Answer:
D) 3 X 10⁷
Step-by-step explanation:
<u>Estimated days:</u>
- Jan 2000 to June 2001 = 1.5 years = 365*1.5 days ≈ 548 days
- 1 day = 24 hours = 24*60 minutes = 24*60*60 seconds =
- 548 days = 548 * 86400 seconds =
Best estimate is D) 3 X 10⁷
Price before membership= price 1 = $6
price after membership = price 2 = $4
Membership price = $100
SO according to price 1 and price 2; price after membership saves up $2 for each session.
Hence to justify the price of membership number of sessions can be calculated as follows:-
$2 saved = 1 session
to make it $100 multiply both sides by 50
2×50 = 1×50
100$ saved = 50 sessions
so 50 sessions ate required to justify buying the membership.
Hope this helped :)
Answer:
r = 13
Step-by-step explanation:
As the vertically opposite angles are equal,
8r + 6 = 9r - 7
<u>Now you can find the value of r.</u>
8r - 9r = -6 - 7
-r = -13
r = 13
Hope this helps you :-)
Let me know if you have any other questions :-)
![f(x,y)=x^2+xy+y^2+y](https://tex.z-dn.net/?f=f%28x%2Cy%29%3Dx%5E2%2Bxy%2By%5E2%2By)
![\nabla f(x,y)=(f_x,f_y)=(2x+y,x+2y+1)](https://tex.z-dn.net/?f=%5Cnabla%20f%28x%2Cy%29%3D%28f_x%2Cf_y%29%3D%282x%2By%2Cx%2B2y%2B1%29)
Set both partial derivatives equal to zero and solve for
![x,y](https://tex.z-dn.net/?f=x%2Cy)
.
![\begin{cases}2x+y=0\\x+2y+1=0\end{cases}\implies x=\dfrac13,y=-\dfrac23](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D2x%2By%3D0%5C%5Cx%2B2y%2B1%3D0%5Cend%7Bcases%7D%5Cimplies%20x%3D%5Cdfrac13%2Cy%3D-%5Cdfrac23)
The Hessian matrix (matrix of second-order partial derivatives) for this function is
![H=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2&1\\1&2\end{bmatrix}\implies\det H=3>0](https://tex.z-dn.net/?f=H%3D%5Cbegin%7Bbmatrix%7Df_%7Bxx%7D%26f_%7Bxy%7D%5C%5Cf_%7Byx%7D%26f_%7Byy%7D%5Cend%7Bbmatrix%7D%3D%5Cbegin%7Bbmatrix%7D2%261%5C%5C1%262%5Cend%7Bbmatrix%7D%5Cimplies%5Cdet%20H%3D3%3E0)
Now since
![\det H>0](https://tex.z-dn.net/?f=%5Cdet%20H%3E0)
for any
![(x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29)
, and
![f_xx=2>0](https://tex.z-dn.net/?f=f_xx%3D2%3E0)
for any
![(x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29)
, it follows by the second partial derivative test that the critical point
![\left(\dfrac13,-\dfrac23\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac13%2C-%5Cdfrac23%5Cright%29)
is the site of a local minimum of
![f(x,y)](https://tex.z-dn.net/?f=f%28x%2Cy%29)
. The value of the minimum is
![f\left(\dfrac13,-\dfrac23\right)=-\dfrac13](https://tex.z-dn.net/?f=f%5Cleft%28%5Cdfrac13%2C-%5Cdfrac23%5Cright%29%3D-%5Cdfrac13)
.
Answer:
For any shape to be congruent, they must be the same size.