Answer:
Step-by-step explanation:
a) The relative minimum of the function from the graph is -18 at x=0.
b) The graph ends with two arrows which means it continues from there indefinitely. So the function increases from x equal to negative infinity to -2 and then from 0 to +2.
Answer:
In order of pictures,
Picture #1: 230
Picture #2: 140
Picture #3: 9.9
Picture #4: 13.5
Picture #5: 7.07
Step-by-step explanation:
I am not entirely sure that 3 - 5 are correct, but I know that 1 and 2 are correct. I am sorry if they are incorrect.
Hope that this helps!
Answer:
C. None of The Above
Step-by-step explanation:
The peak is at 2 years, not 4. And there is no gap.
Answer:
The length of the flagpole be 41.2 ft .
Option (A) is correct .
Step-by-step explanation:
As given
The angle looking up at the sun is 70°.
A flagpole casts a shadow of 15 ft .
Now by using the trignometric identity .
![tan \theta = \frac{Perpendicular}{Base}](https://tex.z-dn.net/?f=tan%20%5Ctheta%20%3D%20%5Cfrac%7BPerpendicular%7D%7BBase%7D)
![\ theta = 70^{\circ}](https://tex.z-dn.net/?f=%5C%20theta%20%3D%2070%5E%7B%5Ccirc%7D)
![tan\ 70^{\circ} = \frac{AB}{BC}](https://tex.z-dn.net/?f=tan%5C%2070%5E%7B%5Ccirc%7D%20%3D%20%5Cfrac%7BAB%7D%7BBC%7D)
BC = 15 ft
tan 70° = 2.75 (Approx)
![2.75 = \frac{AB}{15}](https://tex.z-dn.net/?f=2.75%20%3D%20%5Cfrac%7BAB%7D%7B15%7D)
AB = 2.75 × 15
= 41.2 ft
Therefore the length of the flagpole be 41.2 ft .
Option (A) is correct .
The function is not invertible if you think of it as
![f:\mathbb{R}\to\mathbb{R}](https://tex.z-dn.net/?f=f%3A%5Cmathbb%7BR%7D%5Cto%5Cmathbb%7BR%7D)
because it is not injective: ![f(x)=f(-x)](https://tex.z-dn.net/?f=f%28x%29%3Df%28-x%29)
So, if we restrict the domain to the positive numbers only:
![f:\mathbb{R^+}\to\mathbb{R}](https://tex.z-dn.net/?f=f%3A%5Cmathbb%7BR%5E%2B%7D%5Cto%5Cmathbb%7BR%7D)
Note that the range is actually
, so we can be more precise and write
![f:\mathbb{R^+}\to[9,\infty)](https://tex.z-dn.net/?f=f%3A%5Cmathbb%7BR%5E%2B%7D%5Cto%5B9%2C%5Cinfty%29)
To find the inverse, we solve the expression for x:
![y=x^2+9 \iff y-9=x^2 \iff x=\pm\sqrt{y-9}](https://tex.z-dn.net/?f=y%3Dx%5E2%2B9%20%5Ciff%20y-9%3Dx%5E2%20%5Ciff%20x%3D%5Cpm%5Csqrt%7By-9%7D)
But since we restricted to positive values of x, the inverse is
![x=\sqrt{y-9}](https://tex.z-dn.net/?f=x%3D%5Csqrt%7By-9%7D)