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4 years ago

You are asked to run two wires. The total length of the wires is 16m. One of the wires needs

Mathematics

1 answer:

Elenna [48]4 years ago

8 0

One wire is 8.5m, and the other wire is 7.5m.

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Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi

miss Akunina [59]

Answer:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

Step-by-step explanation:

1st boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a$

Equation:

$y=ax^2 -2ax+c$

The y-coordinate of the vertex:

$y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1$

Solve:

$c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}$

Parabola equation:

$y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}$

2nd boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0$

Equation:

$y=ax^2+c$

The y-coordinate of the vertex:

$y_v=a\cdot 0^2+c\Rightarrow c=-7$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-7\\ \\64a-7=1$

Solve:

$a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7$

Parabola equation:

$y=\dfrac{1}{8}x^2 -7$

System of two equations:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

7 0

3 years ago

Read 2 more answers

The area of the shape is 54 cm2.<br> Find the value of r.

Bond [772]

Radius is half the circumference
c= 2(square root) pieA

4 0

2 years ago

Make D the subject of S=D/T<br> You may use the flowchart to help you if you wish.

hammer [34]

Given the equation, S = D/T:

To make the D the subject of the equation, we can start by multiplying both sides by T to isolate D:

(T) S = D/T (T)

TS = D

Therefore, the final answer is D = TS

8 0

3 years ago

Can someone help me understand how to do this?

Crazy boy [7]

Answer:

1/3

Step-by-step explanation:

To get no solution, you want to get rid of x and leave an incorrect equation.

In this case, we will use 1/3x.

1/3x + 2 = 1/3x - 3

We subtract 1/3x on both sides. This will cause the 1/3x's to cancel out.

1/3x - 1/3x + 2 = 1/3x - 1/3x - 3

2 ≠ -3

As we know, 2 is not 3. Therefore, there is no solution if 1/3x is used.

6 0

3 years ago

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Find the slope of the line y = 1/6x + 3/2

AURORKA [14]

Answer: 1/6

Step-by-step explanation:

Slope is the m in y=mx+b

7 0

3 years ago

Read 2 more answers