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3 years ago

Find a point d(x, y) such that the points a(−4, 1), b(3, 0), c(−1, −3), and d are the corners of a square.

1 answer:

5 0

- draw the points
- you will see thet AC has the same M as BD
- also AC = BD distance because it is a square
- calculate the M of AC
$\frac{1 - ( - 3)}{ - 4 - ( - 1)} = \frac{4}{ - 3} = - \frac{4}{3} = m$
- calculate AC distance
$\sqrt{ {(1 - ( - 3))}^{2} + {( - 4 - ( - 1))}^{2} } = \\ \sqrt{ {4}^{2} + {( - 3)}^{2} } = \\ \sqrt{25} = 5 = ac$
- lets say d is (x,y)
- now just make to equations with BD distance and M

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Two triangles are similar.The the smaller triangle has side 10,20 and 15 units the larger triangles longest side is 52 units.Wha

Oliga [24]

Answer: The perimeter of the largest triangle = 117 units.

Step-by-step explanation:

Sides of smaller triangle = 10,20 and 15 units

Longest side = 20 units

Longest side of larger triangle = 52 units

Sides of two similar triangles are proportional.

Let k be proportionality constant.

$k=\dfrac{\text{Length in larger triangle}}{\text{Length in smaller triangle}}$

$k=\dfrac{52}{20}\\\\\Rightarrow\ k=\dfrac{13}{5}$

Length of other two sides,

$10\times\dfrac{13}{5}, 15\times\dfrac{13}{5}\ i.e.\ 26\text{ units}, 39\text{ units.}$

So sides of larger triangle = 52 units, 26 units , 39 units

Perimeter of largest triangle = 52 +26+39 = 117 units

Hence, the perimeter of the largest triangle = 117 units.

4 0

3 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).
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

Please answer- what is the length of BW? ANSWER DIRECTLY NO LINK ( will give brainlist to whoever answers)

Yuki888 [10]

Answer:

148.49

Step-by-step explanation:

105 x √2 = 148.49

have a great day

4 0

3 years ago

Which rule best described the following pattern 5,6,15,16,25,26,35

ad-work [718]

The pattern is increasing by 10 then a ding 1 to the next number. Hope this helps! :)

6 0

3 years ago

One rectangle has a base of 12 inches and an altitude of 6inches, The other has a base of 10 inches and an altitude of 5 inches.

liubo4ka [24]

Sides of first rectangle are 12 inches and 6 inches

and sides of second rectangle are 10 inches and 5 inches

So to find the ration of sides we can do

Ratio of bases = 12/10 = 6/5

Ratio of altitudes = 6/5

Area of first rectangle = base * altitude = 12 *6 = 72 square inches

6 0

4 years ago