
2% decrease
Step-by-step explanation:
The growth factor is the base of the exponent: 0.98. Its relation to the rate of change is ...
growth factor = 1 + rate of change
0.98 = 1 + (-0.02)
So, the rate of change is -0.02 = -2%. Since the rate of change is a 2% decrease, it represents decay.
You add all of the numbers up then divide them by the number of values you added
When you add something, you gain more of it. Therefore, it should be positive 2
2
As given by the question
There are given that the vector:

Now,
From the formula to find the unit vector in same direction is:

Then,
![\begin{gathered} \vec{u}=\frac{\vec{v}}{\lvert\vec{v}\rvert} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\lvert\vec{2i}+\vec{3j}\rvert} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\lvert\sqrt[]{2^2+3^2}\rvert} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7Bv%7D%7D%7B%5Clvert%5Cvec%7Bv%7D%5Crvert%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Clvert%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%5Crvert%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Clvert%5Csqrt%5B%5D%7B2%5E2%2B3%5E2%7D%5Crvert%7D%20%5Cend%7Bgathered%7D)
Then,
![\begin{gathered} \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{2^2+3^2}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{4+9}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B2%5E2%2B3%5E2%7D%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B4%2B9%7D%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%20%5Cend%7Bgathered%7D)
Then,
Rationalize the denominator:
So,
![\begin{gathered} \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}} \\ \vec{u}=\frac{\vec{2i}+\vec{3j}}{\sqrt[]{13}}\times\frac{\sqrt[]{13}}{\sqrt[]{13}} \\ \vec{u}=\frac{\vec{\sqrt[]{13}(2i}+\vec{3j})}{13} \\ \vec{u}=\frac{2\sqrt[]{13}}{13}i+\frac{3\sqrt[]{13}}{13}j \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B2i%7D%2B%5Cvec%7B3j%7D%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%5Ctimes%5Cfrac%7B%5Csqrt%5B%5D%7B13%7D%7D%7B%5Csqrt%5B%5D%7B13%7D%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B%5Cvec%7B%5Csqrt%5B%5D%7B13%7D%282i%7D%2B%5Cvec%7B3j%7D%29%7D%7B13%7D%20%5C%5C%20%5Cvec%7Bu%7D%3D%5Cfrac%7B2%5Csqrt%5B%5D%7B13%7D%7D%7B13%7Di%2B%5Cfrac%7B3%5Csqrt%5B%5D%7B13%7D%7D%7B13%7Dj%20%5Cend%7Bgathered%7D)
Hence, the unit vector is shown below:
Answer:
The sheet should be turned up 7.5cm on each side to obtain maximum volume.
Step-by-step explanation:
If we make a rectangular eavesdrop, by bending the sheet along dotted line, then.
Height of eaves trough = x cm
Length of eaves trough = 600 cm
Width of eaves trough = (30 - 2x) cm
We know that Volume is given by:
V = Length · Width · Height
V = (x)(30 - 2x)(600)
V = -1200x² + 18000x
To maximize the volume, we take the derivative and put it equal to zero.
