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uysha [10]
3 years ago
12

Find the magnitude of a vector with initial point A(3, 4, 10) and terminal point B(8, 4, –2).

Mathematics
1 answer:
Fantom [35]3 years ago
4 0

Answer:

B

Step-by-step explanation:

Use the distance formula in 3 dimensions

d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1})^2      }

with (x₁, y₁, z₁ ) = (3, 4, 10) and (x₂, y₂, z₂ ) = (8, 4, - 2)

d = \sqrt{(8-3)^2+(4-4)^2+(-2-10)^2}

   = \sqrt{5^2+0^2+(-12)^2}

    = \sqrt{25+144}

    = \sqrt{169}

     = 13 → B

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xy represents the diameter

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What is the remainder of 67 divided by 3?
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8 0
3 years ago
Fred wants to find 48+34 using compensation.He says you can take 2 from 34 and give it to 48 to make 50.What is the sum?Explain
Montano1993 [528]
It is easier to add 50 to a number than 48 because 50 has a zero in it which makes an addition simpler.

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6 0
3 years ago
Trevor is analyzing a circle, y2 + x2 = 100, and a linear function g(x). Will they intersect?
lakkis [162]
Given a circle described by the equation:
y^2+x^2=100
and a function g(x) given by the table
\begin{center}
\begin{tabular}{ |c |c |c }
 x & g(x) \\
 -1 & -22 \\
 0 & -20  \\
1 & -18   
\end{tabular}
\end{center}

The function g(x) describes a straight line with the equation:
\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}  \\  \\  \frac{y-(-22)}{x-(-1)} = \frac{-20-(-22)}{0-(-1)}  \\  \\ \frac{y+22}{x+1} = \frac{-20+22}{0+1} = \frac{2}{1}  \\  \\ y+22=2(x+1)=2x+2 \\  \\ y=2x-20

To check if the circle and the line intersects, we substitute the equation of the line into the equation of the circle to see if we have a real solution.
i.e.
y^2+x^2=100 \\  \\ (2x-20)^2+x^2=100 \\  \\ 4x^2-80x+400+x^2=100 \\  \\ 5x^2-80x+300=0 \\  \\ x^2-16x+60=0 \\  \\ (x-6)(x-10)=0 \\  \\ x-6=0 \ or \ x-10=0 \\  \\ x=6 \ or \ x=10

When x = 6, y = 2(6) - 20 = 12 - 20 = -8 and when x = 10, y = 2(10) - 20 = 20 - 20 = 0

Therefore, the circle and the line intersect at the points (6, -8) and (10, 0).
8 0
4 years ago
Read 2 more answers
And an equation of the line. Write the equation using function notation.
NeTakaya

Answer:

F(x) = - 2/5x - 11

Step-by-step explanation:

F(x) = - 2/5x + c

-9 = - 2/5(-5) + c

-9 = 2 + c

- 11= c

F(x) = - 2/5x - 11

7 0
3 years ago
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