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3 years ago

What is 18.23 rounded to the nearest tenth?

Mathematics

2 answers:

irakobra [83]3 years ago

6 0

Answer: 18.2

Step-by-step explanation:

you would round to 18.2 because with 5 and above, you give it a shove, 4 and below let it go

kenny6666 [7]3 years ago

3 0

Answer:

The answer is 18.2.

Hope this helps!

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It is known that Ray AP bisects angle CAT. If m<CAT = 5x+17 and m<PAT = 3x-4, then determine the value of x.

Sonja [21]

Answer:

x = 25

Step-by-step explanation:

It is given that, ray Ray AP bisects angle CAT. It means,

$\angle CAT=\angle CAP+\angle PAT$

Also, $\angle CAP = \angle PAT$

It gives, $\angle CAT=2\angle PAT$

ATQ,

$\angle CAT = 5x+17 \ \text{and}\ \text{PAT}=3x-4$

So,

$5x+17=2(3x-4)\\\\5x+17=6x-8$

Taking like terms together,

$5x-6x=-8-17\\\\-x=-25\\\\x=25$

So, the value of x is 25.

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Given function f(x, y) = x 2 + xy + y 2 + y (1) Locate critical points (2) Classify those critical point (determine it’s local m

zvonat [6]

$f(x,y)=x^2+xy+y^2+y$
$\nabla f(x,y)=(f_x,f_y)=(2x+y,x+2y+1)$

Set both partial derivatives equal to zero and solve for $x,y$ .

$\begin{cases}2x+y=0\\x+2y+1=0\end{cases}\implies x=\dfrac13,y=-\dfrac23$

The Hessian matrix (matrix of second-order partial derivatives) for this function is

$H=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2&1\\1&2\end{bmatrix}\implies\det H=3>0$

Now since $\det H>0$ for any $(x,y)$ , and $f_xx=2>0$ for any $(x,y)$ , it follows by the second partial derivative test that the critical point $\left(\dfrac13,-\dfrac23\right)$ is the site of a local minimum of $f(x,y)$ . The value of the minimum is $f\left(\dfrac13,-\dfrac23\right)=-\dfrac13$ .

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3 years ago