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Svetllana [295]
2 years ago
8

Choose the equation of the horizontel line that passes through the point (-2,-1)

Mathematics
1 answer:
vitfil [10]2 years ago
8 0

Answer:

y = -1

Step-by-step explanation:

A horizontal line is of the form

y =

The y coordinate of the point (-2,-1) is -1

The equation is y = -1

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Find the absolute maximum and minimum values of the following function in the closed region bounded by the triangle with vertice
alukav5142 [94]

f(x,y)=2x^2-8x+y^2-8y+2

f_x(x,y)=4x-8=0\implies x=2

f_y(x,y)=2y-8=0\implies y=4

There is one critical point at (2, 4), but this point happens to fall on one of the boundaries of the region. We'll get to that point in a moment.

Along the boundary x=0, we have

f(0,y)=y^2-8y+2=(y-4)^2-14

which attains a maximum value of

f(0,4)=-14

Along y=44, we have

f(x,44)=2x^2-8x+1586=2(x-2)^2+1578

which attains a maximum of

f(2,44)=1578

Along y=2x, we have

f(x,2x)=6x^2-24x+2=6(x-2)^2-22

which attains a maximum of

f(2,4)=-22

So over the given region, the absolute maximum of f(x,y) is 1578 at (2, 44).

8 0
3 years ago
Bashir works in a weather station and has launched a weather balloon. The height of the balloon is 4 kilometers and it is 1 kilo
Aleksandr [31]

Consider triangle WBG, where points W, B and G represent Weather Station, Balloon and Ground, respectively. This triangle is right with right angle at vertex G. The legs of this triangle are GB and GW, the hypotenuse is BW.

From the question you know that GB=4 km and GW=1 km. By the Pythagorean theorem,

BW^2=GB^2+GW^2,\\ \\BW^2=4^2+1^2,\\ \\BW^2=17,\\ \\BW=\sqrt{17}\approx 4.123\text{ km.}

Answer: nearly 4.123 km

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Determine if x-6 is a zero and find the quotiant and the remainder​
Genrish500 [490]

Answer:

○ A. No, x = -6 is not a zero of the polynomial.

The quotient is x - 29, and the remainder is 234.

Step-by-step explanation:

[x - 3][x - 20] >> Factored Form

Obviously, this is not a zero. Now, to get the remainder, we have to plug in the vertical line of <em>x = -6</em> into its conjugate, meaning an expression with opposite signs, which is <em>x + 6</em>. This is the expression we divide the dividend by, so you will have this:

\frac{{x}^{2} - 23x - 60}{x + 6}

Since the divisor is in the form of <em>x - c</em>, using Synthetic Division, we get this:

x - 29 + \frac{234}{x + 6}

You see? You have <em>x - 29</em> in the quotient, and you have 234 as the numerator remainder.

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3 years ago
What is the length of AC on the number line
Nesterboy [21]

Answer: The answer would be -3

Step-by-step explanation:

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