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Dmitry [639]
2 years ago
12

Find the original price given the total amount and tip rate. Total price 307.32 tip rate 20%

Mathematics
1 answer:
eduard2 years ago
5 0

Answer:

the answer is 61.3

Step-by-step explanation:

you have to dived one number by the other

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F(x,y) = x^2+y^2+x^2y+6 find the absolute max and min
Stels [109]
f(x,y)=x^2+y^2+x^2y+6 has critical points where the partial derivatives simultaneously vanish:

f_x=2x+2xy=2x(1+y)=0\implies x=0\text{ or }y=-1
f_y=2y+x^2=0
x=0\implies 2y=0\implies y=0
y=-1\implies-2+x^2=0\implies x=\pm\sqrt2

So we have three critical points to consider, (0,0), (-\sqrt2,-1), and (\sqrt2,-1).

The function has Hessian

\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2+2y&2x\\2x&2\end{bmatrix}

At the critical points, we have

|\mathbf H(0,0)|=\begin{vmatrix}2&0\\0&2\end{vmatrix}=4>0
f_{xx}(0,0)=2>0

which means there is a minimum at (0, 0) of f(0,0)=6;

|\mathbf H(-\sqrt2,-1)|=\begin{vmatrix}0&-2\sqrt2\\-2\sqrt2&2\end{vmatrix}=-8

which means (-\sqrt2,-1) is a saddle point; and

|\mathbf H(\sqrt2,-1)|=\begin{vmatrix}0&2\sqrt2\\2\sqrt2&2\end{vmatrix}=-8

which means (\sqrt2,-1) is also a saddle point.
4 0
3 years ago
TON OF POINTS, EASY QUESTION<br><br> What is the inverse for this equation: <br> y=3x+5
Paraphin [41]

Step-by-step explanation:

y = 3x + 5 \\ y - 5 = 3x \\ x =  \frac{y - 5}{3}  \\ is \: the \: inverse \: of \: given \: equation \\

7 0
3 years ago
Simplify -2(3x-10)=15​
kow [346]

Answer:

-2(3x-10)=15

-6x+20=15

-6x=-5

x=5/6

Step-by-step explanation:

7 0
2 years ago
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Lacey pays $15 for each hour of golf lessons and $10 for equipment rental. Is the total cost of Lacey's lesson a function of the
lisabon 2012 [21]

Answer:

60

Step-by-step explanation:

15x3=45

5x3=15

15+45=60

3 0
3 years ago
WILL GIVE BRAINLIEST!!
Inessa05 [86]
1-D
2-C
3-?
4- A
5- B
Give me a second to work on number three. I'll respond ASAP
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