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2 years ago

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*WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER**

1 answer:

FromTheMoon [43]2 years ago

6 0

Pythagorean theorem

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If 24 extra large cans of soup will serve 96 people, how many cans should Ann buy to serve 28 people?

klio [65]

Answer:

She should buy a total of 25, so one more can

4 0

2 years ago

(a)5%)Let fx, y) = x^4 + y^4 - 4xy + 1. and classify each critical point Find all critical points of fx,y) as a local minimum, l

lara31 [8.8K]

$f(x,y)=x^4+y^4-4xy+1$

has critical points wherever the partial derivatives vanish:

$f_x=4x^3-4y=0\implies x^3=y$

$f_y=4y^3-4x=0\implies y^3=x$

Then

$x^3=y\implies x^9=x\implies x(x^8-1)=0\implies x=0\text{ or }x=\pm1$

If $x=0$ , then $y=0$ ; critical point at (0, 0)
If $x=1$ , then $y=1$ ; critical point at (1, 1)
If $x=-1$ , then $y=-1$ ; critical point at (-1, -1)

$f(x,y)$ has Hessian matrix

$H(x,y)=\begin{bmatrix}12x^2&-4\\-4&12y^2\end{bmatrix}$

with determinant

$\det H(x,y)=144x^2y^2-16$

At (0, 0), the Hessian determinant is -16, which indicates a saddle point.
At (1, 1), the determinant is 128, and $f_{xx}(1,1)=12$ , which indicates a local minimum.
At (-1, -1), the determinant is again 128, and $f_{xx}(-1,-1)=12$ , which indicates another local minimum.

4 0

3 years ago

Solve 2 log x = log 36<br> Answer<br> x = 72<br> x = 6<br> x = ±6<br> x = 18

astra-53 [7]

$2\log x=\log 36\\
\log x^2=\log 36\\
x^2=36\\
x=-6 \vee x=6
$

6 0

2 years ago

Read 2 more answers

There were 42 apples in each crate. 12 such crates of apples were delivered to a factory. 4 apples were rotten and had to be thr

algol [13]

Answer:

50 boxes

Step-by-step explanation:

first we can find how many apples there are

42*12=504

then subtract 4 of the rotten apples

504-4=500

then find how many boxes there can be

500/10=50

7 0

3 years ago

What is the inverse of the function f(x)=3^x

Leokris [45]

Answer:

$f^{-1}(x) = \log_3(x)$

Step-by-step explanation:

The inverse operation for an exponential ( $a^x$ ) is the logarithm: $\log_a(x)$ .

8 0

2 years ago