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3 years ago

To the nearest hundredth, how many cm are in 47 in? (1 in = 2.54 cm)

Mathematics

2 answers:

4vir4ik [10]3 years ago

5 0

Easy. If 1 In. = 2.54 Cm. then the equation would be 47 * 2.54 = 119.38.

aleksley [76]3 years ago

4 0

It is 119.38 bc 47 times 2.54 equals 119.38... C hope this helps

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The measure of an angle is two times the measure of a supplementary angle. what is the measure of each angle

lara31 [8.8K]

Let the angles be x and (180-x).

Let 2x = 180-x.

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2 years ago

Find the absolute maximum and absolute minimum values of the function f(x, y) = x 2 + y 2 − x 2 y + 7 on the set d = {(x, y) : |

dsp73

Looks like $f(x,y)=x^2+y^2-x^2y+7$ .

$f_x=2x-2xy=0\implies2x(1-y)=0\implies x=0\text{ or }y=1$

$f_y=2y-x^2=0\implies2y=x^2$

If $x=0$ , then $y=0$ - critical point at (0, 0).
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The latter two critical points occur outside of $D$ since $|\pm\sqrt2|>1$ so we ignore those points.

The Hessian matrix for this function is

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

The value of its determinant at (0, 0) is $\det H(0,0)=4>0$ , which means a minimum occurs at the point, and we have $f(0,0)=7$ .

Now consider each boundary:

If $x=1$ , then

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which has 3 extreme values over the interval $-1\le y\le1$ of 31/4 = 7.75 at the point (1, 1/2); 8 at (1, 1); and 10 at (1, -1).

If $x=-1$ , then

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$f(x,1)=8$

which doesn't tell us about anything we don't already know (namely that 8 is an extreme value).

If $y=-1$ , then

$f(x,-1)=2x^2+8$

which has 3 extreme values, but the previous cases already include them.

Hence $f(x,y)$ has absolute maxima of 10 at the points (1, -1) and (-1, -1) and an absolute minimum of 0 at (0, 0).

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3 years ago

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2 years ago

2. CHEMISTRY How many liters of 15% acid and

Wewaii [24]

Answer:

<h3> 26²/₃ liters of 15% acid and 13¹/₃ liters of 33% acid</h3>

Step-by-step explanation:

Concentration Amount of Amount

of Solution Solution (L) of Acid

15% x 0.15x

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x + y = 40 ⇒ x = 40 - y

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2 years ago

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3 years ago

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