Answer:
3%
Step-by-step explanation:
This equation represents exponential decay. Whenever the base is less than 1, the function represents decay. When the base is greater than 1, the function represents growth. In this case, the base is .97 which is less than 1, representing decay.
The formula for exponential decay is y=a(1-r)x.
r is the decay rate, expressed as a decimal.
In this case, r = .03 which represents 3%!
Answer:
x = 8.3.
Step-by-step explanation:
According to solve for the length of x, we need to use SOH CAH TOA.
This means...
Sine: Opposite over Hypotenuse
Cosine: Adjacent over Hypotenuse
Tangent: Opposite over Adjacent
In this case, we are given the angle, the hypotenuse, and we need to solve for the adjacent. This means that we will use cosine, since we have the adjacent and the hypotenuse.
cosine(41) = x / 11
x = (cosine(41)) * 11
x = 0.7547095802 * 11
x = 8.301805382
The question asks us to round to the nearest <em>tenth</em>.
So, your final answer is that x = 8.3.
Hope this helps!
find the orthogonal projection of v= [19,12,14,-17] onto the subspace W spanned by [ [ -4,-1,-1,3] ,[ 1,-4,4,3] ] proj w (v) = [
12345 [234]
<h2>
Answer:</h2>
Hence, we have:
![proj_W(v)=[\dfrac{464}{21},\dfrac{167}{21},\dfrac{71}{21},\dfrac{-131}{7}]](https://tex.z-dn.net/?f=proj_W%28v%29%3D%5B%5Cdfrac%7B464%7D%7B21%7D%2C%5Cdfrac%7B167%7D%7B21%7D%2C%5Cdfrac%7B71%7D%7B21%7D%2C%5Cdfrac%7B-131%7D%7B7%7D%5D)
<h2>
Step-by-step explanation:</h2>
By the orthogonal decomposition theorem we have:
The orthogonal projection of a vector v onto the subspace W=span{w,w'} is given by:
Here we have:
![v=[19,12,14,-17]\\\\w=[-4,-1,-1,3]\\\\w'=[1,-4,4,3]](https://tex.z-dn.net/?f=v%3D%5B19%2C12%2C14%2C-17%5D%5C%5C%5C%5Cw%3D%5B-4%2C-1%2C-1%2C3%5D%5C%5C%5C%5Cw%27%3D%5B1%2C-4%2C4%2C3%5D)
Now,
![v\cdot w=[19,12,14,-17]\cdot [-4,-1,-1,3]\\\\i.e.\\\\v\cdot w=19\times -4+12\times -1+14\times -1+-17\times 3\\\\i.e.\\\\v\cdot w=-76-12-14-51=-153](https://tex.z-dn.net/?f=v%5Ccdot%20w%3D%5B19%2C12%2C14%2C-17%5D%5Ccdot%20%5B-4%2C-1%2C-1%2C3%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cv%5Ccdot%20w%3D19%5Ctimes%20-4%2B12%5Ctimes%20-1%2B14%5Ctimes%20-1%2B-17%5Ctimes%203%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cv%5Ccdot%20w%3D-76-12-14-51%3D-153)
![w\cdot w=[-4,-1,-1,3]\cdot [-4,-1,-1,3]\\\\i.e.\\\\w\cdot w=(-4)^2+(-1)^2+(-1)^2+3^2\\\\i.e.\\\\w\cdot w=16+1+1+9\\\\i.e.\\\\w\cdot w=27](https://tex.z-dn.net/?f=w%5Ccdot%20w%3D%5B-4%2C-1%2C-1%2C3%5D%5Ccdot%20%5B-4%2C-1%2C-1%2C3%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cw%5Ccdot%20w%3D%28-4%29%5E2%2B%28-1%29%5E2%2B%28-1%29%5E2%2B3%5E2%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cw%5Ccdot%20w%3D16%2B1%2B1%2B9%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cw%5Ccdot%20w%3D27)
and
![v\cdot w'=[19,12,14,-17]\cdot [1,-4,4,3]\\\\i.e.\\\\v\cdot w'=19\times 1+12\times (-4)+14\times 4+(-17)\times 3\\\\i.e.\\\\v\cdot w'=19-48+56-51\\\\i.e.\\\\v\cdot w'=-24](https://tex.z-dn.net/?f=v%5Ccdot%20w%27%3D%5B19%2C12%2C14%2C-17%5D%5Ccdot%20%5B1%2C-4%2C4%2C3%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cv%5Ccdot%20w%27%3D19%5Ctimes%201%2B12%5Ctimes%20%28-4%29%2B14%5Ctimes%204%2B%28-17%29%5Ctimes%203%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cv%5Ccdot%20w%27%3D19-48%2B56-51%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cv%5Ccdot%20w%27%3D-24)
![w'\cdot w'=[1,-4,4,3]\cdot [1,-4,4,3]\\\\i.e.\\\\w'\cdot w'=(1)^2+(-4)^2+(4)^2+(3)^2\\\\i.e.\\\\w'\cdot w'=1+16+16+9\\\\i.e.\\\\w'\cdot w'=42](https://tex.z-dn.net/?f=w%27%5Ccdot%20w%27%3D%5B1%2C-4%2C4%2C3%5D%5Ccdot%20%5B1%2C-4%2C4%2C3%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cw%27%5Ccdot%20w%27%3D%281%29%5E2%2B%28-4%29%5E2%2B%284%29%5E2%2B%283%29%5E2%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cw%27%5Ccdot%20w%27%3D1%2B16%2B16%2B9%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cw%27%5Ccdot%20w%27%3D42)
Hence, we have:
![proj_W(v)=(\dfrac{-153}{27})[-4,-1,-1,3]+(\dfrac{-24}{42})[1,-4,4,3]\\\\i.e.\\\\proj_W(v)=\dfrac{-17}{3}[-4,-1,-1,3]+(\dfrac{-4}{7})[1,-4,4,3]\\\\i.e.\\\\proj_W(v)=[\dfrac{68}{3},\dfrac{17}{3},\dfrac{17}{3},-17]+[\dfrac{-4}{7},\dfrac{16}{7},\dfrac{-16}{7},\dfrac{-12}{7}]\\\\i.e.\\\\proj_W(v)=[\dfrac{464}{21},\dfrac{167}{21},\dfrac{71}{21},\dfrac{-131}{7}]](https://tex.z-dn.net/?f=proj_W%28v%29%3D%28%5Cdfrac%7B-153%7D%7B27%7D%29%5B-4%2C-1%2C-1%2C3%5D%2B%28%5Cdfrac%7B-24%7D%7B42%7D%29%5B1%2C-4%2C4%2C3%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cproj_W%28v%29%3D%5Cdfrac%7B-17%7D%7B3%7D%5B-4%2C-1%2C-1%2C3%5D%2B%28%5Cdfrac%7B-4%7D%7B7%7D%29%5B1%2C-4%2C4%2C3%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cproj_W%28v%29%3D%5B%5Cdfrac%7B68%7D%7B3%7D%2C%5Cdfrac%7B17%7D%7B3%7D%2C%5Cdfrac%7B17%7D%7B3%7D%2C-17%5D%2B%5B%5Cdfrac%7B-4%7D%7B7%7D%2C%5Cdfrac%7B16%7D%7B7%7D%2C%5Cdfrac%7B-16%7D%7B7%7D%2C%5Cdfrac%7B-12%7D%7B7%7D%5D%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cproj_W%28v%29%3D%5B%5Cdfrac%7B464%7D%7B21%7D%2C%5Cdfrac%7B167%7D%7B21%7D%2C%5Cdfrac%7B71%7D%7B21%7D%2C%5Cdfrac%7B-131%7D%7B7%7D%5D)
ANSWER
Q(5,-2),S(-3,4)
The given points have coordinates,
P(5,2) and R(-3,-4).
The mapping for a reflection across the x-axis is
This implies that,
and
The correct choice is A.
Answer:
Order of Operations
Step-by-step explanation:
I'm not sure what terms you're using but the order of operations gives you the order of what operation to do first in a problem
