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2 years ago

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Luiza delivers newspapers in her neighborhood. If you plot the points (−1, 1), (4, 1), (4, −2) and (−1, −2), you will create a r

epresentation of the route she takes, in miles. How many miles does her route cover?

2 answers:

wel2 years ago

5 0

The first thing to do in this case is to draw the ordered pairs in the Cartesian plane and join the points.
We have then that the resulting figure is a rectangle.
We must find the perimeter of the rectangle that is given by:
P = 2L + 2W
Where,
L: long
W: width
Restoring the values:
P = 2 * (5) + 2 * (3)
P = 16
Answer:
her route cover 16 miles.

disa [49]2 years ago

5 0

Answer: 16 i just did this

Step-by-step explanation:

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Find the point (x,y) of x2+14xy+49y2=100 that is closest to the origin and lies in the first quadrant.

Gala2k [10]

Notice that

$x^2+14xy+49y^2=(x+7y)^2$

so the constraint is a set of two lines,

$(x+7y)^2=100\implies\begin{cases}x+7y=10\\x+7y=10\end{cases}$

and only the first line passes through the first quadrant.

The distance between any point $(x,y)$ in the plane is $\sqrt{x^2+y^2}$ , but we know that $\sqrt{f(x,y)}$ and $f(x,y)$ share the same critical points, so we need only worry about minimizing $x^2+y^2$ . The Lagrangian for this problem is then

$L(x,y,\lambda)=x^2+y^2+\lambda(x+7y-10)$

with partial derivatives (set equal to 0)

$L_x=2x+\lambda=0$

$L_y=2y+7\lambda=0$

$L_\lambda=x+7y-10=0$

We have

$L_y-7L_x=2y-14x=0\implies y=7x$

which tells us that

$x+7y-10=0\iff x+49x=10\implies x=\dfrac15\implies y=\dfrac75$

so that $\left(\dfrac15,\dfrac75\right)$ is a critical point. The Hessian for the target function $x^2+y^2$ is

$H(x,y)=\begin{bmatrix}2&0\\0&2\end{bmatrix}$

which is positive definite for all $x,y$ , so the critical point is the site of a minimum. The minimum distance itself (which we don't seem to care about for this problem, but we might as well state it) is $\sqrt{\left(\dfrac15\right)^2+\left(\dfrac75\right)^2}=2$ .

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2 years ago

Solve for x in the equation ]x^{2} - 12x + 59 = 0

Vedmedyk [2.9K]

Step-by-step explanation:

$x^{2} - 12x + 59 = 0$

Given equaiton is in the form of ax^2 +bx+c=0

we apply quadratic formula to solve for x

$x= \frac{-b+-\sqrt{b^2-4ac} }{2a}$

a= 1 b = -12 and c= 59

$x= \frac{12+-\sqrt{(-12)^2-4(1)(59)}}{2(1)}$

$x= \frac{12+-\sqrt{92}}{2}$

$x= \frac{12+-2\sqrt{23}}{2}$

Divide the 12 and square root terms by 2

$x=6+-\sqrt{23}$

so $x=6+\sqrt{23}$ and $x=6-\sqrt{23}$

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2 years ago

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30 hours is how much she would work

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Given 8x-3y=-21, 3x+y=-10; Prove x=-3

Mashcka [7]

The numbers start from the top

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2 years ago

If 49x2 + 28x - 10 is rewritten as p2 + 4p -10, what is p in terms of<br> p=

madam [21]

Answer:

p=7x

Step-by-step explanation:

49x^[2] + 28x - 10 = p^[2] + 4p -10

This equation is in the form a^[2]x + bx + c.

<u><em>The 'c' is common for both equations, this means the 'a' and 'b' must also be common. </em></u>

There are two ways to find p: 'a' or 'b'

<u>a method</u>

49x^[2] = p^[2]

=> The square root of both sides = 7x = p

<u>b method</u>

28x = 4p

28x/4 = 4p/4

7x = p

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2 years ago