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3 years ago

Which one of the following measurements represents the longest distance

Mathematics

1 answer:

strojnjashka [21]3 years ago

5 0

It Would be A 1km because its 1000 meters

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Ethan rode 25.65 kilometers on Saturday and 14.23 kilometers on Sunday. About how far did Ethan ride during the two days?

vazorg [7]

So for this problem we are looking for a sum (total). So first we are going to round 25.65 to 25.7 and round 14.23 to 14.2

Now we are going to add 25.7 and 14.2 to get a total of 39.9

Ethan rode 39.9 kilometers.

3 0

3 years ago

Read 2 more answers

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).
If $y=1$ , then $x=\pm\sqrt2$ - two critical points at $(-\sqrt2,1)$ and $(\sqrt2,1)$

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

$f(1,y)=8-y+y^2=\left(y-\dfrac12\right)^2+\dfrac{31}4$

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

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

and we get the same extrema as in the previous case: 8 at (-1, 1), and 10 at (-1, -1).

If $y=1$ , then

$f(x,1)=8$

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).

3 0

3 years ago

If 90 percent of a is 44, what is 30 percent of 3a?

Lesechka [4]

90% of "a" is 44.......turn ur percent into a decimal...." of " means multiply..." is " means equals...

0.90a = 44...divide both sides by 0.90
a = 44 / 0.90
a = 48.89.....this is rounded

what is 30% of 3a.....and we know that "a" is 48.89...

0.30(3 * 48.89) = 0.30(146.67) = 44 <=== ur answer

3 0

3 years ago

Mrs. Lopez had $150.55 in her checking account. She wrote checks for the following amounts: $45.76, $35.82, and $79.00. What is

Vanyuwa [196]

The answer is -10.03

4 0

3 years ago

Read 2 more answers

6xy^3 * 4x^2y^2 answer

Fudgin [204]

6x y³ × 4x² y²
=

24 x¹+² y³+²
=
24x³ y⁵

7 0

3 years ago