Answer:
n = 100, -100
Step-by-step explanation:
Rang(1,2,3,4) only X, Y mean the domain
Answer:
You would need a total of 3 3/4 cups. First double the amount of butter= 3 cups, then half 1 1/2 cups for the last cup of flour which would be 3/4. Add them together, it would equal 3 3/4 cups.
Step-by-step explanation:
The answer is 57.04 meters.
Solution:
The height y of the rock above the ground as a function of the horizontal distance x from the starting point on top of the hill can be modeled by the equation
y = -0.04x^2 + 1.3x + 56
We now set this equation equal to zero because the height of the ground where the rock will land is zero:
0 = -0.04x^2 + 1.3x + 56
Since we have a quadratic equation, we can calculate for the horizontal distance x by using the quadratic formula
x = [-b ± sqrt(b^2 - 4ac)] / 2a
x = {-1.3 ± sqrt[1.3^2 - 4(-0.04)(56)]} / 2(-0.04)
x = (-1.3 ± sqrt(10.65)) / (-0.08)
x = -24.54 meters or 57.04 meters
There are two solutions for x but one is negative, so we choose the positive value.
Dot product has the following definition:

Where

is the angle between two vectors and

are their lengths.
The dot product of the vector with itself will give you the square of its length.

If you are given end points of a vector dot product is defined in the following fashion:
![a=[a_1,a_2,a_3]\\ b=[b_1,b_2,b_3]\\ \textbf{a}\cdot \textbf{b}=\textbf{a} \sum b_i \textbf{e}_i= \sum b_i (\textbf{a} \cdot \textbf{e}_i)= \sum b_i a_i](https://tex.z-dn.net/?f=a%3D%5Ba_1%2Ca_2%2Ca_3%5D%5C%5C%20b%3D%5Bb_1%2Cb_2%2Cb_3%5D%5C%5C%20%5Ctextbf%7Ba%7D%5Ccdot%20%5Ctextbf%7Bb%7D%3D%5Ctextbf%7Ba%7D%20%5Csum%20b_i%20%5Ctextbf%7Be%7D_i%3D%20%5Csum%20b_i%20%28%5Ctextbf%7Ba%7D%20%5Ccdot%20%5Ctextbf%7Be%7D_i%29%3D%20%5Csum%20b_i%20a_i)

Where

are unit vectors. These are vectors of a unit length and they span in direction of a coordinate axis (if you are working with Cartesian<span> coordinate system). If you do a dot product of a unit vector of x-axis and unit vector of y-axis you get zero, because the angle between them is 90 degrees.
</span>Now we can apply the above formula to this problem:
![v= [7,24]\\ \textbf{v}\cdot \textbf{v}=|v|^2=(7\cdot 7)+(24\cdot 24)=625\\ |v|=\sqrt{625}=25](https://tex.z-dn.net/?f=v%3D%20%5B7%2C24%5D%5C%5C%20%5Ctextbf%7Bv%7D%5Ccdot%20%5Ctextbf%7Bv%7D%3D%7Cv%7C%5E2%3D%287%5Ccdot%207%29%2B%2824%5Ccdot%2024%29%3D625%5C%5C%20%7Cv%7C%3D%5Csqrt%7B625%7D%3D25)
So the answer is A.
This formula will give you the length of a vector in Euclidian geometry:

Where

are the coordinates of the end point of that vector.