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anyanavicka [17]
3 years ago
6

(8b^3 − 6 + 3b^4 ) − (b^4 − 7b^3 − 3) =

Mathematics
1 answer:
Scrat [10]3 years ago
3 0

Answer:

2b^4 + 15b^3 - 3

Step-by-step explanation:

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Find the local maximum and minimum values and saddle point(s) of the function.
iogann1982 [59]
f(x,y)=9e^y(y^2-x^2)
\nabla f=\left\langle-18xe^y,9ye^y(2+y)\right\rangle

Critical points occur where the gradient is zero. This is guaranteed whenever x=0 and either y=0 or y=-2.

The Hessian matrix for this function looks like

H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}-18e^y&-18xe^y\\-18xe^y&9e^y(2-x^2+4y+y^2)\end{bmatrix}

and has determinant

|H(x,y)|=-162e^{2y}(2+x^2+4y+y^2)

Maxima occur whenever the determinant is positive and f_{xx}. Minima occur whenever both the determinant and f_{xx} are positive. Saddle points occur whenever the determinant is negative.

At (0,0), you have a saddle point since the determinant reduces to -324, so (0,0,0) is the saddle point.

At (0,-2), the determinant is \dfrac{324}{e^4}>0 and f_{xx}(0,-2)=-\dfrac{18}{e^2}, so \left(0,-2,\dfrac{36}{e^2}\right) is a local maximum.

No other critical points remain, so you're done.
4 0
2 years ago
Transforming data
Papessa [141]

Answer:

See below in bold.

Step-by-step explanation:

Mean = 150 cm = 150 * 0.033 feet

= 4.95 feet.

The standard deviation =  10 cm = 10 * 0.033

= 0.33 feet.

7 0
3 years ago
Write the coordinates of origin​
aleksklad [387]
The origin is (0, 0)
6 0
3 years ago
Read 2 more answers
NEED HELP RIGHT AWAY DONT HAVE ANY TIME TO WAIT!!
Fiesta28 [93]
Question 1:
------------------------

Total points = 100
Total question = 40
Type of questions : 2-points question and 4-points questions

Assumed all 40 questions are 2-points questions.
Total points = 40 x 2 = 80

Difference in points = 100 - 80 = 20 points
Difference in the 2 type of questions = 4 - 2 = 2

Number of 4 marks questions = 20 ÷ 2 = 10 

Number of 2 marks questions = 40 - 10 = 30

Answer: There are 10 4-marks questions and 30 2-marks questions.

------------------------------------------------------------------------------------------------

Question 2:
------------------------

Let x be the number of offices you need to clean.

Total cost = 315 + 4x
Total revenue = 25x

To break even,
315 + 4x = 25x
21x = 315
x = 15

Answer: You need to clean 15 offices to break even.

------------------------------------------------------------------------------------------------

Question 3:
------------------------

Total distance (including return trip) = 255 + 255 = 510 miles

Total time taken = 1.7 + 1.5 = 3.2 hours

Speed = Distance ÷ time

Speed = 510 ÷ 3.2 = 159.38 miles/hour

Answer: The average speed is 159.38 miles/hour

5 0
3 years ago
Read 2 more answers
Can someone help me please
LenaWriter [7]

Answer:

the correct graph is b for this problem

8 0
3 years ago
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